2024/11/01 by Zhaohua Yang, Yang, Zhaohua, Pengyu Wang +10
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2411.00370
openalex publication_date 2024/11/01 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28
This paper provides a comprehensive analysis of the design of optimal structured and sparse H_∞ controllers for continuous-time linear time-invariant (LTI) systems. Three problems are considered. First, designing the sparsest H_∞ controller, which minimizes the sparsity of the controller while satisfying the given performance requirements. Second, designing a sparsity-promoting H_∞ controller, which balances system performance and controller sparsity. Third, designing a H_∞ 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.