Guaranteed cost consensus for multi‐agent systems with switching topologies

Summary Firstly, guaranteed cost consensus for multi-agent systems is introduced based on state errors among neighboring agents and control inputs of all agents, where a tradeoff between the consensus regulation performance and the control effort is considered. Then, a sufficient condition for guaranteed cost consensus is given by the state-space decomposition approach and the Lyapunov method, where an upper bound of the cost function is determined and an approach is proposed to determine the control gain. It is worth mentioning that the criterions for guaranteed cost consensus are only dependent on the maximum eigenvalue of the Laplacian matrices of switching topologies. Finally, numerical simulations are given to demonstrate theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.

[1]  Jiandong Zhu On consensus speed of multi-agent systems with double-integrator dynamics , 2011 .

[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]  Valery A. Ugrinovskii,et al.  Guaranteed performance leader-follower control for multi-agent systems with linear IQC coupling , 2013, 2013 American Control Conference.

[4]  W. Ren,et al.  Multi‐vehicle coordination for double‐integrator dynamics under fixed undirected/directed interaction in a sampled‐data setting , 2010 .

[5]  Jie Huang,et al.  Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems , 2011, IEEE Transactions on Automatic Control.

[6]  Ravi N. Banavar,et al.  Rendezvous in space with minimal sensing and coarse actuation , 2013, Autom..

[7]  Ian R. Petersen Guaranteed Cost Control of Stochastic Uncertain Systems with Slope Bounded Nonlinearities via the use of Dynamic Multipliers , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[9]  Zhi-Hong Guan,et al.  Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delays , 2004, J. Frankl. Inst..

[10]  Qingling Zhang,et al.  Robust normalization and guaranteed cost control for a class of uncertain descriptor systems , 2012, Autom..

[11]  Paul D. Ezhilchelvan,et al.  Consensus in Sparse, Mobile Ad Hoc Networks , 2012, IEEE Transactions on Parallel and Distributed Systems.

[12]  Ji-Feng Zhang,et al.  Necessary and Sufficient Conditions for Consensusability of Linear Multi-Agent Systems , 2010, IEEE Transactions on Automatic Control.

[13]  D. McFarlane,et al.  Optimal guaranteed cost control and filtering for uncertain linear systems , 1994, IEEE Trans. Autom. Control..

[14]  Yongcan Cao,et al.  Optimal Linear-Consensus Algorithms: An LQR Perspective , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[16]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

[17]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[18]  Mahdi Jalili,et al.  Weighted coupling for geographical networks: Application to reducing consensus time in sensor networks , 2010 .

[19]  Daizhan Cheng,et al.  Consensus of multi-agent linear dynamic systems† , 2008 .

[20]  Yisheng Zhong,et al.  Swarm stability for high-order linear time-invariant singular multi-agent systems , 2015, Int. J. Syst. Sci..

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

[22]  Huajing Fang,et al.  Improvement for Consensus Performance of Multi-Agent Systems Based on Weighted Average Prediction , 2012, IEEE Transactions on Automatic Control.

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

[24]  Xiao Fan Wang,et al.  Flocking of Multi-Agents With a Virtual Leader , 2009, IEEE Trans. Autom. Control..

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

[26]  Guanghui Wen,et al.  Guaranteed cost tracking for uncertain coupled multi-agent systems using consensus over a directed graph , 2013, 2013 Australian Control Conference.

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

[28]  C. Wu Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling , 2003 .

[29]  Yisheng Zhong,et al.  Stable‐protocol output consensualization for high‐order swarm systems with switching topologies , 2013 .

[30]  Yisheng Zhong,et al.  Output consensus analysis and design for high-order linear swarm systems: Partial stability method , 2012, Autom..

[31]  Peng Lin,et al.  Average consensus in networks of multi-agents with both switching topology and coupling time-delay , 2008 .

[32]  Frank Allgöwer,et al.  Consensus in Multi-Agent Systems With Coupling Delays and Switching Topology , 2011, IEEE Transactions on Automatic Control.

[33]  Yang Liu,et al.  Consensus problem of high‐order multi‐agent systems with external disturbances: An H∞ analysis approach , 2010 .

[34]  Tao Li,et al.  Consensus Conditions of Multi-Agent Systems With Time-Varying Topologies and Stochastic Communication Noises , 2010, IEEE Transactions on Automatic Control.

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