Property:Abstract
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T
This paper presents a general framework for the control of mechanical
systems with as many inputs as degrees of freedom. The notes of error
functions and transport map are introduced to properly define a configuration
and velocity error. These are the crucial ingredients in designing a
proportional derivative feedback and feedforward control. The proposed
approach includes various results on control of manipulators, autonomous
vehicles and pointing devices. +
A
This paper presents a mathematical model for a synthetic transcriptional regulatory network in vitro. This circuit design resembles one of the well-known network motifs, the inco- herent feed-forward loop, in which an activator regulates both a gene and a repressor of the gene. Through mathematical analysis, we show how the circuit can be controlled to demonstrate exact adaptation to input signals. +
C
This paper presents a method for optimal trajectory generation for discrete-time nonlinear systems with linear temporal logic (LTL) task specifications. Our approach is based on recent advances in stochastic optimization algorithms for optimal trajectory generation. These methods rely on estimation of the rare event of sampling optimal trajectories, which is achieved by incrementally improving a sampling distribution so as to minimize the cross-entropy. A key component of these stochastic optimization algorithms is determining whether or not a trajectory is collision-free. We generalize this collision checking to e�ciently verify whether or not a trajectory satisfies a LTL formula. Interestingly, this verification can be done in time polynomial in the length of the LTL formula and the trajectory. We also propose a method for e�ciently re-using parts of trajectories that only partially satisfy the specification, instead of simply discarding the entire sample. Our approach is demonstrated through numerical experiments involving Dubins car and a generic point-mass model subject to complex temporal logic task specifications. +
S
Synthesis of Control Protocols for Switched Electrical Power Systems for Commercial Applications with Safety Specifications +
This paper presents a method for synthesizing fault tolerant control protocols for a deterministic discrete event system subject to safety specifications. The system discussed in the paper is modeled as a finite state machine (FSM) and Behavior Tree (BT). The synthesis procedure involves formulating the policy problem as a shortest path dynamic programming problem, and performing a backward search from the desire sates or behavior to the initial configuration. The search is performed over all possible states when applied to the FSM, or over all possible actions when applied to the BT. The resulting strategy minimizes the number of actions performed to meet operational objectives without violating safety conditions. The effectiveness of the procedure on FSMs and BTs is demonstrated through three examples of switched electrical power systems for commercial applications. +
This paper presents a new singular perturbation approach for analysing
flexibility in manipulators. This approach does not treat the flexible
manipulator as a perturbation of the rigid manipulator, and therefore,
allows for significant amounts of flexibility (beyond the linear
range). Analysis based on this approach leads to some provably stable
control schemes for the position and force control of flexible-link
manipulators. Simulation results are presented for a single flexible
manipulator pushing against a wall. +
R
This paper presents a survey of recent research in cooperative control of multivehicle systems, using a common mathematical framework to allow different methods to be described in a unified way. The survey has three primary parts: an overview of current applications of cooperative control, a summary of some of the key technical approaches that have been explored, and a description of some possible future directions for research. Specific technical areas that are discussed include formation control, cooperative tasking, spatiotemporal planning, and consensus. +
D
Dynamic Separation Control in a Low-Speed Asymmetric Diffuser with Varying Downstream Boundary Condition +
This paper presents an experimental investigation
into the effect of a varying downstream boundary
condition on dynamic separation control in a twodimensional
low-speed asymmetric diffuser. The potential
for coupling between the downstream boundary
condition and the separation dynamics is relevant,
for example, in using separation control to enable
more aggressive serpentine aircraft inlets, where
the compressor may be close to the separation point.
Separation control in the experiment is obtained using
spanwise unsteady forcing from a single tangential
actuator located directly upstream of the separation
point. The downstream boundary condition
simulates the dominant quasi-steady and reflection
characteristics of a compressor. Although the
boundary condition affects the uncontrolled pressure
recovery, the optimal forcing frequency is shown to
depend only on the mass flow rate and not on either
the presence, impedance, or location of the downstream
boundary condition. At the conditions tested
herein, we therefore conclude that the mechanism
underlying dynamic separation control is local in nature,
and is not influenced by global system dynamics. +
E
Experimental Evaluation of Air Injection for Actuation of Rotating Stall in a Low Speed, Axial Fan +
This paper presents an experimental investigation of the effects of
air injection on the rotating stall instability in a low speed axial
compressor. Two experiments concerning air injection were tried. The
first experiment used a continuous forcing perpendicular to the flow
in the same or opposite direction of the tip velocity. The results
show a dramatic difference between the two directions, with opposite
direction forcing causing a significant increase in performance, and
same direction forcing causing a significant decrease in performance.
