CDS course discussion, Apr 2014 - Revision history

Murray: /* Catalog entries */

2014-04-29T00:15:32Z

Catalog entries

← Older revision		Revision as of 00:15, 29 April 2014
Line 126:		Line 126:
	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. Instructors: Burdick, MacMartin, Doyle, Murray}}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. Instructors: Burdick, MacMartin, Doyle, Murray}}

	'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.		'''CDS 140 {{delete\|ab}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.

	{{insert\|'''CDS 240. Nonlinear Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}		{{insert\|'''CDS 240. Nonlinear Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}
Line 132:		Line 132:
	{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}		{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}

	'''CDS 190. Independent Work in Control and Dynamical Systems.''' Units to be arranged; first, second, third terms; maximum two terms. Prerequisite: CDS 110 ab or CDS 140 ab. Research project in control and dynamical systems, supervised by a CDS faculty member.		'''CDS 190. Independent Work in Control and Dynamical Systems.''' Units to be arranged; first, second, third terms; maximum two terms. Prerequisite: CDS 110 {{delete\|ab}} or CDS 140 {{delete\|ab}}. Research project in control and dynamical systems, supervised by a CDS faculty member.

	{{delete\|'''CDS 201. Linear Algebra and Applied Operator Theory.''' 9 units (3-0-6); first term. Linear spaces, subspaces, spans of sets, linear independence, bases, dimensions; linear transformations and operators, examples, nullspace/kernel, range-space/image, one-to-one and onto, isomorphism and invertibility, rank-nullity theorem; products of linear transformations, left and right inverses, generalized inverses. Adjoints of linear transformations, singular-value decomposition and Moore-Penrose inverse; matrix representation of linear transformations between finite-dimensional linear spaces, determinants, multilinear forms; metric spaces: examples, limits and convergence of sequences, completeness, continuity, fixed-point (contraction) theorem, open and closed sets, closure; normed and Banach spaces, inner product and Hilbert spaces: examples, Cauchy-Schwarz inequality, orthogonal sets, Gram-Schmidt orthogonalization, projections onto subspaces, best approximations in subspaces by projection; bounded linear transformations, principle of superposition for infinite series, well-posed linear problems, norms of operators and matrices, convergence of sequences and series of operators; eigenvalues and eigenvectors of linear operators, including their properties for self-adjoint operators, spectral theorem for self-adjoint and normal operators; canonical representations of linear operators (finite-dimensional case), including diagonal and Jordan form, direct sums of (generalized) eigenspaces. Schur form; functions of linear operators, including exponential, using diagonal and Jordan forms, Cayley-Hamilton theorem. Taught concurrently with ACM 104. Instructor: Beck.}}		{{delete\|'''CDS 201. Linear Algebra and Applied Operator Theory.''' 9 units (3-0-6); first term. Linear spaces, subspaces, spans of sets, linear independence, bases, dimensions; linear transformations and operators, examples, nullspace/kernel, range-space/image, one-to-one and onto, isomorphism and invertibility, rank-nullity theorem; products of linear transformations, left and right inverses, generalized inverses. Adjoints of linear transformations, singular-value decomposition and Moore-Penrose inverse; matrix representation of linear transformations between finite-dimensional linear spaces, determinants, multilinear forms; metric spaces: examples, limits and convergence of sequences, completeness, continuity, fixed-point (contraction) theorem, open and closed sets, closure; normed and Banach spaces, inner product and Hilbert spaces: examples, Cauchy-Schwarz inequality, orthogonal sets, Gram-Schmidt orthogonalization, projections onto subspaces, best approximations in subspaces by projection; bounded linear transformations, principle of superposition for infinite series, well-posed linear problems, norms of operators and matrices, convergence of sequences and series of operators; eigenvalues and eigenvectors of linear operators, including their properties for self-adjoint operators, spectral theorem for self-adjoint and normal operators; canonical representations of linear operators (finite-dimensional case), including diagonal and Jordan form, direct sums of (generalized) eigenspaces. Schur form; functions of linear operators, including exponential, using diagonal and Jordan forms, Cayley-Hamilton theorem. Taught concurrently with ACM 104. Instructor: Beck.}}

