Abstract
This study investigates the consensus problem of a nonlinear discrete-time multi-agent system (MAS) under bounded additive disturbances. We propose a self-triggered robust distributed model predictive control consensus algorithm. A new cost function is constructed and MAS is coupled through this function. Based on the proposed cost function, a self-triggered mechanism is adopted to reduce the communication load. Furthermore, to overcome additive disturbances, a local minimum-maximum optimization problem under the worst-case scenario is solved iteratively by the model predictive controller of each agent. Sufficient conditions are provided to guarantee the iterative feasibility of the algorithm and the consensus of the closed-loop MAS. For each agent, we provide a concrete form of compatibility constraint and a consensus error terminal region. Numerical examples are provided to illustrate the effectiveness and correctness of the proposed algorithm.
摘要
针对一类有界加性扰动下的非线性离散多智能体系统一致性问题, 提出一种基于自触发鲁棒分布式模型预测控制的一致性算法. 首先构造了一个新的代价函数, 多智能体系统通过该函数进行耦合控制. 在该代价函数基础上, 采用自触发机制, 有效降低了通信负担. 为克服加性扰动, 利用每个智能体的模型预测控制器迭代求解最坏情况下的局部最小—最大优化问题. 然后, 给出保证算法迭代可行性和闭环多智能体系统达到一致性的充分条件. 对于每个智能体, 设计了兼容性约束和一致性误差终端域. 最后, 通过仿真算例验证了所提算法的有效性和正确性.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Al-Gherwi W, Budman H, Elkamel A, 2013. A robust distributed model predictive control based on a dual-mode approach. Comput Chem Eng, 50(5):130–138. https://doi.org/10.1016/j.compchemeng.2012.11.002
Cheng ZM, Zhang HT, Fan MC, et al., 2015. Distributed consensus of multi-agent systems with input constraints: a model predictive control approach. IEEE Trans Circ Syst I, 62(3):825–834. https://doi.org/10.1109/TCSI.2014.2367575
Dunbar WB, 2005. A distributed receding horizon control algorithm for dynamically coupled nonlinear systems. Proc 44th IEEE Conf on Decision and Control, p.6673–6679. https://doi.org/10.1109/CDC.2005.1583234
Feng YM, Yang XS, Song Q, et al., 2018. Synchronization of memristive neural networks with mixed delays via quantized intermittent control. Appl Math Comput, 339:874–887. https://doi.org/10.1016/j.amc.2018.08.009
Ferrara A, Oleari AN, Sacone S, et al., 2012. An event-triggered model predictive control scheme for freeway systems. Proc 51st IEEE Conf on Decision and Control, p.6975–6982. https://doi.org/10.1109/CDC.2012.6426241
Gao YL, Dai L, Xia YQ, et al., 2017. Distributed model predictive control for consensus of nonlinear second-order multi-agent systems. Int J Rob Nonl Contr, 27(5):830–842. https://doi.org/10.1002/rnc.3603
Hashimoto K, Adachi S, Dimarogonas DV, 2017. Self-triggered model predictive control for nonlinear input-affine dynamical systems via adaptive control samples selection. IEEE Trans Autom Contr, 62(1):177–189. https://doi.org/10.1109/TAC.2016.2537741
Heemels WPMH, Johansson KH, Tabuada P, 2012. An introduction to event-triggered and self-triggered control. Proc 51st IEEE Conf on Decision and Control, p.3270–3285. https://doi.org/10.1109/CDC.2012.6425820
Lazar M, de la Peña DM, Heemels WPMH, et al., 2008. On input-to-state stability of min-max nonlinear model predictive control. Syst Contr Lett, 57(1):39–48. https://doi.org/10.1016/j.sysconle.2007.06.013
Lehmann D, Henriksson E, Johansson KH, 2013. Event-triggered model predictive control of discrete-time linear systems subject to disturbances. European Control Conf, p.1156–1161. https://doi.org/10.23919/ecc.2013.6669580
Li HP, Shi Y, 2014. Event-triggered robust model predictive control of continuous-time nonlinear systems. Automatica, 50(5):1507–1513. https://doi.org/10.1016/j.automatica.2014.03.015
Li HP, Yan WS, 2015. Receding horizon control based consensus scheme in general linear multi-agent systems. Automatica, 56:12–18. https://doi.org/10.1016/j.automatica.2015.03.023
Li HP, Shi Y, Yan WS, 2016. On neighbor information utilization in distributed receding horizon control for consensus-seeking. IEEE Trans Cybern, 46(9):2019–2027. https://doi.org/10.1109/TCYB.2015.2459719
Li HP, Yan WS, Shi Y, 2018. Triggering and control codesign in self-triggered model predictive control of constrained systems: with guaranteed performance. IEEE Trans Autom Contr, 63(11):4008–4015. https://doi.org/10.1109/TAC.2018.2810514
Liu CX, Li HP, Gao J, et al., 2018. Robust self-triggered min-max model predictive control for discrete-time nonlinear systems. Automatica, 89:333–339. https://doi.org/10.1016/j.automatica.2017.12.034
Magni L, de Nicolao G, Scattolini R, et al., 2003. Robust model predictive control for nonlinear discrete-time systems. Int J Rob Nonl Contr, 13(3–4):229–246. https://doi.org/10.1002/rnc.815
Mayne DQ, Rawlings JB, Rao CV, et al., 2000. Constrained model predictive control: stability and optimality. Automatica, 36(6):789–814. https://doi.org/10.1016/S0005-1098(99)00214-9
