Sparse optimization of H2 controllers for LTI Systems: A log-barrier Method - Yang, Nachuan; Tang, Jiawei; Li, Yuzhe; Shi, Ling (Automatica (Oxford), 2025)
This paper studies the sparse optimization of H2 controllers for linear time-invariant systems. Due to the emergence of large-scale networked control systems in the past decades, the sparsity of a controller usually determines the communication and computation efficiency for implementation. However, the sparse design of optimal controllers has been a difficult problem because of its nonconvexity and nonsmoothness. In this paper, we consider the sparse design of controllers subject to the constraint on H2 performance, which can be used to describe the robustness margin for a control system. Unlike the sparsity promoting control which enhances the controller’s sparsity by regularization, we study the constrained sparse optimization directly. Moreover, we propose an interior point method using log-barrier functions and develop an alternating direction method of multipliers (ADMM) algorithm for computation. Besides, we also characterize the first-order optimality conditions for optimal sparse controllers and show that the accumulation point of our algorithm will be a Karush–Kuhn–Tucker (KKT) point of the original problem, which is the highest pursuit in nonconvex optimization problems. Finally, we provide several simulations on a 40-dimensional mass–spring system to illustrate the effectiveness of our proposed results.