Formation-containment control for second-order multi-agent systems with time-varying delays

Abstract In this paper, formation-containment control problems for multi-agent systems with second-order dynamics and time-varying delays are studied. The states of leaders are designed to achieve the time-varying formation and the states of followers are required to converge to the convex hull spanned by those of leaders simultaneously, which differs from conventional formation control or containment control problems. Using the neighboring positions and velocities, formation-containment protocols with time-varying delays are constructed. By exploiting the space decomposition approach, formation-containment problems are transformed into the asymptotically stable problems. Sufficient conditions for second-order multi-agent systems with time-varying delays to realize formation-containment are presented. A method to obtain the unknown gain matrices in the protocols is proposed. Numerical simulations are shown to illustrate the effectiveness of the theoretical results.

[1]  Lihua Xie,et al.  Containment control of multi‐agent systems by exploiting the control inputs of neighbors , 2014 .

[2]  Wei Ren,et al.  Consensus strategies for cooperative control of vehicle formations , 2007 .

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

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

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

[6]  Javad Askari,et al.  Distributed containment output-feedback control for a general class of stochastic nonlinear multi-agent systems , 2016, Neurocomputing.

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

[8]  Yong He,et al.  Delay-dependent stabilization of linear systems with time-varying state and input delays , 2005, Autom..

[9]  Magnus Egerstedt,et al.  Laplacian Sheep: A Hybrid, Stop-Go Policy for Leader-Based Containment Control , 2006, HSCC.

[10]  Huijun Gao,et al.  Coordination for Linear Multiagent Systems With Dynamic Interaction Topology in the Leader-Following Framework , 2014, IEEE Transactions on Industrial Electronics.

[11]  Guoliang Chen,et al.  Some generalized inverses of partition matrix and quotient identity of generalized Schur complement , 2008, Appl. Math. Comput..

[12]  Changbin Yu,et al.  Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition , 2013, Autom..

[13]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[14]  Lihua Xie,et al.  Containment control of leader-following multi-agent systems with Markovian switching network topologies and measurement noises , 2015, Autom..

[15]  Sarangapani Jagannathan,et al.  Hybrid consensus-based formation control of agents with second order dynamics , 2015, 2015 American Control Conference (ACC).

[16]  Dimos V. Dimarogonas,et al.  A Leader-based Containment Control Strategy for Multiple Unicycles , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[18]  Junmin Li,et al.  Adaptive iterative learning control for coordination of second‐order multi‐agent systems , 2014 .

[19]  Junwei Lu,et al.  Distributed reference model based containment control of second-order multi-agent systems , 2015, Neurocomputing.

[20]  Guangming Xie,et al.  Moving formation convergence of a group of mobile robots via decentralised information feedback , 2009, Int. J. Syst. Sci..

[21]  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.

[22]  Asuman E. Ozdaglar,et al.  Constrained Consensus and Optimization in Multi-Agent Networks , 2008, IEEE Transactions on Automatic Control.

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

[24]  Ziyang Meng,et al.  Distributed finite-time attitude containment control for multiple rigid bodies , 2010, Autom..

[25]  Ping Wang,et al.  Robust H∞ containment control for second-order multi-agent systems with nonlinear dynamics in directed networks , 2015, Neurocomputing.

[26]  Tan Min,et al.  Containment control with multiple interacting leaders under switching topologies , 2013, Proceedings of the 32nd Chinese Control Conference.

[27]  Guangming Xie,et al.  Necessary and sufficient conditions for containment control of networked multi-agent systems , 2012, Autom..

[28]  Vijay Kumar,et al.  Decentralized formation control with variable shapes for aerial robots , 2012, 2012 IEEE International Conference on Robotics and Automation.

[29]  Abdelkader Abdessameud,et al.  Formation control of VTOL Unmanned Aerial Vehicles with communication delays , 2011, Autom..

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

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

[32]  Youmin Zhang,et al.  Tracking control of spacecraft formation flying with collision avoidance , 2015 .

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

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

[35]  Antonios Tsourdos,et al.  Consensus-based reconfigurable controller design for unmanned aerial vehicle formation flight , 2012 .

[36]  Wei Xing Zheng,et al.  Exponential Synchronization of Complex Networks of Linear Systems and Nonlinear Oscillators: A Unified Analysis , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[37]  P. K. A. Menon,et al.  Short-Range Nonlinear Feedback Strategies for Aircraft Pursuit-Evasion , 1989 .

[38]  Guangming Xie,et al.  Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays , 2008, Syst. Control. Lett..

[39]  Shihua Chen,et al.  Formation control for second-order multi-agent systems with time-varying delays under directed topology , 2012 .

[40]  Yang Wang,et al.  Multi-agent system design and evaluation for collaborative wireless sensor network in large structure health monitoring , 2010, Expert Syst. Appl..