Murray at 00:14, 29 April 2014

2014-04-29T00:14:04Z

← Older revision		Revision as of 00:14, 29 April 2014
Line 34:		Line 34:
	\|		\|
	* CDS 112 - Control system design		* CDS 112 - Control system design
	* CDS 140 - ~~Dynamical systems~~		* CDS 140 - Introduction to dynamics
	* CDS 212 - Feedback control theory		* CDS 212 - Feedback control theory
	\|		\|
	* CDS ~~141~~ - Nonlinear systems		* CDS 240 - Nonlinear dynamical systems
	* CDS 213 - Robust control		* CDS 213 - Robust control
	* CDS 270 - Advanced topics (nonlinear control, adaptive control, system ID)		* CDS 270 - Advanced topics (nonlinear control, adaptive control, system ID)
Line 79:		Line 79:
	* Ae/CDS/ME 251a - Closed loop flow control (alt years)		* Ae/CDS/ME 251a - Closed loop flow control (alt years)
	\|		\|
	* CDS {{delete\|140b}} {{insert\|~~141~~}} - Nonlinear systems (alt years)		* CDS {{delete\|140b}} {{insert\|240}} - Nonlinear systems (alt years)
	* {{delete\|CDS 150 - Stochastic system analysis}}		* {{delete\|CDS 150 - Stochastic system analysis}}
	* {{delete\|CDS 205 - Geometric mechanics (alt years)}}		* {{delete\|CDS 205 - Geometric mechanics (alt years)}}
Line 128:		Line 128:
	'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.		'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.

	{{insert\|'''CDS ~~141~~. Nonlinear Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}		{{insert\|'''CDS 240. Nonlinear Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}

	{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}		{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}

Murray: /* Proposed CDS course requirements */

2014-04-21T01:03:10Z

Proposed CDS course requirements

← Older revision		Revision as of 01:03, 21 April 2014
Line 44:		Line 44:
	=== Proposed CDS course requirements ===		=== Proposed CDS course requirements ===
	CDS graduate major:		CDS graduate major:
	* Core: {{delete\|CDS 201}} {{insert\|ACM 104}}, {{delete\|CDS 202}} {{insert\|ACM 113}}, ACM/EE 116, CDS ~~140a~~, {{insert\|CDS 212}}		* Core: {{delete\|CDS 201}} {{insert\|ACM 104}}, {{delete\|CDS 202}} {{insert\|ACM 113}}, ACM/EE 116, CDS 140{{delete\|a}}, {{insert\|CDS 212}}
	* Depth: 45 units in CDS or other advanced courses in systems theory, dynamical systems, and/or applied mathematics.		* Depth: 45 units in CDS or other advanced courses in systems theory, dynamical systems, and/or applied mathematics.
	* Breadth: 27 units in a particular area outside of CDS. Courses taken to satisfy the focus must represent a coherent program of advanced study in the chosen area.		* Breadth: 27 units in a particular area outside of CDS. Courses taken to satisfy the focus must represent a coherent program of advanced study in the chosen area.

Murray: /* Catalog entries */

2014-04-21T01:01:37Z

Catalog entries

← Older revision		Revision as of 01:01, 21 April 2014
Line 128:		Line 128:
	'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.		'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.

	{{insert\|'''CDS 141. Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. ~~Basics topics in~~ dynamical systems, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging. Additional topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}		{{insert\|'''CDS 141. Nonlinear Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}

	{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}		{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}

Murray: /* Catalog entries */

2014-04-21T00:48:53Z

Catalog entries

← Older revision		Revision as of 00:48, 21 April 2014
Line 124:		Line 124:
	'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1abc and Ma 2/102 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.		'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1abc and Ma 2/102 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.

	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. Instructors: Burdick, MacMartin, Doyle, Murray}}

	'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.		'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.

Murray: /* Catalog entries */

2014-04-21T00:48:02Z

Catalog entries

← Older revision		Revision as of 00:48, 21 April 2014
Line 122:		Line 122:
	{{delete\|'''CDS 101. Design and Analysis of Feedback Systems.''' 6 units (2-0-4); first term. Prerequisites: Ma 1 and Ma 2 or equivalents. An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110 a, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. Instructors: MacMartin, Burdick, Murray.}}		{{delete\|'''CDS 101. Design and Analysis of Feedback Systems.''' 6 units (2-0-4); first term. Prerequisites: Ma 1 and Ma 2 or equivalents. An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110 a, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. Instructors: MacMartin, Burdick, Murray.}}

	'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1 and Ma 2 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.		'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1abc and Ma 2/102 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.

