# Property:Abstract

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A Bayesian approach to inferring chemical signal timing and amplitude in a temporal logic gate using the cell population distributional response +

Stochastic gene expression poses an important challenge for engineering robust behaviors in a heterogeneous cell population. Cells address this challenge by operating on distributions of cellular responses generated by noisy processes. Similarly, a previously published temporal logic gate considers the distribution of responses across a cell population under chemical inducer pulsing events. The design uses a system of two integrases to engineer an E. coli strain with four DNA states that records the temporal order of two chemical signal events. The heterogeneous cell population response was used to infer the timing and duration of the two chemical signals for a small set of events. Here we use the temporal logic gate system to address the problem of extracting information about chemical signal events. We use the heterogeneous cell population response to infer whether any event has occurred or not and also to infer its properties such as timing and amplitude. Bayesian inference provides a natural framework to answer our questions about chemical signal occurrence, timing, and amplitude. We develop a probabilistic model that incorporates uncertainty in the how well our model captures the cell population and in how well a sample of measured cells represents the entire population. Using our probabilistic model and cell population measurements taken every five minutes on generated data, we ask how likely it was to observe the data for parameter values that describe square-shaped inducer pulses. We compare the likelihood functions associated with the probabilistic models for the event with the chemical signal pulses turned on versus turned off. Hence, we can determine whether an event of chemical induction of integrase expression has occurred or not. Using Markov Chain Monte Carlo, we sample the posterior distribution of chemical pulse parameters to identify likely pulses that produce the data measurements. We implement this method and obtain accurate results for detecting chemical inducer pulse timing, length, and amplitude. We can detect and identify chemical inducer pulses as short as half an hour, as well as all pulse amplitudes that fall under biologically relevant conditions.

The acrobot is a simple mechanical system patterned after a gymnast
performing on a single parallel bar. By swinging her legs, a gymnast
is able to bring herself into an inverted position with her center of
mass above the part and is able to perform manuevers about this
configuration. This report studies the use of nonlinear control
techniques for designing a controller to operate in a neighborhood of
the manifold of inverted equilibrium points. The techniques described
here are of particular interest because the dynamic model of the
acrobot violates many of the necessary conditions required to apply
current methods in linear and nonlinear control theory.
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The approach used in this report is to approximate the system in such
a way that the behavior of the system about the manifold of
equilibrium points is correctly captured. In particular, we construct
an approximating system which agrees with the linearization of the
original system on the equilibrium manifold and is full state
linearizable. For this class of approximations, controllers can be
constructed using recent techniques from differential geometric control
theory. We show that application of control laws derived in this
manner results in approximate trajectory tracking for the system under
certain restrictions on the class of desired trajectories. Simulation
results based on a simplified model of the acrobot are included. +

We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. Each individual reachability problem is solved via the Hamilton-Jacobi-Bellman (HJB) partial differential equation of stochastic optimal control theory. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the partial differential equation allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to conservatively satisfy a complex temporal logic specification. +

We introduce an algorithm for the optimal con- trol of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We directly compute on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. The solution to each reachability problem corresponds to the solution to a corresponding Hamilton-Jacobi-Bellman (HJB) partial differential equation. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification. +

A computational approach to generating aggressive trajectories in real-time for
constrained mechanical systems is presented. The algorithm is based
on a combination of nonlinear control theory, spline theory, and sequential
quadratic programming. It is demonstrated that real-time trajectory
generation for constrained mechanical systems is possible by mapping the
problem to one of finding trajectory curves in a lower dimensional space.
Performance of the algorithm is compared with existing optimal
trajectory generation techniques. Numerical results are reported using the NTG
software package. +

This paper presents an optimization framework for broadcast power-control, specifically addressed
at wireless networking issues arising in implementing information flows for multi-vehicle
systems. We formulate an optimization problem for the minimization of an aggregate cost subject
to a constraint on a quantity we call the geometric connection robustness, which is a locally
computable numerical assessment of the robustness of the an information flow to perturbations
in position. Our main result is a location-aided distributed power-control algorithm based on
a gradient-like optimization scheme. We also use geometric connection robustness to develop a
cheap distributed heuristic for the construction of sparse connected information flow. +

In an aircraft electric power system, one or more supervisory control units actuate a set of electromechanical switches to dynamically distribute power from generators to loads, while satisfying safety, reliability, and real-time performance requirements. To reduce expensive redesign steps, this control problem is generally addressed by minor incremental changes on top of consolidated solutions. A more systematic approach is hindered by a lack of rigorous design methodologies that allow estimating the impact of earlier design decisions on the final implementation. To achieve an optimal implementation that satisfies a set of requirements, we propose a platform-based methodology for electric power system design, which enables independent implementation of system topology (i.e., interconnection among elements) and control protocol by using a compositional approach. In our flow, design space exploration is carried out as a sequence of refinement steps from the initial specification toward a final implementation by mapping higher level behavioral and performance models into a set of either existing or virtual library components at the lower level of abstraction. Specifications are first expressed using the formalisms of linear temporal logic, signal temporal logic, and arithmetic constraints on Boolean variables. To reason about different requirements, we use specialized analysis and synthesis frameworks and formulate assume guarantee contracts at the articulation points in the design flow. We show the effectiveness of our approach on a proof-of-concept electric power system design. +