This result contradicts the Emmons stall propagation model. The
second experiment investigated the differences with respect to
different frequencies of air injection, with the injector pointed at
the fan, parallel to the flow. We found that the change in the
compressor characteristic in the unstalled region was highly dependent
upon the forcing frequency with the maximum change occurring near the
frequency of stall. +
A
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. +
Active Control of Rotating Stall Using Pulsed Air Injection: A Parametric Study on a Low-Speed, Axial Flow Compressor +
This paper presents preliminary results on the use of low flow, high
momentum, pulsed air injectors to control the onset of stall in a
low-speed, axial flow compressor. By measuring the unsteady pressures
in front of the rotor, the controller determines the magnitude and
phase of a stall cell and controls the injection of air in front of
the rotor face. Initial experimental results have verified that
controller slightly extends the stall point of the compressor and
virtually eliminates the hysteresis loop normally associated with
stall. An explanation of this effect is proposed based on the
quasi-steady effects of air injection on the compressor characteristic
curve. +
This paper presents the use of pulsed air injection to control the onset of rotating
stall in a low-speed, axial flow compressor. By measuring the unsteady pressures near the
rotor face, a control algorithm determines the magnitude and phase of the first mode of
rotating stall and controls the injection of air in the front of the rotor face.
Experimental results show that this technique slightly extends the stall point of the
compressor and eliminates the hysteresis loop normally associated with rotating stall. A
parametric study is used to determine the optimal control parameters for suppression of
stall. Analytic results---using a low-dimensional model developed by Moore and Greitzer
combined with an unsteady shift in the compressor characteristic to model the
injectors---give further insights into the operation of the controller. Based on this
model, we show that the behavior of the experiment can be explained as a change in the
bifurcation behavior of the system under nonlinear feedback. A higher fidelity simulation
model is then used to further verify some of the specific performance characteristics that
are observed in experiments. +
T
This paper proposes a method of improving per- formance of scalar discrete-time systems with substantial delay by adding additional delayed feedback channels (i.e. imposing a distributed delay feedback). The optimal weights for the added feedback channels are found using optimization techniques. In particular, we reduce the H1 norm of the closed loop transfer function with multiple delayed feedback using techniques from static output feedback design. We impose constraints on the feedback gain in order to highlight the effectiveness of the distribution. In this manner, improvement on performance is a result of the distribution and not a change in the overall effective gain. The concept of applying a multiple delayed feedback channel is inspired by biological systems, where substantial delays can be present in feedback control. To show the effectiveness of this idea we apply our method to an example of a scalar genetic autoregulatory network. The constraint on the gain allows one to implement the feedback in a genetic regulatory network without having to change the reaction rates. A possible method of synthesizing such a system in a wet lab is explained in more detail. Finally, stability results indicate the possibility of stabilizing an unstable system with added delayed feedbacks (by adding larger delays). This approach may also be applicable to systems with large delays in which simple controllers are needed due to limitations in computational power. This paper motivates and provides preliminary results towards direct design of purely delay based controllers for network systems with large delays. +
F
Feasible Trajectories of Linear Dynamic Systems with Inequality Constraints Using Higher-Order Representations +
This paper proposes a method to determine trajectories of dynamic systems that steer
between two end points while satisfying linear inequality constraints arising from limits
on states and inputs. The method exploits the structure of the dynamic system written in a
higher-order form to explicitly eliminate the state equations. The feasible trajectories
of the dynamic system are sought within a characterization with a finite sum of mode
functions. In this paper, the linear inequalities on inputs and states are replaced by a
finite set of linear inequalities on the mode coefficients. This step changes the problem
of trajectory generation into finding a convex polytope enclosed by the linear
inequalities on the mode coefficients. A procedure is then developed to efficiently find
the vertices of this bounding polytope. It is demonstrated in this paper that this method
can generate feasible trajectories of the system in real-time and can quickly update the
trajectories as the terminal conditions are changed. The procedure is demonstrated
numerically by two examples. The results of one of the examples is implemented in hardware
to explore the issues of real-time planning and control. +
D
