Event-triggered distributed optimization of multi-agent systems with time delay

Run Tang; Wei Zhu; Huizhu Pu; Run Tang; Wei Zhu; Huizhu Pu

doi:10.3934/mbe.2023916

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 12: 20712-20726. doi: 10.3934/mbe.2023916

Previous Article Next Article

Research article

Event-triggered distributed optimization of multi-agent systems with time delay

Key Laboratory of Intelligent Analysis and Decision on Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received: 10 August 2023 Revised: 13 October 2023 Accepted: 07 November 2023 Published: 16 November 2023

In this article, the distributed optimization based on multi-agent systems was studied, where the global optimization objective of the optimization problem is a convex combination of local objective functions. In order to avoid continuous communication among neighboring agents, an event-triggering algorithm was proposed. Time delay was also considered in the designed algorithm. The triggering time of each agent was determined by the state measurement error, the state of its neighbors at the latest triggering instant and the exponential decay threshold. Some sufficient conditions for optimal consistency were obtained. In addition, Zeno-behavior in triggering time sequence was eliminated. Finally, a numerical simulation was given to prove the effectiveness of the proposed algorithm.
- multi-agent systems,
- event-triggered,
- distributed optimization,
- time delay
Citation: Run Tang, Wei Zhu, Huizhu Pu. Event-triggered distributed optimization of multi-agent systems with time delay[J]. Mathematical Biosciences and Engineering, 2023, 20(12): 20712-20726. doi: 10.3934/mbe.2023916

Related Papers:

Abstract

In this article, the distributed optimization based on multi-agent systems was studied, where the global optimization objective of the optimization problem is a convex combination of local objective functions. In order to avoid continuous communication among neighboring agents, an event-triggering algorithm was proposed. Time delay was also considered in the designed algorithm. The triggering time of each agent was determined by the state measurement error, the state of its neighbors at the latest triggering instant and the exponential decay threshold. Some sufficient conditions for optimal consistency were obtained. In addition, Zeno-behavior in triggering time sequence was eliminated. Finally, a numerical simulation was given to prove the effectiveness of the proposed algorithm.