Insects exhibit unparalleled and incredibly robust
flight dynamics in the face of uncertainties. A fundamental principle contributing to this amazing behavior is rapid processing
and convergence of visual sensory information to flight motor
commands via spatial wide-field integration, accomplished by
motion pattern sensitive interneurons in the lobula plate portion
of the visual ganglia. Within a control-theoretic framework, a
model for wide-field integration of retinal image flow is developed, establishing the connection between image flow kernels
(retinal motion pattern sensitivities) and the feedback terms
they represent. It is demonstrated that the proposed output
feedback methodology is sufficient to give rise to experimentally
observed navigational heuristics as the centering and forward
speed regulation responses exhibited by honeybees. +

A reactor for the deposition of superconducting \ybcolong\;thin films is modeled and
studied from a control perspective to determine the heat transfer dynamics of the reactor
under active thermal control. A nonlinear wavelength-dependent heat transfer model is
developed to predict reactor heat transfer throughout the film growth process, and
preliminary component testing is conducted to validate the model. The model is linearized
about a typical operating point and analyzed with linear feedback control methods to
determine the performance of the reactor under observer-based feedback control with film
growth disturbances. The controller and observer are selected through linear quadratic
regulator and linear quadratic estimator methods. Rates of convergence of the controller
and observer are determined through examination of the eigenvalues of the linearized
system, and disturbance rejection is assessed with ${\mathcal H}_2$ and ${\mathcal
H}_\infty$ norms. The eigenvalue and norm analysis is applied to varying reactor design
parameters to quantify performance tradeoffs. The maximum errors associated with control
and with estimation of a nominal design case are both 21 K, and the longest time scales
are 45 seconds and 10 seconds for the controller and observer, respectively. +

This paper describes the use of a domain-specific language, and an accompanying software tool, in constructing correct- by-construction control protocols for aircraft electric power systems. Given a base topology, the language consists of a set of primitives for standard specifications. The accompanying tool converts these primitives into formal specifica- tions, which are used to synthesize control protocols. We can then use TuLiP, a Python-based software toolbox, to synthesize centralized and distributed controllers. For sys- tems with no time involved in the specifications, this tool also provides an option to output specifications into a SAT-solver compatible format, thus reducing the synthesis problem to a satisfiability problem. We provide the results of our synthesis procedure on a range of topologies. +

This paper explores the problem of finding a real--time optimal tra jectory for unmanned air vehicles (UAV) in order to minimize their probability of detection by opponent multiple radar detection systems. The problem is handled using the Nonlinear Tra jectory Generation (NTG) method developed by Milam et al. The paper presents a formulation of the trajectory generation task as an optimal control problem, where temporal constraints allow periods of high observability interspersed with periods of low observability. This feature can be used strategically to aid in avoiding detection by an opponent radar. The guidance is provided in the form of sampled tabular data. It is then shown that the success of NTG on the proposed low--observable tra jectory generation problem depends upon an accurate parameterization of the guidance data. In particular, such an approximator is desired to have a compact architecture, a minimum number of design parameters, and a smooth continuously--differentiable input-output mapping. Artificial Neural Networks (ANNs) as universal approximators are known to possess these features, and thus are considered here as appropriate candidates for this task. Comparison of ANNs against B-spline approximators is provided, as well. Numerical simulations on multiple radar scenarios illustrate UAV
trajectories optimized for both detectability and time. +

In this paper we present a dynamical systems representation for multi-agent rendezvous on
the phase plane. We restrict our attention to two agents, each with scalar dynamics. The problem of rendezvous is cast as a stabilization problem, with a set of constraints on the trajectories
of the agents, defined on the phase plane. We also describe a method to generate control Lyapunov functions that when used in conjunction with a stabilizing control law, such as Sontag's
formula, make sure that the two-agent system attains rendezvous. The main result of this paper
is a Lyapunov-like certificate theorem that describes a set of constraints, which when satisfied
are su±cient to guarantee rendezvous. +

In this paper analysis of interconnected dynamical systems
is considered. A framework for the analysis of the stability
of interconnection is given. The results from Fax and
Murray that studies the SISO-case for a constant interconnection
matrix are genralized to the MIMO-case where
arbitrary interconnection is allowed. The analysis show existness
of a separation principle that is very useful in the
sense of the simplicity for stability analysis. Stability could
be checked graphically using a Nyquist-like criterion. The
problem with time-delays and interconnection variation and
robustness appear to be natural special cases of the general
framework, and hence, simple stability criteria are derived
easly. +

