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Communication-Aware Dissipative Output Feedback Control

Ingyu Jang, Leila J. Bridgeman

Abstract

Communication-aware control is essential to reduce costs and complexity in large-scale networks. This work proposes a method to design dissipativity-augmented output feedback controllers with reduced online communication. The contributions of this work are three fold: a generalized well-posedness condition for the controller network, a convex relaxation for the constraints that infer stability of a network from dissapativity of its agents, and a synthesis algorithm integrating the Network Dissipativity Theorm, alternating direction method of multipliers, and iterative convex overbounding. The proposed approach yields a sparsely interconnected controller that is both robust and applicable to networks with heterogeneous nonlinear agents. The efficiency of these methods is demonstrated on heterogeneous networks with uncertain and unstable agents, and is compared to standard $\cH_\infty$ control.

Communication-Aware Dissipative Output Feedback Control

Abstract

Communication-aware control is essential to reduce costs and complexity in large-scale networks. This work proposes a method to design dissipativity-augmented output feedback controllers with reduced online communication. The contributions of this work are three fold: a generalized well-posedness condition for the controller network, a convex relaxation for the constraints that infer stability of a network from dissapativity of its agents, and a synthesis algorithm integrating the Network Dissipativity Theorm, alternating direction method of multipliers, and iterative convex overbounding. The proposed approach yields a sparsely interconnected controller that is both robust and applicable to networks with heterogeneous nonlinear agents. The efficiency of these methods is demonstrated on heterogeneous networks with uncertain and unstable agents, and is compared to standard control.

Paper Structure

This paper contains 19 sections, 7 theorems, 25 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. QSR-Dissipativity of Large-Scale Systems
  5. ico
  6. Sparsity-Promoting Dissipativity-Augmented Control
  7. Well-Posedness of Controller Interconnection
  8. Closed-loop Networked System
  9. Dual-Model Synthesis
  10. Sparsity Promoting Controller Synthesis
  11. Advantage of
  12. Algorithm
  13. Convex Overbounding of BMI Constraints
  14. Initialization
  15. Sparsity Promotion
  16. ...and 4 more sections

Key Result

Theorem 1

The operator is $\mathcal{L}_2$ stable if and only if it is $QSR$-dissipative with $\mathbf{Q}\prec0$.

Figures (2)

  • Figure 1: Two representations of a multi-agent system and its controller.
  • Figure 2: $\mathcal{H}_\infty$-norm of resulting sparse controllers; In \ref{['fig:Hinf_uncertain']}, the number of nonzero blocks in $\widetilde{\mathbf{H}}_y$ and $\widetilde{\mathbf{H}}_{\widehat{y}}$ is $100$ and $102$ for weighted $\ell_1$ norm and cardinality, respectively.

Theorems & Definitions (13)

  • Definition 1: $QSR$-Dissipativity, vidyasagar1981input
  • Definition 2: or $\mathcal{L}_2$-stability, lozano2013dissipative
  • Theorem 1
  • Theorem 2: , moylan2003stability
  • Theorem 3: sebe2018sequential
  • Remark 1
  • Definition 3: Chapter 5.2 khalil1996robust
  • Lemma 1
  • proof
  • Corollary 1
  • ...and 3 more