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Distributed convex optimization for nonlinear multi-agent systems disturbed by a second-order stationary process over a digraph

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Abstract

In this paper, we investigate the distributed convex optimization problem for a class of nonlinear multi-agent systems disturbed by random noise over a directed graph. The target problem involves designing a continuous-time algorithm to minimize the sum of all local cost functions associated with each agent. The target noise is considered as a second-order stationary process under mild assumptions. The noise-to-state exponential stability for the multi-agent system based on random differential equations is analyzed using a random field method. Sufficient conditions corresponding to the second moment relative to the optimal solution in the form of matrix inequalities are established. Then, the grid search method is employed to determine the best system parameters such that the second moment of the estimation error has the minimum value. In addition, the obtained results are applied to solve the average consensus problem in the presence of a stationary process. Finally, a numerical example is presented to verify the effectiveness of the proposed algorithm.

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61973050, 61773089, 62073275), Fundamental Research Funds for the Central Universities (Grant Nos. DUT20GJ209, DUT20JC14). The authors are very grateful to anonymous reviewers for their valuable comments to improve the quality of the paper.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian, 116024, China

    Dong Wang, Zhu Wang & Wei Wang

  2. School of Control Science and Engineering, Dalian University of Technology, Dalian, 116024, China

    Dong Wang, Zhu Wang & Wei Wang

  3. School of Mathematics and Informational Science, Yantai University, Yantai, 264005, China

    Zhaojing Wu

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  1. Dong Wang
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  2. Zhu Wang
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  4. Wei Wang
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Correspondence to Dong Wang.

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Wang, D., Wang, Z., Wu, Z. et al. Distributed convex optimization for nonlinear multi-agent systems disturbed by a second-order stationary process over a digraph. Sci. China Inf. Sci. 65, 132201 (2022). https://doi.org/10.1007/s11432-020-3111-4

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  • DOI: https://doi.org/10.1007/s11432-020-3111-4

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