Synchronization in multi-agent systems with switching topologies and non-homogeneous communication delays

We study the synchronization problem for n single state agents with linear continuous time dynamics. The agent states are required to synchronize and travel at a desired common speed. This problem arises naturally in the design of coordinated path-following algorithms problem [9] and in studies on the synchronization of Kuramoto oscillator networks [17]. When the desired speed is zero or there are no time delays, it has been shown in the literature that a so-called neighboring control rule makes the states synchronize asymptotically under some connectivity conditions on the union of the underlying communication graphs. We will show that when both the desired speed and the communication delay are non-zero, the behavior of the synchronization system changes significantly. We start by considering asymmetric networks and switching topologies with homogeneous time delays. We then address some issues related to the behavior of the synchronization system in the presence of heterogeneous time delays. We provide connectivity conditions under which the synchronization problem is solved and introduce synchronization laws that compensates for the effect of non-zero speed and time delays. Simulations illustrate the synchronization of three agents.

[1]  Michael Athans,et al.  Convergence and asymptotic agreement in distributed decision problems , 1982, 1982 21st IEEE Conference on Decision and Control.

[2]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

[3]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[4]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[5]  Didier Theilliol,et al.  Fault-tolerant control in dynamic systems: application to a winding machine , 2000 .

[6]  Mario Innocenti,et al.  Autonomous formation flight , 2000 .

[7]  Xiaoming Hu,et al.  Formation constrained multi-agent control , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[8]  P. Encarnacao,et al.  Combined trajectory tracking and path following: an application to the coordinated control of autonomous marine craft , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[9]  Randal W. Beard,et al.  A coordination architecture for spacecraft formation control , 2001, IEEE Trans. Control. Syst. Technol..

[10]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[11]  Xiaoming Hu,et al.  A control Lyapunov function approach to multiagent coordination , 2002, IEEE Trans. Robotics Autom..

[12]  Roger Skjetne,et al.  Nonlinear formation control of marine craft , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[13]  Antonio M. Pascoal,et al.  Coordinated motion control of marine robots , 2003 .

[14]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[15]  Carlos Silvestre,et al.  Coordinated path following control of multiple wheeled robots , 2004 .

[16]  João Pedro Hespanha,et al.  Uniform stability of switched linear systems: extensions of LaSalle's Invariance Principle , 2004, IEEE Transactions on Automatic Control.

[17]  L. Moreau,et al.  Stability of continuous-time distributed consensus algorithms , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[18]  A. Jadbabaie,et al.  On the stability of the Kuramoto model of coupled nonlinear oscillators , 2005, Proceedings of the 2004 American Control Conference.

[19]  P.J. Antsaklis,et al.  Asynchronous Consensus Protocols: Preliminary Results, Simulations and Open Questions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[20]  J.N. Tsitsiklis,et al.  Convergence in Multiagent Coordination, Consensus, and Flocking , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[21]  A. Jadbabaie,et al.  Synchronization in Oscillator Networks: Switching Topologies and Non-homogeneous Delays , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[22]  Jorge Cortes,et al.  Adaptive and Distributed Coordination Algorithms for Mobile Sensing Networks , 2005 .

[23]  Naomi Ehrich Leonard,et al.  Collective motion and oscillator synchronization , 2005 .

[24]  Francesco Bullo,et al.  Coordination and Geometric Optimization via Distributed Dynamical Systems , 2003, SIAM J. Control. Optim..

[25]  Thor I. Fossen,et al.  Passivity-Based Designs for Synchronized Path Following , 2006, CDC.

[26]  I. Kaminer,et al.  Coordinated path-following control of multiple underactuated autonomous vehicles in the presence of communication failures , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[27]  Mehran Mesbahi,et al.  On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian , 2006, IEEE Transactions on Automatic Control.

[28]  Manfredi Maggiore,et al.  State Agreement for Continuous-Time Coupled Nonlinear Systems , 2007, SIAM J. Control. Optim..