Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Nonlinear Cooperative Output Regulation with Input Delay Compensation

Shiqi Zheng, Choon Ki Ahn, Xiaowei Jiang, Huaicheng Yan, Peng Shi

TL;DR

This work tackles cooperative output regulation (COR) for nonlinear multi-agent systems subject to long input delays, by integrating periodic event-triggered control (PETC) with a distributed predictor feedback to actively compensate delays. A fully asynchronous PETC-based distributed observer estimates the leader dynamics, while a certainty-equivalence predictor maps each follower to a coupled ODE-PDE target system, enabling Lyapunov-Krasovskii stability analysis. Key contributions include exponential convergence of the asynchronous observer, delay-tolerant predictor-based control for nonlinear MASs, and a PETC filter in the sensor-to-controller path that markedly reduces communications while preserving stability. Simulations with a 1-leader/4-follower network show accurate tracking, substantial transmission savings (below 10% of conventional sampling), and robustness to delay mismatches and external disturbances, illustrating practical viability for energy-efficient networked coordination.

Abstract

This paper investigates the cooperative output regulation (COR) of nonlinear multi-agent systems (MASs) with long input delay based on periodic event-triggered mechanism. Compared with other mechanisms, periodic event-triggered control can automatically guarantee a Zeno-free behavior and avoid the continuous monitoring of triggered conditions. First, a new periodic event-triggered distributed observer, which is based on the fully asynchronous communication data, is proposed to estimate the leader information. Second, a new distributed predictor feedback control method is proposed for the considered nonlinear MASs with input delay. By coordinate transformation, the MASs are mapped into new coupled ODE-PDE target systems with some disturbance-like terms. Then, we show that the COR problem is solvable. At last, to further save the communication resource, a periodic event-triggered mechanism is considered in the sensor-to-controller transmission in every agent. A new periodic event-triggered filter is proposed to deal with the periodic event-triggered feedback data. The MASs with input delay are mapped into coupled ODE-PDE target systems with sampled data information. Then, Lyapunov-Krasovskii functions are constructed to demonstrate the exponential stability of the MASs. Simulations verify the validity of the proposed results.

Nonlinear Cooperative Output Regulation with Input Delay Compensation

TL;DR

This work tackles cooperative output regulation (COR) for nonlinear multi-agent systems subject to long input delays, by integrating periodic event-triggered control (PETC) with a distributed predictor feedback to actively compensate delays. A fully asynchronous PETC-based distributed observer estimates the leader dynamics, while a certainty-equivalence predictor maps each follower to a coupled ODE-PDE target system, enabling Lyapunov-Krasovskii stability analysis. Key contributions include exponential convergence of the asynchronous observer, delay-tolerant predictor-based control for nonlinear MASs, and a PETC filter in the sensor-to-controller path that markedly reduces communications while preserving stability. Simulations with a 1-leader/4-follower network show accurate tracking, substantial transmission savings (below 10% of conventional sampling), and robustness to delay mismatches and external disturbances, illustrating practical viability for energy-efficient networked coordination.

Abstract

This paper investigates the cooperative output regulation (COR) of nonlinear multi-agent systems (MASs) with long input delay based on periodic event-triggered mechanism. Compared with other mechanisms, periodic event-triggered control can automatically guarantee a Zeno-free behavior and avoid the continuous monitoring of triggered conditions. First, a new periodic event-triggered distributed observer, which is based on the fully asynchronous communication data, is proposed to estimate the leader information. Second, a new distributed predictor feedback control method is proposed for the considered nonlinear MASs with input delay. By coordinate transformation, the MASs are mapped into new coupled ODE-PDE target systems with some disturbance-like terms. Then, we show that the COR problem is solvable. At last, to further save the communication resource, a periodic event-triggered mechanism is considered in the sensor-to-controller transmission in every agent. A new periodic event-triggered filter is proposed to deal with the periodic event-triggered feedback data. The MASs with input delay are mapped into coupled ODE-PDE target systems with sampled data information. Then, Lyapunov-Krasovskii functions are constructed to demonstrate the exponential stability of the MASs. Simulations verify the validity of the proposed results.
Paper Structure (18 sections, 9 theorems, 122 equations, 7 figures)

This paper contains 18 sections, 9 theorems, 122 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Periodic event-triggered adaptive distributed observer
  4. Control law
  5. Design of the control law
  6. Proof of Theorem \ref{['thm:1-1-1-1']}
  7. Periodic event-triggered control law
  8. Controller design
  9. Proof of Theorem \ref{['thm:1-1-1-1-1']}
  10. Simulations
  11. Conclusions
  12. Appendix
  13. Proof of Theorem 1
  14. Proof of Proposition 2
  15. Proof of Proposition 3
  16. ...and 3 more sections

Key Result

Theorem 1

Consider the MASs (eq:1)-(eq:8-4) with the distributed observer (eq:5-1-1-1)-(eq:6-1-1), there exists a positive constant $M$ such that for any $\kappa T\leq M$ with $\kappa\triangleq\max\{\kappa_{1},\kappa_{2}\}$ and $T\triangleq\underset{i,j\in\{1,2,...,N\}}{\max}\{T^{ij}\}$, the estimation errors

Figures (7)

  • Figure 1: Proposed control scheme. PETM-A and PETM-B are two periodic event-triggered mechanisms given in (\ref{['eq:26']}) and (\ref{['eq:26-1-1-2-1']}) respectively. PETM-A denotes the PETM between each agent. PETM-B denotes the PETM in the sensor-to-controller transmission for every agent, which will be explained in Section V.
  • Figure 2: Fully asynchronous communication. Each agent pair has different sampling periods and event-triggered time instants.
  • Figure 3: Performance of the proposed periodic event-triggered distributed observer. (a) Variations of the leader state $v$ and the estimation $\hat{v}_{i}(i=1,2,3,4)$; (b) periodic event-triggered instants for every agent pair.
  • Figure 4: Control performance of the proposed controller when the switch is on node 1 in Fig. \ref{['fig:1-3']}. (a)-(b) Outputs and regulation error of the MASs when there is no delay mismatch; (c)-(d) Outputs and regulation error of the MASs when delay mismatch exists.
  • Figure 5: Control performance of the proposed controller with different input delays.
  • ...and 2 more figures

Theorems & Definitions (28)

  • Remark 1
  • Theorem 1
  • proof
  • Remark 2
  • Remark 3
  • Proposition 1
  • Theorem 2
  • proof
  • Remark 4
  • Proposition 2
  • ...and 18 more