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Fixed-Relative-Switched Threshold Strategies for Consensus Tracking Control of Nonlinear Multiagent Systems

Ziming Wang, Yun Gao, Apostolos I. Rikos, Ning Pang, Yiding Ji

TL;DR

The paper addresses consensus tracking in nonlinear leader-follower multi-agent systems under communication constraints. It combines backstepping with radial basis function neural networks and observer design to approximate uncertain dynamics and estimate unmeasured states and disturbances. Three adaptive event-triggered control schemes—fixed, relative, and switched thresholds—are developed and analyzed via Lyapunov methods to ensure asymptotic leader tracking and uniform boundedness while preventing Zeno behavior. An illustrative example demonstrates effective tracking with reduced triggering, highlighting the relative-threshold and switched-threshold strategies as efficient options for balancing performance and communication load.

Abstract

This paper investigates event-triggered consensus tracking in nonlinear semi-strict-feedback multi-agent systems involving one leader and multiple followers. We first employ radial basis function neural networks and backstepping techniques to approximate the unknown nonlinear dynamics, facilitating the design of dual observers to measure the unknown states and disturbances. Then three adaptive event-triggered control schemes are proposed: fixed-threshold, relative-threshold, and switched-threshold configurations, each featuring specialized controller architectures and triggering mechanisms. Through Lyapunov stability analysis, we establish that the follower agents can asymptotically track the reference trajectory of the leader, meanwhile all error signals remain uniform bounded. Our proposed control strategies effectively prevent Zeno behaviors through stringent exclusion criteria. Finally, an illustrative example is presented, demonstrating the competitive performance of our control framework in achieving consensus tracking and optimizing triggering efficiency.

Fixed-Relative-Switched Threshold Strategies for Consensus Tracking Control of Nonlinear Multiagent Systems

TL;DR

The paper addresses consensus tracking in nonlinear leader-follower multi-agent systems under communication constraints. It combines backstepping with radial basis function neural networks and observer design to approximate uncertain dynamics and estimate unmeasured states and disturbances. Three adaptive event-triggered control schemes—fixed, relative, and switched thresholds—are developed and analyzed via Lyapunov methods to ensure asymptotic leader tracking and uniform boundedness while preventing Zeno behavior. An illustrative example demonstrates effective tracking with reduced triggering, highlighting the relative-threshold and switched-threshold strategies as efficient options for balancing performance and communication load.

Abstract

This paper investigates event-triggered consensus tracking in nonlinear semi-strict-feedback multi-agent systems involving one leader and multiple followers. We first employ radial basis function neural networks and backstepping techniques to approximate the unknown nonlinear dynamics, facilitating the design of dual observers to measure the unknown states and disturbances. Then three adaptive event-triggered control schemes are proposed: fixed-threshold, relative-threshold, and switched-threshold configurations, each featuring specialized controller architectures and triggering mechanisms. Through Lyapunov stability analysis, we establish that the follower agents can asymptotically track the reference trajectory of the leader, meanwhile all error signals remain uniform bounded. Our proposed control strategies effectively prevent Zeno behaviors through stringent exclusion criteria. Finally, an illustrative example is presented, demonstrating the competitive performance of our control framework in achieving consensus tracking and optimizing triggering efficiency.

Paper Structure

This paper contains 12 sections, 3 theorems, 42 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. System Model
  4. Observer Design
  5. Directed Graph
  6. Problem Formulation
  7. Event-Triggered Controller Design
  8. Fixed-threshold strategy
  9. Relative-threshold strategy
  10. Switched-threshold strategy
  11. Illustrative Example
  12. Conclusion

Key Result

Lemma 1

For any positive definite matrix ${{H}_{i}}=H_{i}^{T }>0$, with a symmetric positive matrix ${{F}_{i}}$ and a strict Hurwitz matrix $P_i$, it satisfies $P_{i}^{T }{{F}_{i}}+{{F}_{i}}{{P}_{i}}=-2{{H}_{i}}$.

Figures (4)

  • Figure 1: Block diagram of our proposed control framework.
  • Figure 2: Consensus tracking performance.
  • Figure 3: Trajectories of tracking errors $z_{i,1}$($i=1,2,3,4.$)
  • Figure 4: Release instants and interval and three event-triggered control strategies.

Theorems & Definitions (4)

  • Lemma 1: from lemma1
  • Lemma 2: from lemma2
  • Theorem 1
  • proof