References

[1]	J. Wang, Y. Yan, Z. Liu, C. L. Chen, C. Zhang, K. Chen, Finite-time consensus control for multi-agent systems with full-state constraints and actuator failures, Neural Networks, 157 (2023), 350–363. https://doi.org/10.1016/j.neunet.2022.10.028 doi: 10.1016/j.neunet.2022.10.028
[2]	Q. Wang, Z. Duan, J. Wang, Q. Wang, G. Chen, An accelerated algorithm for linear quadratic optimal consensus of heterogeneous multi-agent systems, IEEE Trans. Autom. Control, 67 (2022), 421–428. https://doi.org/10.1109/TAC.2021.3056363 doi: 10.1109/TAC.2021.3056363
[3]	Q. Wang, X. Dong, J. Yu, J. L$\ddot{u}$, Z. Ren, Predefined finite-time output containment of nonlinear multi-agent systems with leaders of unknown inputs, IEEE Trans. Circuits Syst. I Regul. Pap., 68 (2021), 3436–3448. https://doi.org/10.1109/TCSI.2021.3083612 doi: 10.1109/TCSI.2021.3083612
[4]	A. Nandanwar, N. K. Dhar, D. Malyshev, L. Rybak, L. Behera, Stochastic event-based super-twisting formation control for multiagent system under network uncertainties, IEEE Trans. Control Network Syst., 9 (2022), 966–978. https://doi.org/10.1109/TCNS.2021.3089142 doi: 10.1109/TCNS.2021.3089142
[5]	Q. Lu, X. Liao, S. Deng, H. Li, Asynchronous algorithms for decentralized resource allocation over directed networks, IEEE Trans. Parallel Distrib. Syst., 34 (2023), 16–32. https://doi.org/10.1109/TPDS.2022.3212424 doi: 10.1109/TPDS.2022.3212424
[6]	X. Shi, Z. Meng, S. Dong, X. Wang, Distributed resource allocation algorithm for second-order multi-agent systems with external disturbances, Int. J. Control, 96 (2022), 2181–2189. https://doi.org/10.1080/00207179.2022.2086927 doi: 10.1080/00207179.2022.2086927
[7]	B. Polyak, Introduction to Optimization, Chapman Hall, 1987.
[8]	R. Xin, S. Pu, A. Nedic, U. A. Khan, A general framework for decentralized optimization with first-order methods, Proc. IEEE, 108 (2020), 1869–1889. https://doi.org/10.1109/JPROC.2020.3024266 doi: 10.1109/JPROC.2020.3024266
[9]	O. Shorinwa, R. N. Haksar, P. Washington, M. Schwager, Distributed multirobot task assignment via consensus ADMM, IEEE Trans. Rob., 39 (2023), 1781–1800. https://doi.org/10.1109/TRO.2022.3228132
[10]	I. Jeong, A review of decentralized optimization focused on information flows of decomposition algorithms, Comput. Oper. Res., 153 (2023), 106190. https://doi.org/10.1016/j.cor.2023.106190 doi: 10.1016/j.cor.2023.106190
[11]	Z. Yu, J. Sun, S.Yu, H. Jiang, Fixed-time distributed optimization for multi-agent systems with external disturbances over directed networks, Int. J. Robust Nonlinear Control, 33 (2023), 953–972. https://doi.org/10.1002/rnc.6408 doi: 10.1002/rnc.6408
[12]	A. Nedic, A. Olshevsky, Stochastic gradient-push for strongly convex functions on time-varying directed graphs, IEEE Trans. Autom. Control, 61 (2016), 3936–3947. https://doi.org/10.1109/TAC.2016.2529285 doi: 10.1109/TAC.2016.2529285
[13]	Y. Tian, Y. Sun, G. Scutari, Achieving linear convergence in distributed asynchronous multiagent optimization, IEEE Trans. Autom. Control, 65 (2020), 5264–5279. https://doi.org/10.1109/TAC.2020.2977940 doi: 10.1109/TAC.2020.2977940
[14]	P. Lin, W. Ren, J. A. Farrell, Distributed continuous-time optimization: nonuniform gradient gains, finite-time convergence, and convex constraint set, IEEE Trans. Autom. Control, 62 (2017), 2239–2253. https://doi.org/10.1109/TAC.2016.2604324 doi: 10.1109/TAC.2016.2604324
[15]	S. Rahili, W. Ren, Distributed continuous-time convex optimization with time-varying cost functions, IEEE Trans. Autom. Control, 62 (2017), 1590–1605. https://doi.org/10.1109/TAC.2016.2593899 doi: 10.1109/TAC.2016.2593899
[16]	W. Zhu, H. Tian, Distributed convex optimization via proportional-integral-differential algorithm, Meas. Control, 55 (2022), 13–20. https://doi.org/10.1177/00202940211029332 doi: 10.1177/00202940211029332
[17]	S. Li, X. Nian, Z. Deng, Distributed optimization of second-order nonlinear multiagent systems with event-triggered communication, IEEE Trans. Control Network Syst., 8 (2021), 1954–1963. https://doi.org/10.1109/TCNS.2021.3092832 doi: 10.1109/TCNS.2021.3092832
[18]	H. Dai, X. Fang, W. Chen, Distributed event-triggered algorithms for a class of convex optimization problems over directed networks, Automatica, 122 (2020), 109256. https://doi.org/10.1016/j.automatica.2020.109256 doi: 10.1016/j.automatica.2020.109256
[19]	T. Adachi, N. Hayashi, S. Takai, Distributed gradient descent method with edge-based event-driven communication for non-convex optimization, IET Control Theory Appl., 15 (2021), 1588–1598. https://doi.org/10.1049/cth2.12127 doi: 10.1049/cth2.12127
[20]	Z. Wu, Z. Li, Z. Ding, Z. Li, Distributed continuous-time optimization with scalable adaptive event-based mechanisms, IEEE Trans. Syst. Man Cybern. Syst., 50 (2020), 3252–3257. https://doi.org/10.1109/TSMC.2018.2867175 doi: 10.1109/TSMC.2018.2867175
[21]	N. Tran, Y. Wang, X. Liu, Distributed optimization problem for second-order multi-agent systems with event-triggered and time-triggered communication, J. Franklin Inst., 356 (2019), 10196–10215. https://doi.org/10.1016/j.jfranklin.2018.02.009 doi: 10.1016/j.jfranklin.2018.02.009
[22]	S. Chen, H. Jiang, Z. Yu, F. Zhao, Distributed optimization of single-integrator systems with prescribed-time convergence, IEEE Syst. J., 17 (2023), 3235–3245. https://doi.org/10.1109/JSYST.2022.3227024 doi: 10.1109/JSYST.2022.3227024
[23]	D. Wang, J. Liu, J. Lian, Y. Liu, Z. Wang, W. Wang, Distributed delayed dual averaging for distributed optimization over time-varying digraphs, Automatica, 150 (2023), 110869. https://doi.org/10.1016/j.automatica.2023.110869 doi: 10.1016/j.automatica.2023.110869
[24]	X. Xu, Z. Yu, D. Huang, H. Jiang, Distributed optimization for multi-agent systems with communication delays and external disturbances under a directed network, Nonlinear Anal.-Model. Control, 28 (2023), 1–19. https://doi.org/10.15388/namc.2023.28.31563 doi: 10.15388/namc.2023.28.31563
[25]	J. Yan, H. Yu, X. Xia, Distributed optimization of multi-agent systems with delayed sampled-data, Neurocomputing, 296 (2018), 100–108. https://doi.org/10.1016/j.neucom.2018.03.036 doi: 10.1016/j.neucom.2018.03.036
[26]	C. Wang, S. Xu, D. Yuan, Cooperative convex optimization with subgradient delays using push-sum distributed dual averaging, J. Franklin Inst., 358 (2021), 7254–7269. https://doi.org/10.1016/j.jfranklin.2021.07.015 doi: 10.1016/j.jfranklin.2021.07.015
[27]	Z. Deng, J. Luo, Fully distributed algorithms for constrained nonsmooth optimization problems of general linear multi-agent systems and their application, IEEE Trans. Autom. Control, 2023. https://doi.org/10.1109/TAC.2023.3301957
[28]	H. Zhou, X. Zeng, Y. Hong, Adaptive exact penalty design for constrained distributed optimization, IEEE Trans. Autom. Control, 64 (2019), 4661–4667. https://doi.org/10.1109/TAC.2019.2902612 doi: 10.1109/TAC.2019.2902612
[29]	Z. Deng, T. Chen, Distributed algorithm design for constrained resource allocation problems with high-order multi-agent systems, Automatica, 14 (2022), 110492. https://doi.org/10.1016/j.automatica.2022.110492 doi: 10.1016/j.automatica.2022.110492
[30]	P. A. Ioannou, J. Sun, Robust Adaptive Control, Upper Saddle River, NJ, USA: Prentice-Hall, 1995.

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)