	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}

Murray: /* Catalog entries */

2014-04-21T00:47:24Z

Catalog entries

← Older revision		Revision as of 00:47, 21 April 2014
Line 122:		Line 122:
	{{delete\|'''CDS 101. Design and Analysis of Feedback Systems.''' 6 units (2-0-4); first term. Prerequisites: Ma 1 and Ma 2 or equivalents. An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110 a, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. Instructors: MacMartin, Burdick, Murray.}}		{{delete\|'''CDS 101. Design and Analysis of Feedback Systems.''' 6 units (2-0-4); first term. Prerequisites: Ma 1 and Ma 2 or equivalents. An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110 a, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. Instructors: MacMartin, Burdick, Murray.}}

	'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' ~~{{delete\|~~12~~}} {{insert\|9}}~~ units (3-0-~~{{delete}}~~9 ~~{{insert\|6}}~~) first{{delete\|, 9 units (3-0-6) second ~~terms~~}}. Prerequisites: Ma 1 and Ma 2 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.		'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1 and Ma 2 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.

	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}

Murray: /* Catalog entries */

2014-04-21T00:45:51Z

Catalog entries

← Older revision		Revision as of 00:45, 21 April 2014
Line 126:		Line 126:
	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}

	'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: ~~ACM 95~~/~~100 ab~~ or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for ~~discrete and~~ continuous state systems}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. ~~Discussion of bifurcations in applications, invariant manifolds, the method of averaging and singular perturbation theory. Additional topics may include Hamiltonian and Lagrangian systems.~~ Instructors: Murray, MacMartin.		'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.

	{{insert\|'''CDS 141. Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Basics topics in dynamical systems, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging. Additional topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}		{{insert\|'''CDS 141. Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Basics topics in dynamical systems, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging. Additional topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}

Murray: /* Catalog entries */

2014-04-21T00:41:14Z

Catalog entries

← Older revision		Revision as of 00:41, 21 April 2014
Line 126:		Line 126:
	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}

	'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second, third ~~terms~~. Prerequisites: ACM 95/100 ab or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for discrete and continuous state systems}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Discussion of bifurcations in applications, invariant manifolds, the method of averaging and singular perturbation theory. Additional topics may include Hamiltonian and Lagrangian systems. Instructors: Murray, MacMartin.		'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: ACM 95/100 ab or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for discrete and continuous state systems}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Discussion of bifurcations in applications, invariant manifolds, the method of averaging and singular perturbation theory. Additional topics may include Hamiltonian and Lagrangian systems. Instructors: Murray, MacMartin.

	{{insert\|'''CDS 141 ~~a{{delete\|b}}~~. ~~Introduction to Dynamics~~.''' 9 units (3-0-6); ~~second,~~ third ~~terms~~. Prerequisites: ~~ACM 95/100 ab or equivalent, {{insert\|ACM 104}}~~. Basics topics in ~~dynamics {{insert\|for discrete and continuous state~~ systems~~}} {{delete\|in Euclidean space}}~~, including ~~equilibria/~~invariant ~~sets~~, ~~stability~~, ~~Lyapunov functions/invariants~~, ~~attractors~~ and ~~periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Discussion of bifurcations in applications, invariant manifolds~~, the method of averaging ~~and singular perturbation theory~~. Additional topics may ~~include Hamiltonian~~ and ~~Lagrangian systems~~. Instructors: Murray, MacMartin.}}		{{insert\|'''CDS 141. Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Basics topics in dynamical systems, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging. Additional topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}

	{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}		{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}

Murray: /* Catalog entries */

2014-04-21T00:21:31Z

Catalog entries

← Older revision		Revision as of 00:21, 21 April 2014
Line 126:		Line 126:
	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}

	'''CDS 140 ab. Introduction to Dynamics.''' 9 units (3-0-6); second, third terms. Prerequisites: ACM 95/100 ab or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for discrete and continuous state systems}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Discussion of bifurcations in applications, invariant manifolds, the method of averaging and singular perturbation theory. Additional topics may include Hamiltonian and Lagrangian systems. Instructors: Murray, MacMartin.		'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second, third terms. Prerequisites: ACM 95/100 ab or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for discrete and continuous state systems}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Discussion of bifurcations in applications, invariant manifolds, the method of averaging and singular perturbation theory. Additional topics may include Hamiltonian and Lagrangian systems. Instructors: Murray, MacMartin.

