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Distributed Model Predictive Control for Asynchronous Multi-agent Systems with Self-Triggered Coordinator

Qianqian Chen, Shaoyuan Li

TL;DR

A shrinking constraint related to the error between the actual state and the predicted state is introduced into the optimal control problem to enhance the robustness of the system and achieve a trade‐off between control performance and energy loss.

Abstract

This paper investigates the distributed model predictive control for an asynchronous nonlinear multi-agent system with external interference via a self-triggered generator and a prediction horizon regulator. First, a shrinking constraint related to the error between the actual state and the predicted state is introduced into the optimal control problem to enable the robustness of the system. Then, the trigger interval and the corresponding prediction horizon are determined by altering the expression of the Lyapunov function, thus achieving a trade-off between control performance and energy loss. By implementing the proposed algorithm, the coordination objective of the multi-agent system is achieved under asynchronous communication. Finally, the recursive feasibility and stability are proven successively. An illustrative example is conducted to demonstrate the merits of the presented approach.

Distributed Model Predictive Control for Asynchronous Multi-agent Systems with Self-Triggered Coordinator

TL;DR

A shrinking constraint related to the error between the actual state and the predicted state is introduced into the optimal control problem to enhance the robustness of the system and achieve a trade‐off between control performance and energy loss.

Abstract

This paper investigates the distributed model predictive control for an asynchronous nonlinear multi-agent system with external interference via a self-triggered generator and a prediction horizon regulator. First, a shrinking constraint related to the error between the actual state and the predicted state is introduced into the optimal control problem to enable the robustness of the system. Then, the trigger interval and the corresponding prediction horizon are determined by altering the expression of the Lyapunov function, thus achieving a trade-off between control performance and energy loss. By implementing the proposed algorithm, the coordination objective of the multi-agent system is achieved under asynchronous communication. Finally, the recursive feasibility and stability are proven successively. An illustrative example is conducted to demonstrate the merits of the presented approach.
Paper Structure (13 sections, 6 theorems, 74 equations, 8 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 6 theorems, 74 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statements
  3. System Definition
  4. Problem Formulation
  5. Self-triggered DMPC Algorithm
  6. DMPC Optimization Problem
  7. Asynchronous Information Aggregation
  8. Self-Triggered Generator
  9. Analysis
  10. Recursive Feasibility
  11. Stability
  12. Illustrative Example
  13. Conclusions

Key Result

lemma 1

Consider the subsystem (subsystem) and the nominal subsystem (nominal subsystem), at triggering instant $k^t_i$, they are controlled by the identical $l$-step open-loop control action sequence $\{ u_i(k^t_i|k^t_i), u_i(k^t_i+1|k^t_i), ..., u_i(k^t_i+l-1|k^t_i) \}$. Then, the predicted state error be where $\Gamma_{\ast}(l)=\frac{\eta_i \bar{\lambda}(\sqrt{\ast})}{L_i} \left[(1+L_i)^l-1\right]$. Fu

Figures (8)

  • Figure 1: The diagram of DMPC algorithm with self-triggered coordinator.
  • Figure 2: The relationships between $k^t_i$, $k^{t+1}_i$, $\left[k^t_i\right]_j$, $N_{k^t_i}$, $H_{k^t_i}$, and $N_{[k^t_i]_j}$.
  • Figure 3: State trajectories of each agent under Algorithm 1.
  • Figure 4: Control levels of each agent under Algorithm 1.
  • Figure 5: Triggering instants and prediction horizons at each triggered instant of each agent under Algorithm 1.
  • ...and 3 more figures

Theorems & Definitions (15)

  • lemma 1: XDLX-2021
  • remark 1
  • remark 2
  • remark 3
  • lemma 2
  • proof
  • theorem 1
  • proof
  • remark 4
  • lemma 3
  • ...and 5 more