Distributed Cooperative Anti-Disturbance Control for High-Order MIMO Nonlinear Multi-Agent Systems

doi:10.1007/s12204-023-2673-0

Abstract

Abstract: To solve the synchronization and tracking problems, a cooperative control scheme is proposed for a class of higher-order multi-input and multi-output (MIMO) nonlinear multi-agent systems (MASs) subjected to uncertainties and external disturbances. First, coupled relationships among Laplace matrix, leader-following adjacency matrix and consensus error are analyzed based on undirected graph. Furthermore, nonlinear disturbance observers (NDOs) are designed to estimate compounded disturbances in MASs, and a distributed cooperative antidisturbance control protocol is proposed for high-order MIMO nonlinear MASs based on the outputs of NDOs and dynamic surface control approach. Finally, the feasibility and effectiveness of the proposed scheme are proven based on Lyapunov stability theory and simulation experiments.

Key words: nonlinear disturbance observer (NDO), higher-order multi-input and multi-output (MIMO) system, multi-agent system, cooperative control, disturbance suppression

摘要： 对一类具有不确定性和外部动态干扰的高阶多输入多输出(multi-input and multi-output, MIMO)非线性多智能体系统(multi-agent systems, MASs)，研究了协同控制策略以解决MASs的同步跟踪问题。首先，分析了无向通讯拓扑下Laplace矩阵、领导跟随邻接矩阵和MASs一致性误差之间的耦合关系；其次，设计非线性干扰观测器(nonlinear disturbance observers, NDOs)在线估计MASs中的未知复合扰动，并基于NDO输出和动态面控制为高阶MIMO非线性MASs设计了分布式协同抗干扰控制协议；最后，基于Lyapunov稳定理论和仿真试验证明所设计控制策略的可行性和有效性。

关键词: 非线性干扰观测器，高阶多输入多输出系统，多智能体系统，协同控制，干扰抑制

CLC Number:

TM712
TP273

JIN Feiyu (金飞宇), CHEN Longsheng^∗ (陈龙胜), LI Tongshuai (李统帅), SHI Tongxin (石童昕). Distributed Cooperative Anti-Disturbance Control for High-Order MIMO Nonlinear Multi-Agent Systems[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(4): 656-666.

