Guaranteed cost consensus for high-dimensional multi-agent systems with time-varying delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with timevarying delays are investigated. The idea of guaranteed cost control is introduced into consensus problems for high-dimensional multi-agent systems with time-varying delays, where a cost function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality U+0028 LMI U+0029, sufficient conditions for guaranteed cost consensus and consensualization are given. Moreover, a guaranteed cost upper bound of the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independent of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.

[1]  Valery A. Ugrinovskii,et al.  Leader–follower tracking control with guaranteed consensus performance for interconnected systems with linear dynamic uncertain coupling , 2015, Int. J. Control.

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

[3]  Yongduan Song,et al.  Consensus stability of a class of second-order multi-agent systems with nonuniform time-delays , 2014, J. Frankl. Inst..

[4]  Daniel Liberzon,et al.  Rendezvous Without Coordinates , 2012, IEEE Trans. Autom. Control..

[5]  Songlin Hu,et al.  Event-triggered guaranteed cost control for uncertain discrete-time networked control systems with time-varying transmission delays , 2012 .

[6]  T. K. C. Peng,et al.  Adaptive Guaranteed Cost of Control of Systems with Uncertain Parameters , 1970 .

[7]  Donghua Zhao,et al.  Flocking of multi-agent systems with multiplicative and independent measurement noises , 2015 .

[8]  Jianxiang Xi,et al.  Guaranteed cost consensus for multi‐agent systems with switching topologies , 2015 .

[9]  Zengqiang Chen,et al.  Impulsive observer-based consensus control for multi-agent systems with time delay , 2015, Int. J. Control.

[10]  Wei Xing Zheng,et al.  Second-order consensus for multi-agent systems with switching topology and communication delay , 2011, Syst. Control. Lett..

[11]  Ali Saberi,et al.  Consensus in the network with uniform constant communication delay , 2013, Autom..

[12]  Pingfang Zhou,et al.  Robust guaranteed cost control for singular Markovian jump systems with time-varying delay. , 2012, ISA transactions.

[13]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[14]  Jiming Chen,et al.  Study of consensus-based time synchronization in wireless sensor networks. , 2014, ISA transactions.

[15]  Qingjie Zhang,et al.  Average consensus seeking of high-order continuous-time multi-agent systems with multiple time-varying communication delays , 2011 .

[16]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[17]  Haibin Yu,et al.  MAS based distributed automatic generation control for cyber-physical microgrid system , 2016, IEEE/CAA Journal of Automatica Sinica.

[18]  Zhi-Hong Guan,et al.  Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control , 2014, Autom..

[19]  Yong He,et al.  Delay-dependent stabilization of linear systems with time-varying state and input delays , 2005, Autom..

[20]  J. Xi,et al.  Guaranteed Cost Consensus for Multi‐Agent Systems with Fixed Topologies , 2015 .

[21]  Xiaojun Zhou,et al.  Event based guaranteed cost consensus for distributed multi-agent systems , 2015, J. Frankl. Inst..

[22]  Xinzhi Liu,et al.  Distributed stochastic consensus of multi-agent systems with noisy and delayed measurements , 2013 .

[23]  Wenwu Yu,et al.  An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination , 2012, IEEE Transactions on Industrial Informatics.

[24]  Zhongkui Li,et al.  High-order multi-agent consensus with dynamically changing topologies and time-delays , 2011 .

[25]  Tianping Chen,et al.  Consensus of Multi-Agent Systems With Unbounded Time-Varying Delays , 2010, IEEE Transactions on Automatic Control.

[26]  Hyo-Sung Ahn,et al.  Formation Control of Mobile Agents Based on Distributed Position Estimation , 2013, IEEE Transactions on Automatic Control.

[27]  Rifat Sipahi,et al.  Delay-dependent coupling for a multi-agent LTI consensus system with inter-agent delays , 2014 .

[28]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[29]  Deliang Zeng,et al.  Consensus analysis of continuous‐time second‐order multi‐agent systems with nonuniform time‐delays and switching topologies , 2013 .

[30]  Y. Jia,et al.  Brief Paper - L 2 -L ∞ consensus control for high-order multi-agent systems with switching topologies and time-varying delays , 2012 .

[31]  Yisheng Zhong,et al.  Consensus problems for high-order linear time-invariant swarm systems , 2010 .

[32]  Bin Zhou,et al.  Consensus of high-order multi-agent systems with large input and communication delays , 2014, at - Automatisierungstechnik.

[33]  Zhenhua Wang,et al.  Consensusability of multi-agent systems with time-varying communication delay , 2014, Syst. Control. Lett..