This paper proposes a new synthetic in vitro circuit that aims at regulating the rate of RNA transcription through positive feedback interactions. This design is dual to a previously synthesized transcriptional rate regulator based on self-repression. Two DNA templates are designed to interact through their transcripts, creating cross activating feedback loops that will equate their transcription rates at steady state. A mathematical model is developed for this circuit, consisting of a set of ODEs derived from the mass action laws and Michaelis--Menten kinetics involving all the present chemical species. This circuit is then compared to its regulatory counterpart based on negative feedback. A global sensitivity analysis reveals the fundamental features of the two designs, by evaluating their equilibrium response to changes in the most crucial parameters of the system. +
Differentially Flat Systems with Inequality Constraints: An Approach to Real-Time Feasible Trajectory Generation +
This paper proposes a real-time planning scheme and its implementation for a class of dynamic systems. The planner is aimed to satisfy the state equations, the path and actuator constriants, and the given initial and terminal constraints. In order to generate trajectories in real-time, three broad steps are performed: (1) the structure of differentially flat systems is used to explicitly encapsulate the state equations into linear differential constraints in a flat space, and appropriately transform the boundary conditions; (ii) using semi-infinite optimization theory, an inner approximation of nonlinear constraints is made to replace these by a set of linear inequalities in the flat space, i.e., by a polytope; (iii) this polytopic representation of the system that satisfies the state equations and the constraints is then parameterized using basis functions and the planning problem is turned around into solution of a set of linear inequalities in the coefficient space of the basis functions. It is then demonstrated that numerically efficient algorithms can be built to solve the planning problem in real-time. The essence of the approach is demonstrated by two examples: (1) an implementation is performed on a spring-mass-damper system to demonstrate the real-time capability of evasion-pursuit; (ii) a VTOL aircraft is used to illustrate the application of this approach in simulation to nonlinear problems. +
A
This paper proposes a set-based parameter identi- fication method for biochemical systems. The developed method identifies not a single parameter but a set of parameters that all explains time-series experimental data, enabling the systematic characterization of the uncertainty of identified parameters. Our key idea is to use a state-space realization that has the same input-output behavior as experimental data instead of the experimental data itself for the identification. This allows us to relax the originally nonlinear identification problem to an LMI feasibility problem validating the norm bound of an error system. We show that regions of parameters can be efficiently classified into consistent and inconsistent parameter sets by combining the LMI feasibility problems and a generalized bisection algorithm. +
N
This paper proposes an intuitive nonlinear lateral control strategy for trajectory tracking in autonomous
nonholonomic vehicles. The controller has been implemented and verified in Alice, Team Caltech's contribution to the 2007 DARPA Urban Challenge competition for autonomous
motorcars. A kinematic model is derived. The control law is described and analyzed. Results from simulations and field tests are given and evaluated. Finally, the key features of the proposed controller are reviewed, followed by a discussion of some limitations of the proposed strategy. +
E
Evaluation Metrics of Object Detection for Quantitative System-Level Analysis of Autonomous Systems +
This paper proposes two new metrics to evalu- ate learned object detection models for quantitative system-level analysis via probabilistic model-checking. In particular, proposition-labeled and distance-parametrized confusion matrices are defined for evaluating object detection, and these metrics are leveraged to compute the probability of the closed- loop system satisfying its system-level formal specifications. Instead of using object class labels, the proposition-labeled confusion matrix uses atomic propositions relevant to the high- level planning strategy. Furthermore, unlike the traditional confusion matrix, the distance-parametrized confusion matrix accounts for variations in detection performance with respect to the distance between the ego and the object. We empirically show that these evaluation metrics chosen with the context of i) system-level specifications and ii) the planning module lead to a less conservative analysis in comparison to canonical metrics that do not take these into account. We demonstrate this framework on a discrete-state car-pedestrian example by computing the satisfaction probabilities for safety requirements formalized in Linear Temporal Logic (LTL). +
C
This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations. +
E
This paper provides analytical results regarding the stability of linear discrete-time systems with stochastic delays. Necessary and sufficient stability conditions are derived by using the second moment dynamics which can be used to draw stability charts. The results are applied to a simple connected vehicle system where the stability regions are com- pared to those given by the mean dynamics. Our results reveal some fundamental limitations of connected cruise control which becomes more significant as the packet drop ratio increases. +