References

[1] ZHANG X, CHEN M Y, WANG L, et al. Fault-tolerant consensus for a network of multi-agent systems with actuator faults [J]. Journal of Shanghai Jiao Tong University, 2015, 49(6): 806-811 (in Chinese).
[2] OH K K, PARK M C, AHN H S. A survey of multi-agent formation control [J]. Automatica, 2015, 53: 424-440.
[3] THUNBERG J, GONCALVES J, HU X M. Consensus and formation control on SE(3) for switching topologies [J]. Automatica, 2016, 66: 109-121.
[4] DASGUPTA P. A multiagent swarming system for distributed automatic target recognition using unmanned aerial vehicles [J]. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 2008, 38(3): 549-563.
[5] SHI H, WANG L, CHU T G. Swarming behavior of multi-agent systems [J]. Journal of Control Theory and Applications, 2004, 2(4): 313-318.
[6] QIN J H, FU W M, GAO H J, et al. Distributed kmeans algorithm and fuzzy c-means algorithm for sensor networks based on multiagent consensus theory [J]. IEEE Transactions on Cybernetics, 2017, 47(3): 772-783.
[7] LI X G, HU X Y, ZHANG R Q, et al. Routing protocol design for underwater optical wireless sensor networks: A multiagent reinforcement learning approach [J]. IEEE Internet of Things Journal, 2020, 7(10): 9805-9818.
[8] PUTRA S A, TRILAKSONO B R, RIYANSYAH M, et al. Intelligent sensing in multiagent-based wireless sensor network for bridge condition monitoring system [J]. IEEE Internet of Things Journal, 2019, 6(3): 5397-5410.
[9] YEUNG C S K, POON A S Y, WU F F. Game theoretical multi-agent modelling of coalition formation for multilateral trades [J]. IEEE Transactions on Power Systems, 1999, 14(3): 929-934.
[10] LIN Z Y, WANG L L, HAN Z M, et al. Distributed formation control of multi-agent systems using complex Laplacian [J]. IEEE Transactions on Automatic Control, 2014, 59(7): 1765-1777.
[11] QIU X F, ZHANG Y X, LI K Z. Successive lag cluster consensus on multi-agent systems via delay-dependent impulsive control [J]. Chinese Physics B, 2019, 28(5): 050501.
[12] HONG Y G, HU J P, GAO L X. Tracking control for multi-agent consensus with an active leader and variable topology [J]. Automatica, 2006, 42(7): 1177-1182.
[13] LIN P, JIA Y M. Multi-agent consensus with diverse time-delays and jointly-connected topologies [J]. Automatica, 2011, 47(4): 848-856.
[14] REN W, BEARD R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies [J]. IEEE Transactions on Automatic Control, 2005, 50(5): 655-661.
[15] BLONDEL V D, HENDRICKX J M, TSITSIKLIS J N. On Krause’s multi-agent consensus model with state-dependent connectivity [J]. IEEE Transactions on Automatic Control, 2009, 54(11): 2586-2597.
[16] WANG F Y, YANG H Y, LIU Z X, et al. Containment control of leader-following multi-agent systems with jointly-connected topologies and time-varying delays [J]. Neurocomputing, 2017, 260: 341-348.
[17] HONG Y G, CHEN G R, BUSHNELL L. Distributed observers design for leader-following control of multiagent networks [J]. Automatica, 2008, 44(3): 846-850.
[18] LI X W, SUN Z Y, TANG Y, et al. Adaptive eventtriggered consensus of multiagent systems on directed graphs [J]. IEEE Transactions on Automatic Control, 2021, 66(4): 1670-1685.
[19] GARCIA E, CAO Y C, CASBEER D W. Decentralized event-triggered consensus with general linear dynamics [J]. Automatica, 2014, 50(10): 2633-2640.
[20] YU M, YAN C, XIE D M, et al. Event-triggered tracking consensus with packet losses and time-varying delays [J]. IEEE/CAA Journal of Automatica Sinica, 2016, 3(2): 165-173.
[21] BORGERS D P, HEEMELS W P M H. Eventseparation properties of event-triggered control systems [J]. IEEE Transactions on Automatic Control, 2014, 59(10): 2644-2656.
[22] WANG L, XIAO F. Finite-time consensus problems for networks of dynamic agents [J]. IEEE Transactions on Automatic Control, 2010, 55(4): 950-955.
[23] LI S H, DU H B, LIN X Z. Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics [J]. Automatica, 2011, 47(8): 1706-1712.
[24] CAO Y C, REN W. Finite-time consensus for multiagent networks with unknown inherent nonlinear dynamics [J]. Automatica, 2014, 50(10): 2648-2656.
[25] LIU X Y, LAM J, YU W W, et al. Finite-time consensus of multiagent systems with a switching protocol [J]. IEEE Transactions on Neural Networks and Learning Systems, 2016, 27(4): 853-862.
[26] LI C Y, QU Z H. Distributed finite-time consensus of nonlinear systems under switching topologies [J]. Automatica, 2014, 50(6): 1626-1631.
