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Data-Driven Structured Robust Control of Linear Systems

Jared Miller, Jaap Eising, Florian Dörfler, Roy S. Smith

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.

Data-Driven Structured Robust Control of Linear Systems

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 -suboptimal regulation under a common structured state-feedback controller for a class of data-consistent plants. The certification of -performance is attained through a combination of standard 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 -regulation control is demonstrated on example systems.

Paper Structure

This paper contains 11 sections, 6 theorems, 29 equations, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Convex Sufficient Conditions for Structured Control
  4. Data-Driven Structured Control
  5. Consistent systems
  6. Controlled set
  7. Computational Considerations
  8. Numerical Examples
  9. Example 1: Sparse Control
  10. Example 2: Sparse Sharing Control
  11. Acknowledgements

Key Result

Lemma 2.1

The feedback gain $K$ is a $\gamma$-suboptimal $H_2$ controller for eq:sys_h2 if there exists matrices $(P, Q, R)$ such that the following holds:

Theorems & Definitions (11)

  • Lemma 2.1: Theorem 1 of de2002extended
  • Lemma 2.2: Theorem 5 of de2002extended
  • Example 2.1: Multi-agents and sparsity patterns
  • Lemma 2.3: Appendix of ferrante2019design
  • Remark 1
  • Example 2.2
  • Remark 2
  • Lemma 2.4
  • Remark 3
  • Lemma 3.1
  • ...and 1 more