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Event-Triggered Robust Cooperative Output Regulation for a Class of Linear Multi-Agent Systems with an Unknown Exosystem

Yangyang Qian, Lu Liu

TL;DR

The paper addresses robust cooperative output regulation for a class of heterogeneous uncertain linear multi-agent systems driven by an unknown exosystem. It develops a distributed adaptive internal model for each agent and couples it with a fully distributed event-triggered control strategy, comprising a distributed adaptive output feedback law and a dynamic event-triggering mechanism that operates at each agent's own triggering times. The approach eliminates the need for global topology information or parameter bounds, tolerates arbitrarily large agent uncertainties, and guarantees boundedness of the closed-loop system with the tracking errors $|e_i(t)|$ converging to a user-specified bound $\varepsilon_i$, while explicitly ruling out Zeno behavior via a positive lower bound on inter-event times. A numerical example demonstrates effective tracking and substantial reductions in controller updates compared with periodic sampling, validating the practical efficiency of the proposed scheme. The work advances distributed control for uncertain MASs under unknown exosystems and offers a framework adaptable to networked settings with limited information exchange.

Abstract

This paper investigates the robust cooperative output regulation problem for a class of heterogeneous uncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizing the internal model approach and the adaptive control technique, a distributed adaptive internal model is constructed for each agent. Then, based on this internal model, a fully distributed ETC strategy composed of a distributed event-triggered adaptive output feedback control law and a distributed dynamic event-triggering mechanism is proposed, in which each agent updates its control input at its own triggering time instants. It is shown that under the proposed ETC strategy, the robust cooperative output regulation problem can be solved without requiring either the global information associated with the communication topology or the bounds of the uncertain or unknown parameters in each agent and the exosystem. A numerical example is provided to illustrate the effectiveness of the proposed control strategy.

Event-Triggered Robust Cooperative Output Regulation for a Class of Linear Multi-Agent Systems with an Unknown Exosystem

TL;DR

The paper addresses robust cooperative output regulation for a class of heterogeneous uncertain linear multi-agent systems driven by an unknown exosystem. It develops a distributed adaptive internal model for each agent and couples it with a fully distributed event-triggered control strategy, comprising a distributed adaptive output feedback law and a dynamic event-triggering mechanism that operates at each agent's own triggering times. The approach eliminates the need for global topology information or parameter bounds, tolerates arbitrarily large agent uncertainties, and guarantees boundedness of the closed-loop system with the tracking errors converging to a user-specified bound , while explicitly ruling out Zeno behavior via a positive lower bound on inter-event times. A numerical example demonstrates effective tracking and substantial reductions in controller updates compared with periodic sampling, validating the practical efficiency of the proposed scheme. The work advances distributed control for uncertain MASs under unknown exosystems and offers a framework adaptable to networked settings with limited information exchange.

Abstract

This paper investigates the robust cooperative output regulation problem for a class of heterogeneous uncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizing the internal model approach and the adaptive control technique, a distributed adaptive internal model is constructed for each agent. Then, based on this internal model, a fully distributed ETC strategy composed of a distributed event-triggered adaptive output feedback control law and a distributed dynamic event-triggering mechanism is proposed, in which each agent updates its control input at its own triggering time instants. It is shown that under the proposed ETC strategy, the robust cooperative output regulation problem can be solved without requiring either the global information associated with the communication topology or the bounds of the uncertain or unknown parameters in each agent and the exosystem. A numerical example is provided to illustrate the effectiveness of the proposed control strategy.
Paper Structure (7 sections, 2 theorems, 49 equations, 8 figures)

This paper contains 7 sections, 2 theorems, 49 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation and Preliminaries
  3. Problem Formulation
  4. Preliminaries
  5. Main Results
  6. A Simulation Example
  7. Conclusions

Key Result

Lemma 1

Consider the closed-loop system (19) under the distributed event-triggering mechanism (17). Suppose that Assumptions Asmp1-Asmp3 are satisfied. Then, for any $w\in \mathbb{W}$ and $\sigma \in \mathbb{S}$, all signals of the closed-loop system (19) are bounded for all $t\geq 0$, and the trigger varia

Figures (8)

  • Figure 1: Communication graph.
  • Figure 2: Outputs of the agents and the exosystem.
  • Figure 3: Tracking errors of the agents.
  • Figure 4: Control input of agent $1$.
  • Figure 5: Total measurement error, triggering threshold, and triggering time instants of agent $1$.
  • ...and 3 more figures

Theorems & Definitions (9)

  • Definition 1: Robust CORP
  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1
  • Remark 4
  • Theorem 1
  • Remark 5
  • Remark 6