Finite-time formation-containment tracking for second-order multi-agent systems with a virtual leader of fully unknown input

Abstract This paper studies the finite-time time-varying formation-containment tracking problems for second-order multi-agent systems with directed topology, where the multi-agent system consists of one virtual leader with fully unknown input, several real leaders and followers. In contrast with traditional formation and containment cases studied in most of the existing literature, apart from accomplishing the expected time-varying formation, the real leaders are required to track the trajectory generated by the virtual leader, and the followers need to get into the convex envelope spanned by the real leaders in finite time. The method for solving the finite-time formation-containment tracking problems is divided into the following steps. First, distributed finite-time observers are designed for each real leader and follower, in order to obtain the estimated states of their neighbor agents. Then, formation-containment tracking protocols are presented by using the neighboring information for both real leaders and followers. Furthermore, based on Lyapunov theory, it is proved that the given formation-containment tracking can be realized in finite time by the multi-agent system under the designed protocols. Finally, a case study on multi-robot transport operation is given to verify the effectiveness of the theoretical results.

[1]  Manfredi Maggiore,et al.  Necessary and sufficient graphical conditions for formation control of unicycles , 2005, IEEE Transactions on Automatic Control.

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

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

[4]  Yu Zhao,et al.  Finite‐time formation tracking control for multiple vehicles: A motion planning approach , 2016 .

[5]  Zhang Ren,et al.  Formation-containment control for second-order multi-agent systems with time-varying delays , 2016, Neurocomputing.

[6]  Zhang Ren,et al.  Formation-containment tracking for high-order linear multi-agent systems on directed graphs , 2017, IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society.

[7]  Yisheng Zhong,et al.  Containment analysis and design for high-order linear time-invariant singular swarm systems with time delays , 2012, Proceedings of the 31st Chinese Control Conference.

[8]  Yongduan Song,et al.  Distributed Adaptive Finite-Time Approach for Formation–Containment Control of Networked Nonlinear Systems Under Directed Topology , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Ziyang Meng,et al.  Distributed Containment Control for Multiple Autonomous Vehicles With Double-Integrator Dynamics: Algorithms and Experiments , 2011, IEEE Transactions on Control Systems Technology.

[10]  Camillo J. Taylor,et al.  A vision-based formation control framework , 2002, IEEE Trans. Robotics Autom..

[11]  Giancarlo Ferrari-Trecate,et al.  Containment Control in Mobile Networks , 2008, IEEE Transactions on Automatic Control.

[12]  Zhang Ren,et al.  Time-varying formation tracking for high-order multi-agent systems with switching topologies and a leader of bounded unknown input , 2018, J. Frankl. Inst..

[13]  Zhang Ren,et al.  Finite-Time Time-Varying Formation Tracking for High-Order Multiagent Systems With Mismatched Disturbances , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[14]  Guanghui Wen,et al.  Distributed finite-time tracking for a multi-agent system under a leader with bounded unknown acceleration , 2015, Syst. Control. Lett..

[15]  Ziyang Meng,et al.  Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking , 2010, Syst. Control. Lett..

[16]  Yisheng Zhong,et al.  Output containment control for swarm systems with general linear dynamics: A dynamic output feedback approach , 2014, Syst. Control. Lett..

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

[18]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[19]  Zengqiang Chen,et al.  Formation control for nonlinear multi-agent systems by robust output regulation , 2014, Neurocomputing.

[20]  Frank L. Lewis,et al.  Time-Varying Output Formation Containment of General Linear Homogeneous and Heterogeneous Multiagent Systems , 2019, IEEE Transactions on Control of Network Systems.

[21]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[22]  Tucker R. Balch,et al.  Behavior-based formation control for multirobot teams , 1998, IEEE Trans. Robotics Autom..

[23]  Guangfu Ma,et al.  Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph , 2012, Autom..

[24]  Guo-Xing Wen,et al.  Adaptive Consensus Control for a Class of Nonlinear Multiagent Time-Delay Systems Using Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Maurizio Porfiri,et al.  Tracking and formation control of multiple autonomous agents: A two-level consensus approach , 2007, Autom..

[26]  Zhang Ren,et al.  Output formation-containment analysis and design for general linear time-invariant multi-agent systems , 2016, J. Frankl. Inst..

[27]  Frank L. Lewis,et al.  Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties , 2013, Autom..

[28]  Tieshan Li,et al.  Containment Control of Multi-Agent Systems With General Noise Based on Hierarchical Topology Reconfiguration , 2019, IEEE Access.

[29]  Zhang Ren,et al.  Formation-containment tracking for general linear multi-agent systems with a tracking-leader of unknown control input , 2018, Syst. Control. Lett..

[30]  Guo-Xing Wen,et al.  Observer-Based Adaptive Backstepping Consensus Tracking Control for High-Order Nonlinear Semi-Strict-Feedback Multiagent Systems , 2016, IEEE Transactions on Cybernetics.

[31]  Zengqiang Chen,et al.  Distributed containment control for bounded unknown second-order nonlinear multi-agent systems with dynamic leaders , 2015, Neurocomputing.

[32]  Shihua Li,et al.  Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics , 2011, Autom..

[33]  Yongduan Song,et al.  Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems , 2015, Autom..

[34]  Qing Zhang,et al.  Containment control of multi-agent systems with fixed time-delays in fixed directed networks , 2016, Neurocomputing.

[35]  Guo-Xing Wen,et al.  Neural-network-based adaptive leader-following consensus control for second-order non-linear multi-agent systems , 2015 .

[36]  Tingwen Huang,et al.  Fully Distributed Formation-Containment Control of Heterogeneous Linear Multiagent Systems , 2019, IEEE Transactions on Automatic Control.