Distributed reliable H∞ consensus control for a class of multi‐agent systems under switching networks: A topology‐based average dwell time approach

SUMMARY This paper investigates the problem of distributed reliable H∞ consensus control for high-order networked agent systems with actuator faults and switching undirected topologies. The Lipschitz nonlinearities, several types of actuator faults, and exogenous disturbances are considered in subsystems. Suppose the communication network of the multi-agent systems may switch among finite connected graphs. By utilizing the relative state information of neighbors, a new distributed adaptive reliable consensus protocol is presented for actuator failure compensations in individual nodes. Note that the Lyapunov function for error systems may not decrease as the communication network is time-varying; as a result, the existing distributed adaptive control technique cannot be applied directly. To overcome this difficulty, the topology-based average dwell time approach is introduced to deal with switching jumps. By applying topology-based average dwell time approach and Lyapunov theory, the distributed controller design condition is given in terms of LMIs. It is shown that the proposed scheme can guarantee that the reliable H∞ consensus problem is solvable in the presence actuator faults and external disturbance. Finally, two numerical examples are given the effectiveness of the proposed theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.

[1]  Guang-Hong Yang,et al.  Reliable $H_{\infty}$ Control of Linear Systems With Adaptive Mechanism , 2010, IEEE Transactions on Automatic Control.

[2]  Zhong-Ping Jiang,et al.  Distributed nonlinear control of mobile autonomous multi-agents , 2014, Autom..

[3]  Guoqiang Hu,et al.  Consensus tracking for higher-order multi-agent systems with switching directed topologies and occasionally missing control inputs , 2013, Syst. Control. Lett..

[4]  Peng Shi,et al.  Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time , 2012, IEEE Transactions on Automatic Control.

[5]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[6]  Huaguang Zhang,et al.  Leader-Based Optimal Coordination Control for the Consensus Problem of Multiagent Differential Games via Fuzzy Adaptive Dynamic Programming , 2015, IEEE Transactions on Fuzzy Systems.

[7]  Huijun Gao,et al.  On Discrete-Time Convergence for General Linear Multi-Agent Systems Under Dynamic Topology , 2014, IEEE Transactions on Automatic Control.

[8]  Huijun Gao,et al.  Coordination for Linear Multiagent Systems With Dynamic Interaction Topology in the Leader-Following Framework , 2014, IEEE Transactions on Industrial Electronics.

[9]  Wenwu Yu,et al.  Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems , 2010, Autom..

[10]  Yongduan Song,et al.  Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems , 2015, Autom..

[11]  Jun Zhang,et al.  Adaptive Fault-Tolerant Tracking Control for Linear and Lipschitz Nonlinear Multi-Agent Systems , 2015, IEEE Transactions on Industrial Electronics.

[12]  Zhong-Ping Jiang,et al.  Distributed Output-Feedback Control of Nonlinear Multi-Agent Systems , 2013, IEEE Transactions on Automatic Control.

[13]  Huaguang Zhang,et al.  Stabilization of Switched Nonlinear Systems With All Unstable Modes: Application to Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[14]  Guanghui Wen,et al.  Consensus and its ℒ2-gain performance of multi-agent systems with intermittent information transmissions , 2012, Int. J. Control.

[15]  Jun Zhao,et al.  Cooperative Adaptive Fuzzy Tracking Control for Networked Unknown Nonlinear Multiagent Systems With Time-Varying Actuator Faults , 2014, IEEE Transactions on Fuzzy Systems.

[16]  Khashayar Khorasani,et al.  $H_{\infty}$ Consensus Achievement of Multi-Agent Systems With Directed and Switching Topology Networks , 2014, IEEE Transactions on Automatic Control.

[17]  Marcel Staroswiecki,et al.  Fault tolerant cooperative control for a class of nonlinear multi-agent systems , 2011, Syst. Control. Lett..

