Optimal Distributed H-infinity State Feedback for Systems with Symmetric and Hurwitz State Matrix

2015/09/30 by Carolina Lidström, Anders Rantzer, Lidström, Carolina +1
Computer Science · Engineering · #FOS: Mathematics #Neural Networks and Applications #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.1510.00070

openalex publication_date 2015/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We address H-infinity structured static state feedback and give a simple form for an optimal control law applicable to linear time invariant systems with symmetric and Hurwitz state matrix. More specifically, the control law as well as the minimal value of the norm can be expressed in the matrices of the system's state space representation, given separate cost on state and control input. Thus, the control law is transparent, easy to synthesize and scalable. Furthermore, if the plant possess a compatible sparsity pattern it is also distributed. Examples of such sparsity patterns are included. Furthermore, we give an extension of the optimal control law that incorporate coordination among subsystems. We demonstrate by a numerical example that the derived optimal controller is equal in performance to an optimal controller derived by the riccati equation approach.

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