Robust consensus tracking of multi-agent systems with uncertain lur'e-type non-linear dynamics

This study addresses the robust consensus tracking problem of multi-agent systems with uncertain Lur'e-type non-linear dynamics under a fixed topology. To achieve consensus tracking, a class of discontinuous control protocols are first proposed, which rely on the relative information among the neighbouring agents. Theoretical analysis indicates that the robust consensus tracking of uncertain Lur'e network can be achieved if the coupling strength and the control gain are both larger than the thresholds depending on some global information of the network. Then, an adaptive consensus tracking protocol is further designed to solve the robust consensus tracking problem as a modification of a fully distributed version without the need of any global information of the multi-agent systems. Furthermore, as an expansion of the discontinuous protocols, a new class of continuous control laws are developed based on the boundary layer concept. Finally, a couple of examples are given to illustrate the effectiveness of the theoretical results.

[1]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[2]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[3]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[4]  Yury Stepanenko,et al.  A Sliding Mode Controller with Improved Adaptation Laws for the Upper Bounds on the Norm of Uncertainties , 1998, Autom..

[5]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

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

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

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

[9]  Kevin L. Moore,et al.  High-Order and Model Reference Consensus Algorithms in Cooperative Control of MultiVehicle Systems , 2007 .

[10]  Wei Ren,et al.  Consensus Tracking Under Directed Interaction Topologies: Algorithms and Experiments , 2008, IEEE Transactions on Control Systems Technology.

[11]  Yiguang Hong,et al.  Distributed Observers Design for Leader-Following Control of Multi-Agent Networks (Extended Version) , 2017, 1801.00258.

[12]  Sezai Emre Tuna,et al.  Synchronizing linear systems via partial-state coupling , 2008, Autom..

[13]  Lin Huang,et al.  Synchronization of weighted networks and complex synchronized regions , 2008 .

[14]  Wei Ren.  On Consensus Algorithms for Double-Integrator Dynamics , 2008, IEEE Trans. Autom. Control..

[15]  Guanrong Chen,et al.  Global Robust Stability and Synchronization of Networks With Lorenz-Type Nodes , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Wei Ren,et al.  Distributed leaderless consensus algorithms for networked Euler–Lagrange systems , 2009, Int. J. Control.

[17]  Yongcan Cao,et al.  Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication , 2009, Autom..

[18]  Yingmin Jia,et al.  Robust h ∞ consensus analysis of a class of second-order multi-agent systems with uncertainty , 2010 .

[19]  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.

[20]  Frank L. Lewis,et al.  Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback , 2011, IEEE Transactions on Automatic Control.

[21]  Frank Allgöwer,et al.  An internal model principle is necessary and sufficient for linear output synchronization , 2011, Autom..

[22]  Guangfu Ma,et al.  Distributed Coordinated Tracking With a Dynamic Leader for Multiple Euler-Lagrange Systems , 2011, IEEE Transactions on Automatic Control.

[23]  Wenwu Yu,et al.  Distributed Higher Order Consensus Protocols in Multiagent Dynamical Systems , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Guanrong Chen,et al.  Global synchronised regions of linearly coupled Lur'e systems , 2011, Int. J. Control.

[25]  Frank L. Lewis,et al.  Distributed Adaptive Tracking Control for Synchronization of Unknown Networked Lagrangian Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[26]  Zhisheng Duan,et al.  Cluster synchronisation of Lur'e dynamical networks , 2012 .

[27]  Guanghui Wen,et al.  Distributed H ∞ consensus of multi-agent systems: a performance region-based approach , 2012, Int. J. Control.

[28]  Xiaohua Xia,et al.  Adaptive consensus of multi-agents in networks with jointly connected topologies , 2012, Autom..

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

[30]  Junping Du,et al.  Tracking control over a finite interval for multi-agent systems with a time-varying reference trajectory , 2012, Syst. Control. Lett..

[31]  Yongcan Cao,et al.  Distributed Coordinated Tracking With Reduced Interaction via a Variable Structure Approach , 2012, IEEE Transactions on Automatic Control.

[32]  Fei Hao,et al.  Event-triggered average consensus control for discrete-time multi-agent systems , 2012 .

[33]  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).

[34]  Wei Ren,et al.  Distributed consensus of linear multi-agent systems with adaptive dynamic protocols , 2011, Autom..

[35]  Tao Li,et al.  Consensus of multi-agent systems with general linear dynamics via dynamic output feedback control , 2013 .