[18]  C. R. Hanke,et al.  The Simulation of a Jumbo Jet Transport Aircraft. Volume 2: Modeling Data , 1970 .

[19]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[20]  Guang-Hong Yang,et al.  Robust adaptive fault-tolerant control for uncertain linear systems with actuator failures , 2012 .

[21]  Guang-Hong Yang,et al.  Adaptive Synchronization of a Class of Uncertain Complex Networks Against Network Deterioration , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Guanghong Yang,et al.  Fault-tolerant control via sliding-mode output feedback for uncertain linear systems with quantisation , 2013 .

[23]  Xidong Tang,et al.  Adaptive actuator failure compensation for nonlinear MIMO systems with an aircraft control application , 2007, Autom..

[24]  Yingmin Jia,et al.  Distributed robust Hinfinity consensus control in directed networks of agents with time-delay , 2008, Syst. Control. Lett..

[25]  Guoqiang Hu,et al.  Distributed ${\cal H}_{\infty}$ Consensus of Higher Order Multiagent Systems With Switching Topologies , 2014, IEEE Transactions on Circuits and Systems II: Express Briefs.

[26]  Guoqiang Hu,et al.  Robust consensus tracking of a class of second-order multi-agent dynamic systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[27]  Lin Huang,et al.  Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Wei Wang,et al.  Adaptive compensation for infinite number of actuator failures or faults , 2011, Autom..

[29]  Lihua Xie,et al.  Global $H_\infty$ Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics , 2012 .

[30]  Jun Zhao,et al.  Robust H∞ control for a class of uncertain nonlinear switched systems with average dwell time , 2013, Int. J. Control.

[31]  Guanghui Wen,et al.  Distributed H ∞ and H 2 consensus control in directed networks , 2014 .

[32]  Yisheng Zhong,et al.  Containment analysis and design for high-order linear time-invariant singular swarm systems with time delays , 2012, Proceedings of the 31st Chinese Control Conference.

[33]  Yongduan Song,et al.  Fault-tolerant output synchronisation control of multi-vehicle systems , 2014 .

[34]  Guang-Hong Yang,et al.  Adaptive logic‐based switching fault‐tolerant controller design for nonlinear uncertain systems , 2011 .

[35]  Daniel W. C. Ho,et al.  Fault-Tolerant Consensus of Multi-Agent System With Distributed Adaptive Protocol , 2015, IEEE Transactions on Cybernetics.

[36]  Marcel Staroswiecki,et al.  Supervisory fault tolerant control for a class of uncertain nonlinear systems , 2009, Autom..

[37]  Guanghong Yang,et al.  Quantized output feedback stabilization of uncertain systems with input nonlinearities via sliding mode control , 2014 .

[38]  Wei Wang,et al.  Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots , 2014, Autom..

[39]  Yisheng Zhong,et al.  Practical consensus for high-order linear time-invariant swarm systems with interaction uncertainties, time-varying delays and external disturbances , 2013, Int. J. Syst. Sci..

[40]  Yisheng Zhong,et al.  Output containment analysis and design for high‐order linear time‐invariant swarm systems , 2015 .

[41]  Jun Zhao,et al.  H∞ Adaptive tracking control for switched systems based on an average dwell-time method , 2015, Int. J. Syst. Sci..

[42]  Guang-Hong Yang,et al.  Adaptive Pinning Control of Deteriorated Nonlinear Coupling Networks With Circuit Realization , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Mengyin Fu,et al.  Consensus of Multi-Agent Systems With General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols , 2011, IEEE Transactions on Automatic Control.

[44]  Aldo A. Ferri,et al.  Application of output feedback to variable structure systems , 1989 .

[45]  Guanghui Wen,et al.  Consensus Tracking of Multi-Agent Systems With Lipschitz-Type Node Dynamics and Switching Topologies , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[46]  Guanghui Wen,et al.  Consensus in multi‐agent systems with communication constraints , 2012 .

[47]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.