In this paper, we analyze the problem of bifurcation control from a
geometric perspective. Our goal is to provide coordinate free,
geometric conditions under which control can be used to alter the
bifurcation properties of a nonlinear control system. These
insights are expected to be useful in understanding the role that
magnitude and rate limits play in bifurcation control, as well as
giving deeper understanding of the types of control inputs that are
required to alter the nonlinear dynamics of bifurcating systems. We
also use a model from active control of rotating stall in axial
compression systems to illustrate the geometric sufficient
conditions of stabilizability. +

In the geometric theory of nonlinear control systems, the notion of a distribution and
the dual notion of codistribution play a central role. Many results in nonlinear control
theory require certain distributions to be integrable. Distributions (and codistributions)
are not generically integrable and, moreover, the integrability property is not likely to
persist under small perturbations of the system. Therefore, it is natural to consider the
problem of approximating a given codistribution by an integrable codistribution, and to
determine to what extent such an approximation may be used for obtaining approximate
solutions to various problems in control theory. In this note, we concentrate on the
purely mathematical problem of approximating a given codistribution by an integrable
codistribution. We present an algorithm for approximating an m-dimensional nonintegrable
codistribution by an integrable one using a homotopy approach. The method yields an
approximating codistribution that agrees with the original codistribution on an
m-dimensional submanifold E_0 of R^n. +

We introduce a MATLAB-based simulation toolbox, called txtlsim, for an Escherichia coli-based Transcription–Translation (TX–TL) system. This toolbox accounts for several cell-free-related phenomena, such as resource loading, consumption and degradation, and in doing so, models the dynamics of TX–TL reactions for the entire duration of solution phase batch-mode experiments. We use a Bayesian parameter inference approach to characterize the reaction rate parameters associated with the core transcription, translation and mRNA degradation mechanics of the toolbox, allowing it to reproduce constitutive mRNA and protein-expression trajectories. We demonstrate the use of this characterized toolbox in a circuit behavior prediction case study for an incoherent feed-forward loop. +

A Method for Cost-Effective and Rapid Characterization of Engineered T7-based Transcription Factors by Cell-Free Protein Synthesis Reveals Insights into the Regulation of T7 RNA Polymerase-Driven Expression +

The T7 bacteriophage RNA polymerase (T7 RNAP) serves as a model for understanding RNA synthesis, as a tool for protein expression, and as an actuator for synthetic gene circuit design in bacterial cells and cell-free extract. T7 RNAP is an attractive tool for orthogonal protein expression in bacteria owing to its compact single subunit structure and orthogonal promoter specificity. Understanding the mechanisms underlying T7 RNAP regulation is important to the design of engineered T7-based transcription factors, which can be used in gene circuit design. To explore regulatory mechanisms for T7 RNAP-driven expression, we developed a rapid and cost-effective method to characterize engineered T7-based transcription factors using cell-free protein synthesis and an acoustic liquid handler. Using this method, we investigated the effects of the tetracycline operator’s proximity to the T7 promoter on the regulation of T7 RNAP-driven expression. Our results reveal a mechanism for regulation that functions by interfering with the transition of T7 RNAP from initiation to elongation and validates the use of the method described here to engineer future T7-based transcription factors. +

This paper considers the problem of motion planning for a car-like robot (i.e., a
mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We
present a fast and exact planner for our mobile robot model, based upon recursive
subdivision of a collision-free path generated by a lower-level geometric planner that
ignores the motion constraints. The resultant trajectory is optimized to give a path that
is of near-minimal length in its homotopy class. Our claims of high speed are supported by
experimental results for implementations that assume a robot moving amid polygonal
obstacles. The completeness and the complexity of the algorithm are proven using an
appropriate metric in the configuration space R2 x S1 of the robot. This metric is defined
by using the length of the shortest paths in the absence of obstacles as the distance
between two configurations. We prove that the new induced topology and the classical one
are the same. Although we concentration upon the car-like robot, the generalization of
these techniques leads to new theoretical issues involving sub-Riemannian geometry and to
practical results for nonholonomic motion planning. +

We present an identification framework for biochemical systems that allows multiple candidate models to be compared. This framework is designed to select a model that fits the data while maintaining model simplicity. The model identification task is divided into a parameter estimation stage and a model comparison stage. Model selection is based on calculating Akaike's Information Criterion, which is a systematic method for determining the model that best represents a set of experimental data. Two case studies are presented: a simulated transcriptional control circuit and a system of oscillators that has been built and characterized in vitro. In both examples the multi-model framework is able to discriminate between model candidates to select the one that best describes the data. +

A New Computational Method for Optimal Control of a Class of Constrained Systems Governed by Partial Differential Equations +

A computationally e±cient technique for the numerical solution of constrained
optimal control problems governed by one-dimensional partial differential
equations is considered in this paper. This technique utilizes inversion to map the
optimal control problem to a lower dimensional space. Results are presented using
the Nonlinear Trajectory Generation software package (NTG) showing that real-time
implementation may be possible. +