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Distributed fixed-time optimization for multi-agent systems over a directed network

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Abstract

This paper proposes some distributed algorithms to solve the multi-agent optimization problem with equality constraints, in which the team objective is a sum of local convex objective functions. Firstly, a directed network related to equality constraints is constructed before converting the constrained optimization problem into an unconstrained one. Secondly, a continuous algorithm is designed by using local information of agents, and the objective function converges to the global optimum in a fixed-time interval. Moreover, in order to reduce the communication cost, an event-triggered algorithm with sign function is devised. It is found that the optimal value can be achieved in a fixed-time interval, but the sign function can cause high-frequency chattering when the sate variables converge to the optimal value. Therefore, an event-triggered algorithm with saturation function is proposed, which can effectively overcome this disadvantage. Finally, the proposed algorithms are verified by some numerical simulations.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62003289, U1703262), the Tianshan Youth Program (Grant No. 2018Q068), the Tianshan Innovation Team Program (Grant No. 2020D14017), the Scientific Research Program of the Higher Education Institution of Xinjiang (Grant Nos. XJEDU2017T001, XJEDU2018Y004), and the Natural Science Foundation of Xinjiang Uygur Autonomous Region (Grant No. 2018D01C039).

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Zhiyong Yu, Shuzhen Yu, Haijun Jiang & Xuehui Mei

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  1. Zhiyong Yu
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  2. Shuzhen Yu
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  3. Haijun Jiang
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  4. Xuehui Mei
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Correspondence to Haijun Jiang.

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Yu, Z., Yu, S., Jiang, H. et al. Distributed fixed-time optimization for multi-agent systems over a directed network. Nonlinear Dyn 103, 775–789 (2021). https://doi.org/10.1007/s11071-020-06116-1

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