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Distributed Event-Triggered Consensus Control of Discrete-Time Linear Multi-Agent Systems under LQ Performance Constraints

Shumpei Nishida, Kunihisa Okano

Abstract

This paper proposes a distributed event-triggered control method that not only guarantees consensus of multi-agent systems but also satisfies a given LQ performance constraint. Taking the standard distributed control scheme with all-time communication as a baseline, we consider the problem of designing an event-triggered communication rule such that the resulting LQ cost satisfies a performance constraint with respect to the baseline cost while consensus is achieved. The main difficulty is that the performance requirement is global, whereas triggering decisions are made locally and asynchronously by individual agents, which cannot directly evaluate the global performance degradation. To address this issue, we decompose allowable degradation across agents and design a triggering rule that uses only locally available information to satisfy the given LQ performance constraint. For general linear agents on an undirected graph, we derive a sufficient condition that guarantees both consensus and the prescribed performance level. We also develop a tractable offline design method for the triggering parameters. Numerical examples illustrate the effectiveness of the proposed method.

Distributed Event-Triggered Consensus Control of Discrete-Time Linear Multi-Agent Systems under LQ Performance Constraints

Abstract

This paper proposes a distributed event-triggered control method that not only guarantees consensus of multi-agent systems but also satisfies a given LQ performance constraint. Taking the standard distributed control scheme with all-time communication as a baseline, we consider the problem of designing an event-triggered communication rule such that the resulting LQ cost satisfies a performance constraint with respect to the baseline cost while consensus is achieved. The main difficulty is that the performance requirement is global, whereas triggering decisions are made locally and asynchronously by individual agents, which cannot directly evaluate the global performance degradation. To address this issue, we decompose allowable degradation across agents and design a triggering rule that uses only locally available information to satisfy the given LQ performance constraint. For general linear agents on an undirected graph, we derive a sufficient condition that guarantees both consensus and the prescribed performance level. We also develop a tractable offline design method for the triggering parameters. Numerical examples illustrate the effectiveness of the proposed method.

Paper Structure

This paper contains 10 sections, 8 theorems, 125 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Consensus and LQ Cost under All-Time Communication
  4. Distributed Event-Triggered Consensus under LQ Performance Constraints
  5. Parameter Design
  6. Numerical Example
  7. Simulation Setup
  8. Simulation Results
  9. Discussion
  10. Conclusion

Key Result

Lemma 1

Suppose that $(A,B)$ is stabilizable and $(A,Q_\ell^{1/2})$ is detectable. Assume that the undirected graph $\mathcal{G}$ is connected. If $c>0$ is chosen so that the multi-agent system eq:mas reaches consensus under the distributed controller eq:nominal_controller.

Figures (4)

  • Figure 1: Communication graph.
  • Figure 2: Transmission instants of each agent for the proposed event-triggered method, where a value of $1$ indicates that agent $i$ transmits at that time instant, and a value of $0$ otherwise.
  • Figure 3: State trajectories $x_{i,1}[k]$ for the all-time communication scheme (top) and the proposed event-triggered method (bottom).
  • Figure 4: Control inputs for the all-time communication scheme (top) and the proposed event-triggered method (bottom).

Theorems & Definitions (20)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Corollary 1
  • proof
  • Remark 3
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • ...and 10 more