Localized LQR Optimal Control

Abstract

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.

Extended version for 2014 CDC submission

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• Structured $H_{\infty }$-Optimal Control for Nested Interconnections: A State-Space Solution
• Sparsity and Spatial Localization Measures for Spatially Distributed Systems
• Distributed Control Subject to Delays Satisfying an ${\mathcal{H}}_{\infty }$ Norm Bound
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Cited by in corpus (5)

• Optimal Sparse Output Feedback Control Design: a Rank Constrained Optimization Approach
• Sample Complexity of Sparse System Identification Problem
• Sparse Linear-Quadratic Feedback Design Using Affine Approximation
• Separable and Localized System Level Synthesis for Large-Scale Systems
• Communication Delay Co-Design in ${\mathcal{H}}_2$ Distributed Control Using Atomic Norm Minimization