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Robust Cooperative Output Regulation of Discrete-Time Heterogeneous Multi-Agent Systems

Kursad Metehan Gul, Selahattin Burak Sarsilmaz

Abstract

This article considers robust cooperative output regulation of discrete-time uncertain heterogeneous (in dimension) multi-agent systems (MASs). We show that the solvability of this problem with an internal model-based distributed control law reduces to the existence of a structured control gain that makes the nominal closed-loop system matrix of the MAS Schur. Accordingly, this article focuses on global and agent-wise local sufficient conditions for the existence and design of such a structured control gain. Based on a structured Lyapunov inequality, we present a convexification that yields a linear matrix inequality (LMI), whose feasibility is a global sufficient condition for the existence and design. Considering the individual nominal dynamics of each agent, the existence is also ensured if each agent solves a structure-free control problem. Its convexification yields LMIs that allow each agent to separately design its structure-free control gain. Lastly, we study the relationships between the sets of control gains emerging from both global and local perspectives.

Robust Cooperative Output Regulation of Discrete-Time Heterogeneous Multi-Agent Systems

Abstract

This article considers robust cooperative output regulation of discrete-time uncertain heterogeneous (in dimension) multi-agent systems (MASs). We show that the solvability of this problem with an internal model-based distributed control law reduces to the existence of a structured control gain that makes the nominal closed-loop system matrix of the MAS Schur. Accordingly, this article focuses on global and agent-wise local sufficient conditions for the existence and design of such a structured control gain. Based on a structured Lyapunov inequality, we present a convexification that yields a linear matrix inequality (LMI), whose feasibility is a global sufficient condition for the existence and design. Considering the individual nominal dynamics of each agent, the existence is also ensured if each agent solves a structure-free control problem. Its convexification yields LMIs that allow each agent to separately design its structure-free control gain. Lastly, we study the relationships between the sets of control gains emerging from both global and local perspectives.
Paper Structure (10 sections, 13 theorems, 57 equations)

This paper contains 10 sections, 13 theorems, 57 equations.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Contribution
  4. Notation
  5. Problem Formulation
  6. Solvability of the RCORP
  7. Structured Global Design of $K$
  8. Agent-Wise Local Design of $K$
  9. Set Inclusions Among Control Gain Sets Emerging from Global and Local Perspectives
  10. Conclusion

Key Result

Lemma 1

If $A_\mathrm{g}$ is Schur and for any $\mathrm{diag}(E_i)$, $F$, and for any $\delta \in \Delta$, where $\Delta = \{ \delta ~|~ \Bar{A}_{\mathrm{g}} \text{ is} \ \text{Schur}\}$, there exists a matrix $X_\mathrm{g}$ such that then Problem prb:mainproblem is solved.

Theorems & Definitions (25)

  • Remark 1
  • Lemma 1
  • Lemma 2: Lemma 4.1 and Remark 4.1 in SarsilmazIJC
  • Lemma 3
  • Lemma 4
  • Theorem 1
  • Remark 2
  • Lemma 5
  • Example 1
  • Lemma 6
  • ...and 15 more