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

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 dist...

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Bibliographic Details
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
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Summary: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.
ISSN:0016-0032
1879-2693
0016-0032
DOI:10.1016/j.jfranklin.2021.05.024