Mi XX, Zou YY, Li SY, et al., 2020. Self-triggered DMPC design for cooperative multiagent systems. IEEE Trans Ind Electr, 67(1):512–520. https://doi.org/10.1109/TIE.2019.2896098
Mohamed TH, Bevrani H, Hassan AA, et al., 2011. Decentralized model predictive based load frequency control in an interconnected power system. Energy Conv Manag, 52(2):1208–1214. https://doi.org/10.1016/j.enconman.2010.09.016
Müller MA, Reble M, Allgöwer F, 2012. Cooperative control of dynamically decoupled systems via distributed model predictive control. Int J Rob Nonl Contr, 22(12):1376–1397. https://doi.org/10.1002/rnc.2826
Rosolia U, Carvalho A, Borrelli F, 2017. Autonomous racing using learning model predictive control. American Control Conf, p.5115–5120. https://doi.org/10.23919/ACC.2017.7963748
Su YX, Shi Y, Sun CY, 2019a. Distributed model predictive control for tracking consensus of linear multiagent systems with additive disturbances and time-varying communication delays. IEEE Trans Cybern, 51(7):3813–3823. https://doi.org/10.1109/TCYB.2019.2939732
Su YX, Wang QL, Sun CY, 2019b. Self-triggered robust model predictive control for nonlinear systems with bounded disturbances. IET Contr Theor Appl, 13(9): 1336–1343. https://doi.org/10.1049/iet-cta.2018.5459
Summers TH, Lygeros J, 2012. Distributed model predictive consensus via the alternating direction method of multipliers. Proc 5th Annual Allerton Conf on Communication, Control, and Computing, p.79–84. https://doi.org/10.1109/Allerton.2012.6483202
Wan XX, Yang XS, Tang RQ, et al., 2019. Exponential synchronization of semi-Markovian coupled neural networks with mixed delays via tracker information and quantized output controller. Neur Netw, 118:321–331. https://doi.org/10.1016/j.neunet.2019.07.004
Xi F, He J, Liu Z, 2010. Adaptive fast consensus algorithm for distributed sensor fusion. Signal Process, 90(5):1693–1699. https://doi.org/10.1016/j.sigpro.2009.11.020
Xu C, Yang XS, Lu JQ, et al., 2018. Finite-time synchronization of networks via quantized intermittent pinning control. IEEE Trans Cybern, 48(10):3021–3027. https://doi.org/10.1109/TCYB.2017.2749248
Yang XS, Cao JD, Xu C, et al., 2018. Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci China Technol Sci, 61(2):299–308. https://doi.org/10.1007/s11431-016-9054-y
Zhan JY, Li X, 2013. Consensus of sampled-data multi-agent networking systems via model predictive control. Automatica, 49(8):2502–2507. https://doi.org/10.1016/j.automatica.2013.04.037
Zhan JY, Jiang ZP, Wang YB, et al., 2019a. Distributed model predictive consensus with self-triggered mechanism in general linear multiagent systems. IEEE Trans Ind Inform, 15(7):3987–3997. https://doi.org/10.1109/TII.2018.2884449
Zhan JY, Chen YZ, Aleksandrov A, et al., 2019b. Robust distributed model predictive control based consensus of general linear multi-agent systems. IEEE Int Symp on Circuits and Systems, p.1–5. https://doi.org/10.1109/ISCAS.2019.8702724
Zheng Y, Li SY, Qiu H, 2013. Networked coordination-based distributed model predictive control for large-scale system. IEEE Trans Contr Syst Technol, 21(3):991–998. https://doi.org/10.1109/TCST.2012.2196280
Zou WC, Xiang ZR, 2019. Event-triggered leader-following consensus of non-linear multi-agent systems with switched dynamics. IET Contr Theor Appl, 13(9): 1222–1228. https://doi.org/10.1049/iet-cta.2018.5126
Zou WC, Shi P, Xiang ZR, et al., 2020a. Consensus tracking control of switched stochastic nonlinear multiagent systems via event-triggered strategy. IEEE Trans Neur Netw Learn Syst, 31(3):1036–1045. https://doi.org/10.1109/TNNLS.2019.2917137
Zou WC, Huang YY, Ahn CK, et al., 2020b. Containment control of linear multiagent systems with stochastic disturbances via event-triggered strategies. IEEE Syst J, 14(4):4810–4819. https://doi.org/10.1109/JSYST.2020.2975247
Zou YY, Su X, Niu YG, 2017. Event-triggered distributed predictive control for the cooperation of multi-agent systems. IET Contr Theor Appl, 11(1):10–16. https://doi.org/10.1049/iet-cta.2016.0638
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 61973074, U1713209, 61520106009, 61533008, and 61921004), the National Key R&D Program of China (No. 2018AAA0101400), and the Science and Technology on Information System Engineering Laboratory, China (No. 05201902)
Contributors
Qingling WANG, Yanxu SU, and Changyin SUN guided the research. Jiaqi LI performed the experiments and drafted the manuscript. Qingling WANG and Yanxu SU helped organize the manuscript. Jiaqi LI revised and finalized the paper.
Compliance with ethics guidelines
Jiaqi LI, Qingling WANG, Yanxu SU, and Changyin SUN declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Li, J., Wang, Q., Su, Y. et al. Robust distributed model predictive consensus of discrete-time multi-agent systems: a self-triggered approach. Front Inform Technol Electron Eng 22, 1068–1079 (2021). https://doi.org/10.1631/FITEE.2000182
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.2000182