			{{insert\|'''CDS 141 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second, third terms. Prerequisites: ACM 95/100 ab or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for discrete and continuous state systems}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Discussion of bifurcations in applications, invariant manifolds, the method of averaging and singular perturbation theory. Additional topics may include Hamiltonian and Lagrangian systems. Instructors: Murray, MacMartin.}}

	{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}		{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}

← Older revision		Revision as of 00:15, 29 April 2014
Line 126:		Line 126:
	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. Instructors: Burdick, MacMartin, Doyle, Murray}}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. Instructors: Burdick, MacMartin, Doyle, Murray}}

	'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.		'''CDS 140 {{delete\|ab}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.

	{{insert\|'''CDS 240. Nonlinear Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}		{{insert\|'''CDS 240. Nonlinear Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}
Line 132:		Line 132:
	{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}		{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}

	'''CDS 190. Independent Work in Control and Dynamical Systems.''' Units to be arranged; first, second, third terms; maximum two terms. Prerequisite: CDS 110 ab or CDS 140 ab. Research project in control and dynamical systems, supervised by a CDS faculty member.		'''CDS 190. Independent Work in Control and Dynamical Systems.''' Units to be arranged; first, second, third terms; maximum two terms. Prerequisite: CDS 110 {{delete\|ab}} or CDS 140 {{delete\|ab}}. Research project in control and dynamical systems, supervised by a CDS faculty member.

	{{delete\|'''CDS 201. Linear Algebra and Applied Operator Theory.''' 9 units (3-0-6); first term. Linear spaces, subspaces, spans of sets, linear independence, bases, dimensions; linear transformations and operators, examples, nullspace/kernel, range-space/image, one-to-one and onto, isomorphism and invertibility, rank-nullity theorem; products of linear transformations, left and right inverses, generalized inverses. Adjoints of linear transformations, singular-value decomposition and Moore-Penrose inverse; matrix representation of linear transformations between finite-dimensional linear spaces, determinants, multilinear forms; metric spaces: examples, limits and convergence of sequences, completeness, continuity, fixed-point (contraction) theorem, open and closed sets, closure; normed and Banach spaces, inner product and Hilbert spaces: examples, Cauchy-Schwarz inequality, orthogonal sets, Gram-Schmidt orthogonalization, projections onto subspaces, best approximations in subspaces by projection; bounded linear transformations, principle of superposition for infinite series, well-posed linear problems, norms of operators and matrices, convergence of sequences and series of operators; eigenvalues and eigenvectors of linear operators, including their properties for self-adjoint operators, spectral theorem for self-adjoint and normal operators; canonical representations of linear operators (finite-dimensional case), including diagonal and Jordan form, direct sums of (generalized) eigenspaces. Schur form; functions of linear operators, including exponential, using diagonal and Jordan forms, Cayley-Hamilton theorem. Taught concurrently with ACM 104. Instructor: Beck.}}		{{delete\|'''CDS 201. Linear Algebra and Applied Operator Theory.''' 9 units (3-0-6); first term. Linear spaces, subspaces, spans of sets, linear independence, bases, dimensions; linear transformations and operators, examples, nullspace/kernel, range-space/image, one-to-one and onto, isomorphism and invertibility, rank-nullity theorem; products of linear transformations, left and right inverses, generalized inverses. Adjoints of linear transformations, singular-value decomposition and Moore-Penrose inverse; matrix representation of linear transformations between finite-dimensional linear spaces, determinants, multilinear forms; metric spaces: examples, limits and convergence of sequences, completeness, continuity, fixed-point (contraction) theorem, open and closed sets, closure; normed and Banach spaces, inner product and Hilbert spaces: examples, Cauchy-Schwarz inequality, orthogonal sets, Gram-Schmidt orthogonalization, projections onto subspaces, best approximations in subspaces by projection; bounded linear transformations, principle of superposition for infinite series, well-posed linear problems, norms of operators and matrices, convergence of sequences and series of operators; eigenvalues and eigenvectors of linear operators, including their properties for self-adjoint operators, spectral theorem for self-adjoint and normal operators; canonical representations of linear operators (finite-dimensional case), including diagonal and Jordan form, direct sums of (generalized) eigenspaces. Schur form; functions of linear operators, including exponential, using diagonal and Jordan forms, Cayley-Hamilton theorem. Taught concurrently with ACM 104. Instructor: Beck.}}

← Older revision		Revision as of 01:01, 21 April 2014
Line 128:		Line 128:
	'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.		'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.

