arXiv subjects

Yuh-Shyang Wang

Publications and source records attributed to Yuh-Shyang Wang.

5 recordsLinked to original sources

arXiv2021

Localized and Distributed H2 State Feedback Control

Distributed linear control design is crucial for large-scale cyber-physical systems. It is generally desirable to both impose information exchange (communication) constraints on the distributed controller, and to limit the propagation of disturbances to a local region without cascading to the global network (localization). Recently proposed System Level Synthesis (SLS) theory provides a framework where such communication and localization requirements can be tractably incorporated in controller design and implementation. In this work, we derive a solution to the localized and distributed H2 state feedback control problem without resorting to Finite Impulse Response (FIR) approximation. Our proposed synthesis algorithm allows a column-wise decomposition of the resulting convex program, and is therefore scalable to arbitrary large-scale networks. We demonstrate superior cost performance and computation time of the proposed procedure over previous methods via numerical simulation.

eess.SY↗

arXiv2019

Verification of Neural Network Control Policy Under Persistent Adversarial Perturbation

Deep neural networks are known to be fragile to small adversarial perturbations. This issue becomes more critical when a neural network is interconnected with a physical system in a closed loop. In this paper, we show how to combine recent works on neural network certification tools (which are mainly used in static settings such as image classification) with robust control theory to certify a neural network policy in a control loop. Specifically, we give a sufficient condition and an algorithm to ensure that the closed loop state and control constraints are satisfied when the persistent adversarial perturbation is l-infinity norm bounded. Our method is based on finding a positively invariant set of the closed loop dynamical system, and thus we do not require the differentiability or the continuity of the neural network policy. Along with the verification result, we also develop an effective attack strategy for neural network control systems that outperforms exhaustive Monte-Carlo search significantly. We show that our certification algorithm works well on learned models and achieves 5 times better result than the traditional Lipschitz-based method to certify the robustness of a neural network policy on a cart pole control problem.

cs.LG↗

arXiv2019

A System Level Approach to Controller Synthesis

Biological and advanced cyberphysical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make constrained controller design feasible and tractable. We introduce a new "system level" (SL) approach involving three complementary SL elements. System Level Parameterizations (SLPs) generalize state space and Youla parameterizations of all stabilizing controllers and the responses they achieve, and combine with System Level Constraints (SLCs) to parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization, generalizing quadratic invariance (QI). SLPs also lead to a generalization of detectability and stabilizability, suggesting the existence of a rich separation structure, that when combined with SLCs, is naturally applicable to structurally constrained controllers and systems. We further provide a catalog of useful SLCs, most importantly including sparsity, delay, and locality constraints on both communication and computing internal to the controller, and external system performance. The resulting System Level Synthesis (SLS) problems that arise define the broadest known class of constrained optimal control problems that can be solved using convex programming. An example illustrates how this system level approach can systematically explore tradeoffs in controller performance, robustness, and synthesis/implementation complexity.

eess.SY↗

arXiv2017

Separable and Localized System Level Synthesis for Large-Scale Systems

A major challenge faced in the design of large-scale cyber-physical systems, such as power systems, the Internet of Things or intelligent transportation systems, is that traditional distributed optimal control methods do not scale gracefully, neither in controller synthesis nor in controller implementation, to systems composed of millions, billions or even trillions of interacting subsystems. This paper shows that this challenge can now be addressed by leveraging the recently introduced System Level Approach (SLA) to controller synthesis. In particular, in the context of the SLA, we define suitable notions of separability for control objective functions and system constraints such that the global optimization problem (or iterate update problems of a distributed optimization algorithm) can be decomposed into parallel subproblems. We then further show that if additional locality (i.e., sparsity) constraints are imposed, then these subproblems can be solved using local models and local decision variables. The SLA is essential to maintaining the convexity of the aforementioned problems under locality constraints. As a consequence, the resulting synthesis methods have $O(1)$ complexity relative to the size of the global system. We further show that many optimal control problems of interest, such as (localized) LQR and LQG, $\mathcal{H}_2$ optimal control with joint actuator and sensor regularization, and (localized) mixed $\mathcal{H}_2/\mathcal{L}_1$ optimal control problems, satisfy these notions of separability, and use these problems to explore tradeoffs in performance, actuator and sensing density, and average versus worst-case performance for a large-scale power inspired system.

math.OC↗

arXiv2014

Localized LQR Optimal Control

This paper introduces a receding horizon like control scheme for localizable distributed systems, in which the effect of each local disturbance is limited spatially and temporally. We characterize such systems by a set of linear equality constraints, and show that the resulting feasibility test can be solved in a localized and distributed way. We also show that the solution of the local feasibility tests can be used to synthesize a receding horizon like controller that achieves the desired closed loop response in a localized manner as well. Finally, we formulate the Localized LQR (LLQR) optimal control problem and derive an analytic solution for the optimal controller. Through a numerical example, we show that the LLQR optimal controller, with its constraints on locality, settling time, and communication delay, can achieve similar performance as an unconstrained H2 optimal controller, but can be designed and implemented in a localized and distributed way.

eess.SY↗