Markov切换拓扑下二阶非线性多智能体编队容错控制

doi:10.19678/j.issn.1000-3428.0066603

摘要/Abstract

摘要：

多智能体系统编队控制过程中存在固定拓扑下智能体之间通信信号易丢失和控制器故障频发的问题。对此，提出一种具有随机切换通信拓扑的二阶非线性多智能体系统领导-跟随编队容错控制协议。为解决二阶非线性多智能体系统编队中控制信号丢失的问题，利用马尔可夫(Markov)随机过程描述切换通信拓扑编队模型，提出一种基于Markov随机切换通信拓扑的多智能体编队控制律，通过建立领导者和追随者之间的状态误差模型，构建具有二重积分的Lyapunov-Krasovskii函数证明多智能体系统在均方意义下的指数收敛稳定。为解决多智能体系统编队控制器故障问题，建立具有随机通信拓扑切换的多智能体编队容错控制模型，设计一种具有Markov随机切换通信拓扑的多智能体编队容错控制算法，利用李雅普诺夫稳定性理论分析所提出算法的稳定性和收敛性。仿真结果体现了多智能体系统随机切换通信拓扑编队控制器超调量小、响应时间快、调整时间短的特点，同时对比实验结果验证了系统在发生故障和无故障情况下的稳定性与有效性。

关键词: 多智能体系统, 编队控制, 容错控制, 马尔可夫过程, 非线性

Abstract:

To solve the problems of communication signal loss and controller failure in the formation control of multi-agent systems, this paper proposes a fault-tolerant control protocol for second-order nonlinear multi-agent system leader-follower formation with a stochastic switching communication topology. First, to solve the problem of control signal loss in the formation of second-order nonlinear multi-agent systems, a Markov stochastic process is adopted to describe the switching communication topology formation model. In addition, a state error model is established between the leader and follower, and the Lyapunov-Krasovskii Function(LKF) is constructed with double integration to prove the exponential convergence stability of the multi-agent system in the mean-square sense. Accordingly, a multi-agent formation control law based on the Markov stochastic switching communication topology is proposed. Second, to solve the multi-agent system formation controller failure problem, a multi-agent formation fault-tolerant control model with random communication topology switching is established, a multi-agent formation fault-tolerant control algorithm with Markov random switching communication topology is designed, and the stability and convergence of the proposed algorithm are analyzed considering the Lyapunov stability theory. Finally, the algorithm is verified through computer simulations, considering the characteristics of formation controller of the multi-agent system with random switching communication topology such as small overshoot, fast response time, and short adjustment time. Further, the stability and effectiveness of the system with and without failure are compared and verified.

Key words: multi-agent system, formation control, fault-tolerant control, Markov process, nonlinear

欧阳凌丛, 杨凯军, 张志雄. Markov切换拓扑下二阶非线性多智能体编队容错控制[J]. 计算机工程, 2023, 49(10): 127-135.

Lingcong OUYANG, Kaijun YANG, Zhixiong ZHANG. Fault-Tolerant Control of Second-Order Nonlinear Multi-Agent Formation Under Markov Switching Topology[J]. Computer Engineering, 2023, 49(10): 127-135.

