Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributed Consensus of Heterogeneous Multi-Agent Systems Based on Feedforward Control

Liping Zhang, Huanshui Zhang

TL;DR

By designing a distributed feedforward controller, a non-standard neighbor error system is transformed into a standard linear system, and then an optimal consensus controller is designed by minimizing a combined state error with neighbour agents.

Abstract

This paper studies the consensus problem of heterogeneous multi-agent systems by the feedforward control and linear quadratic (LQ) optimal control theory. Different from the existing consensus control algorithms, which require to design an additional distributed observer for estimating the leader's information and to solve a set of regulator equations. In this paper, by designing a distributed feedforward controller, a non-standard neighbor error system is transformed into a standard linear system, and then an optimal consensus controller is designed by minimizing a combined state error with neighbour agents. The proposed optimal controller is obtained by solving Riccati equations, and it is shown that the corresponding cost function under the proposed distributed controllers is asymptotically optimal. The proposed consensus algorithm can be directly applicable to solve the consensus problem of homogeneous systems. Simulation example indicates the effectiveness of the proposed scheme and a much faster convergence speed than the existing algorithm.

Distributed Consensus of Heterogeneous Multi-Agent Systems Based on Feedforward Control

TL;DR

By designing a distributed feedforward controller, a non-standard neighbor error system is transformed into a standard linear system, and then an optimal consensus controller is designed by minimizing a combined state error with neighbour agents.

Abstract

This paper studies the consensus problem of heterogeneous multi-agent systems by the feedforward control and linear quadratic (LQ) optimal control theory. Different from the existing consensus control algorithms, which require to design an additional distributed observer for estimating the leader's information and to solve a set of regulator equations. In this paper, by designing a distributed feedforward controller, a non-standard neighbor error system is transformed into a standard linear system, and then an optimal consensus controller is designed by minimizing a combined state error with neighbour agents. The proposed optimal controller is obtained by solving Riccati equations, and it is shown that the corresponding cost function under the proposed distributed controllers is asymptotically optimal. The proposed consensus algorithm can be directly applicable to solve the consensus problem of homogeneous systems. Simulation example indicates the effectiveness of the proposed scheme and a much faster convergence speed than the existing algorithm.
Paper Structure (8 sections, 5 theorems, 61 equations, 6 figures)

This paper contains 8 sections, 5 theorems, 61 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Main Results
  4. State consensus of heterogeneous multi-agent systems
  5. Comparison with traditional consensus algorithms
  6. Output consensus of heterogeneous multi-agent systems
  7. Numerical Simulation
  8. Conclusion

Key Result

Lemma 1

Anderson1971 Suppose that $E(k)$ is available for all agents. Consider system gloabl-closed-error-system with cost cost-function-error. Then, the optimal controller is given where the feedback gain $K$ is given by and $P$ is the solution of the following ARE The corresponding optimal cost function is Moreover, if $P$ is the unique positive definite solution to algebra-riccati-equation, then $\

Figures (6)

  • Figure 1: Communication topology among four agents
  • Figure 2: Observer error trajectories $\tilde{E}_{i}(k)$.
  • Figure 3: The first state trajectories of each agent $x_{i}(k),i=0,1,2,3$.
  • Figure 4: The first state error trajectories by the proposed method.
  • Figure 5: The first state trajectories of each agent by the existing method.
  • ...and 1 more figures

Theorems & Definitions (14)

  • Remark 1
  • Lemma 1
  • Theorem 1
  • proof
  • Lemma 2
  • proof
  • Remark 2
  • Theorem 2
  • proof
  • Remark 3
  • ...and 4 more