Distributed Optimal Control and Application to Consensus of Multi-Agent Systems

TL;DR

A novel approach to the consensus problem of multi-agent systems by minimizing a weighted state error with neighbor agents via linear quadratic (LQ) optimal control theory and it is shown that the corresponding cost function under the proposed controllers is asymptotically optimal.

Abstract

This paper develops a novel approach to the consensus problem of multi-agent systems by minimizing a weighted state error with neighbor agents via linear quadratic (LQ) optimal control theory. Existing consensus control algorithms only utilize the current state of each agent, and the design of distributed controller depends on nonzero eigenvalues of the communication topology. The presented optimal consensus controller is obtained by solving Riccati equations and designing appropriate observers to account for agents' historical state information. It is shown that the corresponding cost function under the proposed controllers is asymptotically optimal. Simulation examples demonstrate the effectiveness of the proposed scheme, and a much faster convergence speed than the conventional consensus methods. Moreover, the new method avoids computing nonzero eigenvalues of the communication topology as in the traditional consensus methods.

Figures (7)

• Figure 1: Communication topology among four agents
• Figure 2: The state trajectories for each agent $x_{i}(k), i=1,2,3,4$.
• Figure 3: The state trajectories $x_{i}(k)$ by the traditional consensus method.
• Figure 4: Observer error trajectories $\tilde{e}_{1}(k)$.
• Figure 5: Communication topology among three agents

Theorems & Definitions (12)

• Lemma 1
• Theorem 1
• proof
• Theorem 2
• proof
• Lemma 2
• Theorem 3
• proof
• Theorem 4
• proof