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Consensus-Based Multi-Objective Controller Synthesis

Ingyu Jang, Leila J. Bridgeman

Abstract

Despite longstanding interest, controller synthesis remains challenging for networks of heterogeneous, nonlinear agents. Moreover, the requirements for computational scalability and information privacy have become increasingly critical. This paper introduces a dissipativity-based distributed controller synthesis framework for networks with heterogeneous agents and diverse performance objectives, leveraging the Network Dissipativity Theorem and iterative convex overbounding. Our approach enables the synthesis of controllers in a distributed way by achieving a network-wide consensus on agents' dissipativity variables while keeping sensitive subsystem information locally. The proposed framework is applied to full-state feedback controller synthesis.

Consensus-Based Multi-Objective Controller Synthesis

Abstract

Despite longstanding interest, controller synthesis remains challenging for networks of heterogeneous, nonlinear agents. Moreover, the requirements for computational scalability and information privacy have become increasingly critical. This paper introduces a dissipativity-based distributed controller synthesis framework for networks with heterogeneous agents and diverse performance objectives, leveraging the Network Dissipativity Theorem and iterative convex overbounding. Our approach enables the synthesis of controllers in a distributed way by achieving a network-wide consensus on agents' dissipativity variables while keeping sensitive subsystem information locally. The proposed framework is applied to full-state feedback controller synthesis.

Paper Structure

This paper contains 17 sections, 7 theorems, 29 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Notation
  4. Alternating Direction Method of Multipliers (ADMM)
  5. QSR-Dissipativity of Large-Scale Multi-Agent Systems
  6. Iterative Convex Overbounding (ICO)
  7. Distributed Controller Synthesis
  8. Multi-Agent Networked System
  9. Controller Synthesis
  10. Distributed Controller Synthesis
  11. Xi Update by ico
  12. Initialization
  13. Application: Full-State Feedback
  14. Agent Level Linearized Dynamics
  15. Tightening Constraints
  16. ...and 2 more sections

Key Result

Lemma 1

An system with minimal realization $\Sigma{:}\dot{\mathbf{x}}{=}\mathbf{A}\mathbf{x}{+}\mathbf{B}\mathbf{u},\ \mathbf{y}{=}\mathbf{C}\mathbf{x}{+}\mathbf{D}\mathbf{u}$ is $\mathbf{Q}\mathbf{S}\mathbf{R}$-dissipative if there exist matrices $\mathbf{P}{\succ}0$, $\mathbf{Q}$, $\mathbf{S}$, and $\math

Figures (5)

  • Figure 3: Two representations of a multi-agent system.
  • Figure 4: Network of .
  • Figure 5: Evolution of performance metrics over \ref{['alg:01']}.
  • Figure 6: System responses to L2 disturbances. The dotted lines indicate equilibrium points of each .
  • Figure 7: Pole locations of $\text{diag}(\mathbf{A}_i^{cl})_{i\in\mathbb{N}_7}$. "Random" denotes poles from sampled realizations, "Vertex" denotes poles corresponding to the 8 vertices of the polytopic uncertainty.

Theorems & Definitions (14)

  • Definition 1: $\mathbf{Q}\mathbf{S}\mathbf{R}$-Dissipativity vidyasagar1981input
  • Lemma 1: gupta1996robust
  • Definition 2: $\mathcal{L}_2$-stability vidyasagar1981input
  • Theorem 1: vidyasagar1981input
  • Theorem 2: sebe2018sequential
  • Remark 1
  • Lemma 2
  • proof
  • Corollary 1
  • proof
  • ...and 4 more