Data-Driven Structured Robust Control of Linear Systems

TL;DR

This paper develops a data-driven approach for designing structured state-feedback controllers that achieve $H_2$-performance for linear systems, using convex optimization that scales efficiently with data size.

Contribution

It introduces a novel convex LMI-based method for data-driven structured $H_2$ control that handles set-membership constraints and scales independently of data volume.

Findings

Successfully applied to example systems demonstrating effectiveness.

Provides convex conditions for structured control with data.

Scales independently of data sample size.

Abstract

Static structured control refers to the task of designing a state-feedback controller such that the control gain satisfies a subspace constraint. Structured control has applications in control of communication-inhibited dynamical systems, such as systems in networked environments. This work performs $H_2$-suboptimal regulation under a common structured state-feedback controller for a class of data-consistent plants. The certification of $H_2$-performance is attained through a combination of standard $H_2$ LMIs, convex sufficient conditions for structured control, and a matrix S-lemma for set-membership. The resulting convex optimization problems are linear matrix inequalities whose size scales independently of the number of data samples collected. Data-driven structured $H_2$-regulation control is demonstrated on example systems.