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Self-Triggered Distributed Model Predictive Control with Synchronization Parameters Interaction

Qianqian Chen, Shaoyuan Li

TL;DR

This work addresses cooperative control of nonlinear multi-agent systems under limited communication by introducing a self-triggered distributed MPC that coordinates via one-dimensional synchronization parameters $s_i(k)$ rather than full-state sharing. Each agent solves an OCP over horizon $N$ with cost $J_i$ that includes a nominal stage cost $H_i$ and a coupling term $\sum_{j\in\mathcal N_i}\rho_{ij}|s_i(\tau|k)-s_j(\tau|k)|^2$, and enforces tightened constraints to guarantee stability within a terminal set $\Omega_i(\varepsilon_{ri})$. Theoretical contributions include a self-triggering rule that ensures Lyapunov decrease under all triggering patterns, plus proofs of recursive feasibility and ISS stability of the closed-loop system. A three-robot formation example demonstrates reduced communication and computation while achieving formation tracking, validating the practicality of the approach.

Abstract

This paper investigates an aperiodic distributed model predictive control approach for multi-agent systems (MASs) in which parameterized synchronization constraints is considered and an innovative self-triggered criterion is constructed. Different from existing coordination methodology, the proposed strategy achieves the cooperation of agents through the synchronization of one-dimensional parameters related to the control inputs. At each asynchronous sampling instant, each agent exchanges the one-dimensional synchronization parameters, solves the optimal control problem (OCP) and then determines the open-loop phase. The incorporation of the selftriggered scheme and the synchronization parameter constraints relieves the computational and communication usage. Sufficient conditions guaranteeing the recursive feasibility of the OCP and the stability of the closed-loop system are proven. Simulation results illustrate the validity of the proposed control algorithm.

Self-Triggered Distributed Model Predictive Control with Synchronization Parameters Interaction

TL;DR

This work addresses cooperative control of nonlinear multi-agent systems under limited communication by introducing a self-triggered distributed MPC that coordinates via one-dimensional synchronization parameters rather than full-state sharing. Each agent solves an OCP over horizon with cost that includes a nominal stage cost and a coupling term , and enforces tightened constraints to guarantee stability within a terminal set . Theoretical contributions include a self-triggering rule that ensures Lyapunov decrease under all triggering patterns, plus proofs of recursive feasibility and ISS stability of the closed-loop system. A three-robot formation example demonstrates reduced communication and computation while achieving formation tracking, validating the practicality of the approach.

Abstract

This paper investigates an aperiodic distributed model predictive control approach for multi-agent systems (MASs) in which parameterized synchronization constraints is considered and an innovative self-triggered criterion is constructed. Different from existing coordination methodology, the proposed strategy achieves the cooperation of agents through the synchronization of one-dimensional parameters related to the control inputs. At each asynchronous sampling instant, each agent exchanges the one-dimensional synchronization parameters, solves the optimal control problem (OCP) and then determines the open-loop phase. The incorporation of the selftriggered scheme and the synchronization parameter constraints relieves the computational and communication usage. Sufficient conditions guaranteeing the recursive feasibility of the OCP and the stability of the closed-loop system are proven. Simulation results illustrate the validity of the proposed control algorithm.
Paper Structure (8 sections, 4 theorems, 29 equations, 6 figures, 1 algorithm)

This paper contains 8 sections, 4 theorems, 29 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statements
  3. Problem Formulation
  4. Optimal Control Problem
  5. Self-triggering mechanism
  6. Feasibility and Stability Analysis
  7. Illustrative Example
  8. Conclusions

Key Result

Lemma 1

Under Assumptions ass: Lipschitz and ass: terminal, if OCP$_i$ is feasible at $k^t_i$, the resulting state from the candidate control input sequence (eqn: feasible solution) satisfies $\|\bar{e}_i(N|k^{t+1}_i)\|^2_{P_i} \leq \varepsilon^2_{i}$ if the following conditions hold: where

Figures (6)

  • Figure 1: The Schematic of the proposed self-triggered DMPC strategy with $M$ agents.
  • Figure 2: The state responses within 0-20 step.
  • Figure 3: The control trajectories within 0-20 step.
  • Figure 4: The error trajectories of the synchronization parameters within 0-20 step.
  • Figure 5: The triggering instants within 0-20 step.
  • ...and 1 more figures

Theorems & Definitions (11)

  • Definition 1
  • Remark 1
  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Remark 2
  • Theorem 2
  • proof
  • Theorem 3
  • ...and 1 more