[27] ZOU W C, SHI P, XIANG Z R, et al. Finite-time consensus of second-order switched nonlinear multi-agent systems [J]. IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(5): 1757-1762.
[28] DU H B, WEN G H, WU D, et al. Distributed fixedtime consensus for nonlinear heterogeneous multiagent systems [J]. Automatica, 2020, 113: 108797.
[29] HONG H F, YU W W, WEN G H, et al. Distributed robust fixed-time consensus for nonlinear and disturbed multiagent systems [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, 47(7): 1464-1473.
[30] HAN J, WANG C H, YI G X. Cooperative control of UAV based on multi-agent system [C]//2013 IEEE 8th Conference on Industrial Electronics and Applications. Melbourne: IEEE, 2013: 96-101.
[31] LIU B, ZHANG H T, WU Y, et al. Distributed consensus control of multi-USV systems [M]//International conference on intelligent robotics and applications. Cham: Springer, 2017: 628-635.
[32] GAO C, WANG Z D, HE X, et al. On consensus of second-order multiagent systems with actuator saturations: A generalized-nyquist-criterion-based approach [J]. IEEE Transactions on Cybernetics, 2022, 52(9): 9048-9058.
[33] LIU T Q, LIU M Q, WEN G H, et al. Consensus of linear MIMO multiagent systems: Appointedtime reduced-order observer-based protocols [J]. IEEE Transactions on Cybernetics, 2022, 52(10): 10604-10610.
[34] WU Z M, WU Y F, YUE D. Distributed adaptive neural consensus tracking control of MIMO stochastic nonlinear multiagent systems with actuator failures and unknown dead zones [J]. International Journal of Adaptive Control and Signal Processing, 2018, 32(12): 1694-1714.
[35] AI X L, YU J Q, JIA Z Y, et al. Disturbance observerbased consensus tracking for nonlinear multiagent systems with switching topologies [J]. International Journal of Robust and Nonlinear Control, 2018, 28(6): 2144-2160.
[36] YANG X W, DENG W X, YAO J Y. Disturbanceobserver-based adaptive command filtered control for uncertain nonlinear systems [J]. ISA Transactions, 2022, 130: 490-499.
[37] ZHANG H W, LEWIS F L. Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics [J]. Automatica, 2012, 48(7): 1432-1439.
[38] ZHOU Y L, CHEN M, JIANG C S. Robust tracking control of uncertain MIMO nonlinear systems with application to UAVs [J]. IEEE/CAA Journal of Automatica Sinica, 2015, 2(1): 25-32.
[39] TONG S C, LI Y M. Adaptive fuzzy output feedback control of MIMO nonlinear systems with unknown dead-zone inputs [J]. IEEE Transactions on Fuzzy Systems, 2013, 21(1): 134-146.
[40] MADANI T, BENALLEGUE A. Adaptive control via backstepping technique and neural networks of a quadrotor helicopter [J]. IFAC Proceedings Volumes, 2008, 41(2): 6513-6518.
[41] SWAROOP D, HEDRICK J K, YIP P P, et al. Dynamic surface control for a class of nonlinear systems [J]. IEEE Transactions on Automatic Control, 2000, 45(10): 1893-1899.
[42] YANG X W, DENG W X, YAO J Y. Neural adaptive dynamic surface asymptotic tracking control of hydraulic manipulators with guaranteed transient performance [J]. IEEE Transactions on Neural Networks and Learning Systems, 2022. https://doi.org/10.1109/TNNLS.2022.3141463.
[43] ZHOU Q, CHEN G D, LU R Q, et al. Disturbanceobserver-based event-triggered control for multi-agent systems with input saturation [J]. Scientia Sinica (Informationis), 2019, 49(11): 1502-1516 (in Chinese).
[44] NGUYEN A T, XUAN-MUNG N, HONG S K. Quadcopter adaptive trajectory tracking control: A new approach via backstepping technique [J]. Applied Sciences, 2019, 9(18): 3873.
[45] ZUO Z Y, TIAN B L, DEFOORT M, et al. Fixed-time consensus tracking for multiagent systems with highorder integrator dynamics [J]. IEEE Transactions on Automatic Control, 2018, 63(2): 563-570.
[46] PU M, WU Q X, JIANG C S, et al. Application of adaptive second-order dynamic terminal sliding mode control to near space vehicle [J]. Journal of Aerospace Power, 2010, 25(5): 1169-1176.
[47] CHEN M, JIANG B. Robust attitude control of near space vehicles with time-varying disturbances [J]. International Journal of Control, Automation and Systems, 2013, 11(1): 182-187.
[48] TEE K P, GE S S. Control of fully actuated ocean surface vessels using a class of feedforward approximators [J]. IEEE Transactions on Control Systems Technology, 2006, 14(4): 750-756.
[49] LI T S, ZHANG H Y, YANG X Y. DSC approach to robust adaptive fuzzy tracking control for strict-feedback nonlinear systems [C]//2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery. Jinan: IEEE, 2008: 70-74.