Time-Varying Formation Tracking for Linear Multiagent Systems With Multiple Leaders

Time-varying formation tracking problems for linear multiagent systems with multiple leaders are studied, where the states of followers form a predefined time-varying formation while tracking the convex combination of the states of multiple leaders. Followers are classified into well-informed ones and uninformed ones, where the neighbor set of the former contains all the leaders, whereas the latter contains no leaders. A formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for multiagent systems with multiple leaders to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraints are also given. An approach to design the formation tracking protocol is presented by solving an algebraic Riccati equation. The obtained results can be applied to deal with time-varying formation tracking problems, target enclosing problems, and consensus tracking problems for linear multiagent systems with one or multiple targets/leaders. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

[1]  Alessandro Astolfi,et al.  A differential game approach to formation control for a team of agents with one leader , 2015, 2015 American Control Conference (ACC).

[2]  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..

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

[4]  W. Ren.  Consensus strategies for cooperative control of vehicle formations , 2007 .

[5]  Jing Guo,et al.  Local control strategy for moving-target-enclosing under dynamically changing network topology , 2010, Syst. Control. Lett..

[6]  Guanrong Chen,et al.  Distributed Average Tracking for Reference Signals With Bounded Accelerations , 2015, IEEE Transactions on Automatic Control.

[7]  Carlos Canudas-de-Wit,et al.  Cooperative Control Design for Time-Varying Formations of Multi-Agent Systems , 2014, IEEE Transactions on Automatic Control.

[8]  João P. Hespanha,et al.  Trajectory-Tracking and Path-Following of Underactuated Autonomous Vehicles With Parametric Modeling Uncertainty , 2007, IEEE Transactions on Automatic Control.

[9]  Hyo-Sung Ahn,et al.  A survey of multi-agent formation control , 2015, Autom..

[10]  X. Dong,et al.  Formation‐containment analysis and design for high‐order linear time‐invariant swarm systems , 2015 .

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

[12]  Guangming Xie,et al.  Forming Circle Formations of Anonymous Mobile Agents With Order Preservation , 2013, IEEE Transactions on Automatic Control.

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

[14]  Wei Ren,et al.  Distributed coordination architecture for multi-robot formation control , 2008, Robotics Auton. Syst..

[15]  Jinde Cao,et al.  $M$-Matrix Strategies for Pinning-Controlled Leader-Following Consensus in Multiagent Systems With Nonlinear Dynamics , 2013, IEEE Transactions on Cybernetics.

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

[17]  Lihua Xie,et al.  Distributed Tracking Control for Linear Multiagent Systems With a Leader of Bounded Unknown Input , 2013, IEEE Transactions on Automatic Control.

[18]  Jinde Cao,et al.  Leader-following consensus of multi-agent systems via sampled-data control with randomly missing data , 2015, Neurocomputing.

[19]  Yisheng Zhong,et al.  Formation Control for High-Order Linear Time-Invariant Multiagent Systems With Time Delays , 2014, IEEE Transactions on Control of Network Systems.

[20]  Yongcan Cao,et al.  Distributed Coordination of Multi-agent Networks , 2011 .

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

[22]  Wei Xing Zheng,et al.  Adaptive tracking control of leader-follower systems with unknown dynamics and partial measurements , 2014, Autom..

[23]  Xiaoli Wang,et al.  Consensus controllability, observability and robust design for leader-following linear multi-agent systems , 2013, Autom..

[24]  Baocang Ding,et al.  Distributed RHC for Tracking and Formation of Nonholonomic Multi-Vehicle Systems , 2014, IEEE Transactions on Automatic Control.

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

[26]  Lili Wang,et al.  A Graph Laplacian Approach to Coordinate-Free Formation Stabilization for Directed Networks , 2016, IEEE Transactions on Automatic Control.

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

[28]  Dimos V. Dimarogonas,et al.  Controlling the Relative Agent Motion in Multi-Agent Formation Stabilization , 2014, IEEE Transactions on Automatic Control.

[29]  Tao Li,et al.  Multi-Agent Consensus With Relative-State-Dependent Measurement Noises , 2013, IEEE Transactions on Automatic Control.

[30]  Zhong-Ping Jiang,et al.  A Distributed Control Approach to A Robust Output Regulation Problem for Multi-Agent Linear Systems , 2010, IEEE Transactions on Automatic Control.

[31]  Qing-Long Han,et al.  Network-based leader-following consensus for distributed multi-agent systems , 2013, Autom..

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