Data-Driven Structured Controller Design Using the Matrix S-Procedure

TL;DR

This paper tackles data-driven optimal structured controller design for discrete-time LTI systems under both $H_2$ and $H_\infty$ performance. It builds a data-driven framework that (i) characterizes the set of system matrices $\Sigma$ consistent with collected data using per-sample quadratic constraints and the matrix $S$-Procedure, and (ii) linearizes the nonconvex structure constraint to yield SDP/ILMI solutions. The authors propose three problem variants—model-based structured, data-driven unstructured, and data-driven structured—for each performance metric, with the data-driven cases solved via SDPs and iterative updates to enforce sparsity patterns. Across simulations, the method shows monotonic improvement with longer data length $T$ and outperforms the prior work miller2024data, at the cost of higher computational load. The work advances sparse, robust data-driven control for networked systems by reducing conservatism and enabling explicit structure in the controller.

Abstract

This paper focuses on the data-driven optimal structured controller design for discrete-time linear time-invariant (LTI) systems, considering both the $H_2$ performance and the $H_\infty$ performance. Specifically, we consider three scenarios: (i) the model-based structured control, (ii) the data-driven unstructured control, and (iii) the data-driven structured control. For the $H_2$ performance, we primarily investigate cases (ii) and (iii), since case (i) has been extensively studied in the literature. For the $H_\infty$ performance, all three scenarios are considered. For the structured control, we introduce a linearization technique that transforms the original nonconvex problem into a semidefinite programming (SDP) problem. Based on this transformation, we develop an iterative linear matrix inequality (ILMI) algorithm. For the data-driven control, we describe the set of all possible system matrices that can generate the sequence of collected data. Additionally, we propose a sufficient condition to handle all possible system matrices using the matrix S-procedure. The data-driven structured control is followed by combining the previous two cases. We compare our methods with those in the existing literature and demonstrate our superiority via several numerical simulations.

Figures (6)

• Figure 1: Computation time comparison between our structured $H_2$ control and miller2024data for different $T$ when $\epsilon=0.1$.
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Theorems & Definitions (14)

• Lemma 1: zhou1996robust
• Lemma 2: gahinet1994linear
• Remark 1
• Proposition 1
• Remark 2
• Theorem 1
• Theorem 2
• Theorem 3
• Proposition 2
• Theorem 4