Distributed optimization of general linear multi-agent systems with external disturbance

• Published in: Journal of the Franklin Institute 2021-07, Vol.358 (11), p.5951-5970
• Main Authors: Li, Shiling, Nian, Xiaohong, Deng, Zhenhua
• Format: Article
• Language: English
• Subjects: Algorithms; Control theory; Convergence; Cost function; Coupling; Graph theory; Internal model principle; Linear systems; Mathematical functions; Multiagent systems; Optimization; Topology
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.05.024

In this paper, we consider the distributed optimization problems with linear coupling constraint of general homogeneous and heterogeneous linear multi-agent systems under weighted-balanced and strongly connected digraphs. In order to control all agents converge to the optimal output, we propose distributed control laws, therein, the optimal output can make the global cost function reach minimum. Then we guarantee the convergence of the proposed algorithms by the properties of Laplacian matrix and Lyapunov stability theorem. Furthermore, we extend the result of heterogeneous linear multi-agent system to the case that dynamics of agents are subject to external disturbances, and prove that the algorithm designed by internal model principle can make all agents reach the optimal output exactly. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms.