Time-varying formation tracking for high-order multi-agent systems with switching topologies and a leader of bounded unknown input

Abstract Time-varying formation tracking problems for high-order multi-agent systems with switching topologies are investigated. Different from the previous work, the states of the followers form a predefined time-varying formation while tracking the state of the leader with bounded unknown control input. Besides, the communication topology can be switching, and the dynamics of each agent can have nonlinearities. Firstly, a nonlinear time-varying formation tracking control protocol is presented which is constructed using only local neighboring information. Secondly, an algorithm with four steps is proposed to design the time-varying formation tracking protocol, where the time-varying formation tracking feasibility condition is introduced. Thirdly, by using the Lyapunov theory, the stability of the proposed algorithm is proven. It is proved that the high-order multi-agent system with switching topologies achieves the time-varying formation tracking if the feasibility condition holds and the dwell time is larger than a positive constant. Finally, a numerical example with six followers and one leader is given to demonstrate the effectiveness of the obtained results.

[1]  Zhisheng Duan,et al.  Distributed consensus protocol design for general linear multi-agent systems: a consensus region approach , 2014 .

[2]  Wei Ren,et al.  Consensus based formation control strategies for multi-vehicle systems , 2006, 2006 American Control Conference.

[3]  Junping Du,et al.  Robust Consensus Tracking Control for Multiagent Systems With Initial State Shifts, Disturbances, and Switching Topologies , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Hong Xia,et al.  Leader-following formation control for second-order multi-agent systems with time-varying delays , 2014 .

[5]  Steven Lake Waslander,et al.  Path Following Using Dynamic Transverse Feedback Linearization for Car-Like Robots , 2015, IEEE Transactions on Robotics.

[6]  Zhang Ren,et al.  Necessary and sufficient conditions for average formation tracking of second-order multi-agent systems with multiple leaders , 2017, J. Frankl. Inst..

[7]  Wei Wang,et al.  Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances , 2017, Autom..

[8]  Zhihua Qu,et al.  Cooperative Control of Dynamical Systems With Application to Autonomous Vehicles , 2008, IEEE Transactions on Automatic Control.

[9]  Huaguang Zhang,et al.  Event-based H∞ consensus control for second-order leader-following multi-agent systems , 2016, J. Frankl. Inst..

[10]  Zhang Ren,et al.  Formation-containment control for high-order linear time-invariant multi-agent systems , 2014, Proceedings of the 33rd Chinese Control Conference.

[11]  Debasish Ghose,et al.  Collective circular motion in synchronized and balanced formations with second-order rotational dynamics , 2018, Commun. Nonlinear Sci. Numer. Simul..

[12]  Zhisheng Duan,et al.  Distributed Robust Consensus of a Class of Lipschitz Nonlinear Multi‐agent Systems with Matching Uncertainties , 2015 .

[13]  Gang Wang,et al.  Distributed adaptive consensus tracking control of higher-order nonlinear strict-feedback multi-agent systems using neural networks , 2016, Neurocomputing.

[14]  Yan Lin,et al.  Distributed adaptive control for time-varying formation tracking of a class of networked nonlinear systems , 2017, Int. J. Control.

[15]  Wenjie Dong,et al.  Robust Formation Control of Multiple Wheeled Mobile Robots , 2011, J. Intell. Robotic Syst..

[16]  Yunhui Liu,et al.  Enclosing a target by nonholonomic mobile robots with bearing-only measurements , 2015, Autom..

[17]  Guoqiang Hu,et al.  Time-Varying Formation Tracking for Linear Multiagent Systems With Multiple Leaders , 2017, IEEE Transactions on Automatic Control.

[18]  Debasish Ghose,et al.  Stabilization of collective formations with speed and controller gain heterogeneity and saturation , 2017, J. Frankl. Inst..

[19]  Guanghui Wen,et al.  Neuro-Adaptive Consensus Tracking of Multiagent Systems With a High-Dimensional Leader , 2017, IEEE Transactions on Cybernetics.

[20]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[21]  Sung Jin Yoo,et al.  Distributed formation tracking of networked mobile robots under unknown slippage effects , 2015, Autom..

[22]  Z. Qu,et al.  Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles , 2009 .

[23]  X. Dong,et al.  Formation-containment control for high-order linear time-invariant multi-agent systems , 2014, CCC 2014.

[24]  Guoqiang Hu,et al.  Time-varying formation control for general linear multi-agent systems with switching directed topologies , 2016, Autom..

[25]  Ahmed Rahmani,et al.  Consensus tracking for second-order nonlinear multi-agent systems with switching topologies and a time-varying reference state , 2016, Int. J. Control.

[26]  Xiwang Dong,et al.  Formation and containment control for high-order linear swarm systems , 2015 .

[28]  Yuezu Lv,et al.  Distributed adaptive consensus protocols for multiple Lur'e systems over directed graphs , 2016 .

[29]  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..

[30]  Zhang Ren,et al.  Distributed Time-Varying Formation Tracking Analysis and Design for Second-Order Multi-Agent Systems , 2017, J. Intell. Robotic Syst..

[31]  Chao Yang,et al.  Time-varying formation tracking of multiple manipulators via distributed finite-time control , 2016, Neurocomputing.

[32]  Meng Liu,et al.  Formation tracking of the second-order multi-agent systems using position-only information via impulsive control with input delays , 2014, Appl. Math. Comput..

[33]  Frank L. Lewis,et al.  Synchronization of nonlinear heterogeneous cooperative systems using input-output feedback linearization , 2014, Autom..

[34]  Zhang Ren,et al.  Distributed adaptive time-varying formation for multi-agent systems with general high-order linear time-invariant dynamics , 2016, J. Frankl. Inst..

[35]  Yisheng Zhong,et al.  Time-Varying Formation Control for Unmanned Aerial Vehicles: Theories and Applications , 2015, IEEE Transactions on Control Systems Technology.

[36]  Yangquan Chen,et al.  Multiple UAV Formations for Cooperative Source Seeking and Contour Mapping of a Radiative Signal Field , 2014, J. Intell. Robotic Syst..

[37]  Zhaoxia Peng,et al.  Distributed consensus-based formation control for nonholonomic wheeled mobile robots using adaptive neural network , 2016 .

[38]  Didier Dumur,et al.  A new control strategy for induction motor based on non-linear predictive control and feedback linearization , 2000 .

[39]  Gang Wang,et al.  Distributed adaptive output consensus tracking of higher-order systems with unknown control directions , 2016, Neurocomputing.

[40]  Guanghui Wen,et al.  Containment of Higher-Order Multi-Leader Multi-Agent Systems: A Dynamic Output Approach , 2016, IEEE Transactions on Automatic Control.

[41]  Xiaoyu Liu,et al.  Consensus for networked multi-agent systems with unknown communication delays , 2016, J. Frankl. Inst..

[42]  Mohammad Bagher Menhaj,et al.  Communication free leader-follower formation control of unmanned aircraft systems , 2016, Robotics Auton. Syst..

[43]  Yu-Ping Tian,et al.  Formation control of multi-agent systems with heterogeneous communication delays , 2009, Int. J. Syst. Sci..

[44]  Jie Huang,et al.  Distributed backstepping-based adaptive fuzzy control of multiple high-order nonlinear dynamics , 2015 .

[45]  Zhang Ren,et al.  Time-Varying Formation Tracking for Second-Order Multi-Agent Systems Subjected to Switching Topologies With Application to Quadrotor Formation Flying , 2017, IEEE Transactions on Industrial Electronics.

[46]  Norman Biggs.  Algebraic Graph Theory: The tree-number , 1974 .

[47]  Guangfu Ma,et al.  Distributed coordination for second-order multi-agent systems with nonlinear dynamics using only relative position measurements , 2013, Autom..

[48]  Han Ho Choi,et al.  Feedback Linearization Direct Torque Control With Reduced Torque and Flux Ripples for IPMSM Drives , 2016, IEEE Transactions on Power Electronics.

[49]  Zengqiang Chen,et al.  Leader-following formation control for second-order multiagent systems with time-varying delay and nonlinear dynamics , 2013 .

[50]  Alireza Doosthoseini,et al.  Coordinated path following for unicycles: A nested invariant sets approach , 2015, Autom..