Second-order Consensus Algorithm with Extensions to Switching Topologies and Reference Models

In this paper, we extend the consensus algorithm for double integrator dynamics to the case that the information exchange topologies switch randomly with time and to the case that the final consensus value evolves according to a given nonlinear reference model. We show sufficient conditions under which consensus is reached under switching directed information exchange topologies. Unlike the consensus algorithm for single integrator dynamics, more stringent conditions are required to guarantee consensus under switching directed topologies in the case of the consensus algorithm for double integrator dynamics. In addition, we propose consensus algorithms so that the information variables of each vehicle approach the solution of a nonlinear reference model when only a portion of the vehicles in the team have access to the model.

[1]  P.J. Antsaklis,et al.  Information consensus of asynchronous discrete-time multi-agent systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[2]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[3]  Mehran Mesbahi,et al.  Agreement over random networks , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[4]  P. Wang,et al.  Coordination and control of multiple microspacecraft moving in formation , 1996 .

[5]  Randal W. Beard,et al.  Synchronized multiple spacecraft rotations , 2002, Autom..

[6]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[7]  Timothy W. McLain,et al.  Coordination Variables and Consensus Building in Multiple Vehicle Systems , 2004 .

[8]  Kevin L. Moore,et al.  High-Order and Model Reference Consensus Algorithms in Cooperative Control of MultiVehicle Systems , 2007 .

[9]  Ella M. Atkins,et al.  Second-order Consensus Protocols in Multiple Vehicle Systems with Local Interactions , 2005 .

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

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

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

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

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

[15]  Mireille E. Broucke,et al.  Local control strategies for groups of mobile autonomous agents , 2004, IEEE Transactions on Automatic Control.

[16]  Pierre-Alexandre Bliman,et al.  Average consensus problems in networks of agents with delayed communications , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[18]  Richard M. Murray,et al.  Flocking with obstacle avoidance: cooperation with limited communication in mobile networks , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[19]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[20]  Randal W. Beard,et al.  A decentralized approach to formation maneuvers , 2003, IEEE Trans. Robotics Autom..

[21]  A. Morse.  Supervisory control of families of linear set-point controllers Part I. Exact matching , 1996, IEEE Trans. Autom. Control..

[22]  R. Pesenti,et al.  Distributed Consensus in Networks of Dynamic Agents , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[23]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[24]  Randal W. Beard,et al.  A decentralized scheme for spacecraft formation flying via the virtual structure approach , 2003, Proceedings of the 2003 American Control Conference, 2003..

[25]  George J. Pappas,et al.  Stable flocking of mobile agents part I: dynamic topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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