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Distributed Optimal Consensus of Nonlinear Multi-Agent Systems

Ziyuan Guo, Chuanzhi lv, Liping Zhang, Huanshui Zhang

Abstract

In this paper, the optimal consensus problem for general nonlinear multi-agent systems is studied, where both leaderless and leader-follower cases are considered in a unified framework. The key idea is to convert consensus problems into optimal control problems where the objective of each agent with nonlinear dynamics is to design the control input minimizing the global consensus cost function. Compared with the existing distributed consensus control for nonlinear multi-agent systems, we propose a distributed optimal consensus algorithm based on the optimal control principle (OCP) method, and two enhanced algorithms are developed under the model predictive control (MPC) framework,these two algorithms demonstrate broader applicability when handling general nonlinear multi-agent systems. Moreover, the convergence and superlinear convergence rate of the proposed algorithms are rigorously analyzed. Numerical simulations demonstrate the effectiveness of the proposed algorithms.

Distributed Optimal Consensus of Nonlinear Multi-Agent Systems

Abstract

In this paper, the optimal consensus problem for general nonlinear multi-agent systems is studied, where both leaderless and leader-follower cases are considered in a unified framework. The key idea is to convert consensus problems into optimal control problems where the objective of each agent with nonlinear dynamics is to design the control input minimizing the global consensus cost function. Compared with the existing distributed consensus control for nonlinear multi-agent systems, we propose a distributed optimal consensus algorithm based on the optimal control principle (OCP) method, and two enhanced algorithms are developed under the model predictive control (MPC) framework,these two algorithms demonstrate broader applicability when handling general nonlinear multi-agent systems. Moreover, the convergence and superlinear convergence rate of the proposed algorithms are rigorously analyzed. Numerical simulations demonstrate the effectiveness of the proposed algorithms.

Paper Structure

This paper contains 15 sections, 2 theorems, 46 equations, 13 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. PROBLEM FORMULATION
  3. Multi-agent system model
  4. Graph theory
  5. Control objectives
  6. distributed optimal consensus
  7. Finite-time leaderless optimal consensus
  8. Finite-time leader-follower optimal consensus
  9. Technical notes of the proposed algorithms
  10. CONVERGENCE ANALYSIS
  11. SIMULATION EXAMPLES
  12. Consensus problem for leaderless case
  13. Consensus problem for leader–follower case
  14. Formation tracking problem
  15. CONCLUSIONS

Key Result

Theorem 1

The sequence$\{U^r\}$ generated by Algorithm 1 converges to the optimal solution of Problem 1, and there exists a scalar $c_1 > 0$ and an integer $r_0 > 0$ such that for any $r > r_0$, That is to say, Algorithm 1 is superlinearly convergent. $\blacktriangleleft$$\blacktriangleleft$

Figures (13)

  • Figure 1: Communication topology of AGVs
  • Figure 2: Actual trajectories of AGVs
  • Figure 3: Consensus errors of AGVs
  • Figure 4: Communication topology of agents
  • Figure 5: The first state tracking trajectory using Algorithm 3
  • ...and 8 more figures

Theorems & Definitions (10)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Theorem 1
  • Proof 1
  • Remark 5
  • Theorem 2
  • Proof 2
  • Remark 6