Sparse $H_\infty$ Controller for Networked Control Systems: Non-Structured and Optimal Structured Design
Abstract
This paper provides a comprehensive analysis of the design of optimal structured and sparse controllers for continuous-time linear time-invariant (LTI) systems. Three problems are considered. First, designing the sparsest controller, which minimizes the sparsity of the controller while satisfying the given performance requirements. Second, designing a sparsity-promoting controller, which balances system performance and controller sparsity. Third, designing a controller subject to a structural constraint, which enhances system performance with a specified sparsity pattern. For each problem, we adopt a linearization technique that transforms the original nonconvex problem into a convex semidefinite programming (SDP) problem. Subsequently, we design an iterative linear matrix inequality (ILMI) algorithm for each problem, which ensures guaranteed convergence. We further characterize the first-order optimality using the Karush-Kuhn-Tucker (KKT) conditions and prove that any limit point of the solution sequence generated by the ILMI algorithm is a stationary point. For the first and second problems, we validate that our algorithms can reduce the number of non-zero elements and thus the communication burden through several numerical simulations. For the third problem, we refine the solutions obtained in existing literature, demonstrating that our approaches achieve significant improvements.
Cite
@article{arxiv.2411.00370,
title = {Sparse $H_\infty$ Controller for Networked Control Systems: Non-Structured and Optimal Structured Design},
author = {Zhaohua Yang and Pengyu Wang and Haishan Zhang and Shiyue Jia and Nachuan Yang and Yuxing Zhong and Ling Shi},
journal= {arXiv preprint arXiv:2411.00370},
year = {2025}
}