A new finite-time cooperative control algorithm for uncertain multi-agent systems

ABSTRACT In this paper, the problem of fixed-time consensus tracking control is investigated for multi-agent networks with input uncertain dynamics under the undirected graph. First, a nonsingular terminal sliding mode manifold is proposed, with which the convergence time is globally bounded irrelevant to initial states. Then, with the aid of the observer method and sliding mode technique, the distributed nonsingular controller is designed for the underlying system to ensure that the consensus tracking errors go into sliding mode manifold and converge to origin within a desired time. Finally, examples are presented to verify the validity of the new control strategy.

[1]  Sergey G. Nersesov,et al.  Finite-time coordination in multiagent systems using sliding mode control approach , 2013, ACC.

[2]  Zongyu Zuo,et al.  A new class of finite-time nonlinear consensus protocols for multi-agent systems , 2014, Int. J. Control.

[3]  Wei Xing Zheng,et al.  Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics , 2013, Autom..

[4]  Dan Zhang,et al.  Containment Control of Linear Multiagent Systems With Aperiodic Sampling and Measurement Size Reduction , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[5]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[6]  Jie Chen,et al.  Distributed Consensus of Second-Order Multi-Agent Systems With Heterogeneous Unknown Inertias and Control Gains Under a Directed Graph , 2016, IEEE Transactions on Automatic Control.

[7]  Pierre Apkarian,et al.  Nonconvex spectral optimization algorithms for reduced‐order H∞ LPV‐LFT controllers , 2017 .

[8]  Hongjing Liang,et al.  Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints , 2018, Appl. Math. Comput..

[9]  Jinzhi Wang,et al.  Observer-based finite-time coordinated tracking for general linear multi-agent systems , 2016, Autom..

[10]  Vadim I. Utkin,et al.  Chattering Problem in Sliding Mode Control Systems , 2006, International Workshop on Variable Structure Systems, 2006. VSS'06..

[11]  Dennis S. Bernstein,et al.  Geometric homogeneity with applications to finite-time stability , 2005, Math. Control. Signals Syst..

[12]  Peng Shi,et al.  Distributed command filtered backstepping consensus tracking control of nonlinear multiple-agent systems in strict-feedback form , 2015, Autom..

[13]  Wang Wei,et al.  DECENTRALIZED OPTIMAL CONTROL FOR THE MEAN FIELD LQG PROBLEM OF MULTI-AGENT SYSTEMS , 2017 .

[14]  ShiPeng,et al.  Distributed command filtered backstepping consensus tracking control of nonlinear multiple-agent systems in strict-feedback form , 2015 .

[15]  Minrui Fei,et al.  Formation stability analysis of unmanned multi-vehicles under interconnection topologies , 2015, Int. J. Control.

[16]  Andrey Polyakov,et al.  Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems , 2012, IEEE Transactions on Automatic Control.

[17]  Jiangping Hu,et al.  Distributed tracking control of leader-follower multi-agent systems under noisy measurement , 2011, Autom..

[18]  Zongyu Zuo,et al.  Nonsingular fixed-time consensus tracking for second-order multi-agent networks , 2015, Autom..

[19]  Changchun Hua,et al.  Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM , 2014 .

[20]  Jay A. Farrell,et al.  Cooperative Control of Multiple Nonholonomic Mobile Agents , 2008, IEEE Transactions on Automatic Control.

[21]  Shen Qikun,et al.  SLIDING MODE FAULT TOLERANT CONTROL WITH PRESCRIBED PERFORMANCE , 2017 .

[22]  Michael Defoort,et al.  Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics , 2015 .

[23]  Xiaoqing Lu,et al.  Finite-Time Distributed Tracking Control for Multi-Agent Systems With a Virtual Leader , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Zongyu Zuo,et al.  Distributed robust finite-time nonlinear consensus protocols for multi-agent systems , 2016, Int. J. Syst. Sci..

[25]  P. Shi,et al.  Observer‐based leader‐following consensus of uncertain nonlinear multi‐agent systems , 2017 .

[26]  Seong Ik Han,et al.  Prescribed consensus and formation error constrained finite-time sliding mode control for multi-agent mobile robot systems , 2018 .

[27]  Andrey Polyakov,et al.  Nonlinear fixed-time control protocol for uniform allocation of agents on a segment , 2012, Doklady Mathematics.

[28]  Long Wang,et al.  Finite-time formation control for multi-agent systems , 2009, Autom..

[29]  Weihua Gui,et al.  Distributed Consensus of Second-Order Multiagent Systems With Nonconvex Velocity and Control Input Constraints , 2018, IEEE Transactions on Automatic Control.

[30]  Guanghui Wen,et al.  Distributed finite-time tracking of multiple non-identical second-order nonlinear systems with settling time estimation , 2016, Autom..

[31]  Peng Shi,et al.  Cooperative Control of Multi-Agent Systems With Unknown State-Dependent Controlling Effects , 2015, IEEE Transactions on Automation Science and Engineering.

[32]  Wen Yang,et al.  Fixed-Time Leader–Follower Output Feedback Consensus for Second-Order Multiagent Systems , 2019, IEEE Transactions on Cybernetics.

[33]  Pavel Shcherbakov,et al.  Nonlinear fixed-time control protocol for uniform allocation of agents on a segment , 2013 .

[34]  Wenwu Yu,et al.  Distributed finite-time containment control for second-order nonlinear multi-agent systems , 2015, Appl. Math. Comput..

[35]  Shouchuan Hu Differential equations with discontinuous right-hand sides☆ , 1991 .