https://www.ecice06.com/CN/Y2023/V49/I10/127

图/表 7

图1 3种可能网络拓扑

Fig.1 Three possible network topologies

图2 编队轨迹

Fig.2 Formation trajectory

图3 控制器输入

Fig.3 Controller input

图4 通信拓扑网络编号

Fig.4 Number of communication topology network

图5 领导者与跟随者的相对误差

Fig.5 The relative error of leaders and followers

图6 故障情况

Fig.6 Failure situation

参考文献 25

1	WANG C R, YAN C X, LIU Z C. Leader-following consensus for second-order nonlinear multi-agent systems under Markovian switching topologies with application to ship course-keeping. International Journal of Control, Automation and Systems, 2021, 19(1): 54- 62. doi: 10.1007/s12555-019-0395-8
2	WANG Y W, WEI Y W, LIU X K, et al. Optimal persistent monitoring using second-order agents with physical constraints. IEEE Transactions on Automatic Control, 2019, 64(8): 3239- 3252. doi: 10.1109/TAC.2018.2879946
3	LV Y Y, HU Q, MA G, et al. Attitude cooperative control of spacecraft formation via output-feedback[EB/OL]. [2022-10-10]. https://www.emerald.com/insight/content/doi/10.1108/00022661211255502/full/html.
4	ZHOU X, WEN X Y, WANG Z P, et al. Swarm of micro flying robots in the wild. Science Robotics, 2022, 7(66): eabm5954. doi: 10.1126/scirobotics.abm5954
5	HOFFMAN G. Evaluating fluency in human-robot collaboration. IEEE Transactions on Human-Machine Systems, 2019, 49(3): 209- 218. doi: 10.1109/THMS.2019.2904558
6	ZHI H, CHEN L M, LI C J, et al. Leader-follower affine formation control of second-order nonlinear uncertain multi-agent systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 2021, 68(12): 3547- 3551. doi: 10.1109/TCSII.2021.3072652
7	YU J L, DONG X W, LI Q D, et al. Practical time-varying formation tracking for second-order nonlinear multiagent systems with multiple leaders using adaptive neural networks. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(12): 6015- 6025. doi: 10.1109/TNNLS.2018.2817880
8	MENG D Y, JIA Y M, DU J P, et al. On iterative learning algorithms for the formation control of nonlinear multi-agent systems. Automatica, 2014, 50(1): 291- 295. doi: 10.1016/j.automatica.2013.11.009
9	WANG J L, WU H N. Leader-following formation control of multi-agent systems under fixed and switching topologies. International Journal of Control, 2012, 85(6): 695- 705. doi: 10.1080/00207179.2012.662720
10	WANG M, ZHANG T. Leader-following formation control of second-order nonlinear systems with time-varying communication delay. International Journal of Control, Automation and Systems, 2021, 19(5): 1729- 1739. doi: 10.1007/s12555-019-0759-0
11	SHANG Y L. Consensus seeking over Markovian switching networks with time-varying delays and uncertain topologies. Applied Mathematics and Computation, 2016, 273, 1234- 1245. doi: 10.1016/j.amc.2015.08.115
12	MO L P, GUO S Y, YU Y G. Mean-square consensus of heterogeneous multi-agent systems with nonconvex constraints, Markovian switching topologies and delays. Neurocomputing, 2018, 291, 167- 174. doi: 10.1016/j.neucom.2018.02.075
13	XIE D M, SHI L, JIANG F C. Group tracking control of second-order multi-agent systems with fixed and Markovian switching topologies. Neurocomputing, 2018, 281, 37- 46. doi: 10.1016/j.neucom.2017.11.040
14	LI F, SHEN H. Finite-time H∞ synchronization control for semi-Markov jump delayed neural networks with randomly occurring uncertainties. Neurocomputing, 2015, 166, 447- 454. doi: 10.1016/j.neucom.2015.03.034
15	SUN F L, LEI C Y, KURTHS J. Consensus of heterogeneous discrete-time multi-agent systems with noise over Markov switching topologies. International Journal of Robust and Nonlinear Control, 2021, 31(5): 1530- 1541. doi: 10.1002/rnc.5360
16	YE D, CHEN M M, YANG H J. Distributed adaptive event-triggered fault-tolerant consensus of multiagent systems with general linear dynamics. IEEE Transactions on Cybernetics, 2019, 49(3): 757- 767. doi: 10.1109/TCYB.2017.2782731
17	GONG P, LAN W Y, HAN Q L. Robust adaptive fault-tolerant consensus control for uncertain nonlinear fractional-order multi-agent systems with directed topologies. Automatica, 2020, 117, 109011. doi: 10.1016/j.automatica.2020.109011
18	DAI J T, GUO G. Exponential consensus of non-linear multi-agent systems with semi-Markov switching topologies. IET Control Theory & Applications, 2017, 11(18): 3363- 3371. URL
19	LIU H W, KARIMI H R, DU S L, et al. Leader-following consensus of discrete-time multiagent systems with time-varying delay based on large delay theory. Information Sciences, 2017, 417, 236- 246. doi: 10.1016/j.ins.2017.07.014
20	SU X J, SHI P, WU L G, et al. Fault detection filtering for nonlinear switched stochastic systems. IEEE Transactions on Automatic Control, 2016, 61(5): 1310- 1315. doi: 10.1109/TAC.2015.2465091
21	PARK P, KO J W, JEONG C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 2011, 47(1): 235- 238. doi: 10.1016/j.automatica.2010.10.014
22	FRAGOSO M D, COSTA O L V. A unified approach for stochastic and mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances. SIAM Journal on Control and Optimization, 2005, 44(4): 1165- 1191. doi: 10.1137/S0363012903434753
23	LI Z K, WEN G H, DUAN Z S, et al. Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs. IEEE Transactions on Automatic Control, 2015, 60(4): 1152- 1157. doi: 10.1109/TAC.2014.2350391
24	OGATA K. Modern control engineering. 5th ed Boston, USA: Prentice Hall, 2010.
25	MAO X. Robustness of exponential stability of stochastic differential delay equations. IEEE Transactions on Automatic Control, 1996, 41(3): 442- 447. doi: 10.1109/9.486647

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