	{{insert\|'''CDS 141. Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. ~~Basics topics in~~ dynamical systems, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging. Additional topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}		{{insert\|'''CDS 141. Nonlinear Dynamical Systems.''' 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Murray, MacMartin, Colonius, McKeon.}}

	{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}		{{delete\|'''CDS 150. Stochastic System Analysis and Bayesian Updating.''' 9 units (3-0-6); third term. Recommended prerequisite: ACM/EE 116. This course focuses on a probabilistic treatment of uncertainty in modeling a dynamical system’s input-output behavior, including propagating uncertainty in the input through to the output. It covers the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information that extends Boolean logic, giving a rigorous meaning for the probability of a model for a system. Approximate analytical methods and efficient stochastic simulation methods for robust system analysis and Bayesian system identification are covered. Topics include: Bayesian updating of system models based on system time-history data, including Markov Chain Monte Carlo techniques; Bayesian model class selection with a recent information-theoretic interpretation that shows why it automatically gives a quantitative Ockham’s razor; stochastic simulation methods for the output of stochastic dynamical systems subject to stochastic inputs, including Subset Simulation for calculating small “failure” probabilities; and Bayes filters for sequential estimation of system states and model parameters, that generalize the Kalman filter to nonlinear dynamical systems. Instructor: Beck.}}

← Older revision		Revision as of 00:48, 21 April 2014
Line 124:		Line 124:
	'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1abc and Ma 2/102 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.		'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1abc and Ma 2/102 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.

	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. Instructors: Burdick, MacMartin, Doyle, Murray}}

	'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.		'''CDS 140 a{{delete\|b}}. Introduction to Dynamics.''' 9 units (3-0-6); second{{delete\|, third}} term{{delete\|s}}. Prerequisites: Ma 2/102 or equivalent, {{insert\|ACM 104}}. Basics topics in dynamics {{insert\|for continuous state systems in continuous and discrete time}} {{delete\|in Euclidean space}}, including equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. Instructors: Murray, MacMartin.

← Older revision		Revision as of 00:48, 21 April 2014
Line 122:		Line 122:
	{{delete\|'''CDS 101. Design and Analysis of Feedback Systems.''' 6 units (2-0-4); first term. Prerequisites: Ma 1 and Ma 2 or equivalents. An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110 a, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. Instructors: MacMartin, Burdick, Murray.}}		{{delete\|'''CDS 101. Design and Analysis of Feedback Systems.''' 6 units (2-0-4); first term. Prerequisites: Ma 1 and Ma 2 or equivalents. An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110 a, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. Instructors: MacMartin, Burdick, Murray.}}

	'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1 and Ma 2 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.		'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1abc and Ma 2/102 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.

	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}

← Older revision		Revision as of 00:47, 21 April 2014
Line 122:		Line 122:
	{{delete\|'''CDS 101. Design and Analysis of Feedback Systems.''' 6 units (2-0-4); first term. Prerequisites: Ma 1 and Ma 2 or equivalents. An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110 a, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. Instructors: MacMartin, Burdick, Murray.}}		{{delete\|'''CDS 101. Design and Analysis of Feedback Systems.''' 6 units (2-0-4); first term. Prerequisites: Ma 1 and Ma 2 or equivalents. An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110 a, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. Instructors: MacMartin, Burdick, Murray.}}

	'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' ~~{{delete\|~~12~~}} {{insert\|9}}~~ units (3-0-~~{{delete}}~~9 ~~{{insert\|6}}~~) first{{delete\|, 9 units (3-0-6) second ~~terms~~}}. Prerequisites: Ma 1 and Ma 2 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.		'''CDS 110 {{delete\|ab}}. Introductory Control Theory.''' 12 units (3-0-9) first{{delete\|, 9 units (3-0-6) second}} term{{delete\|s}}. Prerequisites: Ma 1 and Ma 2 or equivalents; {{delete\|ACM 95/100 may be taken concurrently.}} An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. {{delete\|Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems.}} {{insert\|Design of feedback controls in state space and frequency domain based on stability, performance and robustness specifications.}} Instructors: MacMartin, Doyle, Burdick, Murray.

	{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}		{{insert\|'''CDS 112. Control System Design.''' 9 units (3-0-6); second term. Prerequisite: CDS 110. Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. }}