On the internal model principle in formation control and in output synchronization of nonlinear systems

The role of internal model principle is investigated in this paper in the context of collective synchronization and formation control problems. In the collective synchronization problem for nonlinear systems, we propose distributed control laws for passive systems which synchronize to the solution of an incrementally passive exosystem. This generalizes the result from linear systems where the existence of an internal model is required for the output synchronization of networked systems. In our second result, a distributed control law that solves a formation control problem for incrementally passive systems is proposed based also on the internal model principle.

[1]  Frank Allgöwer,et al.  An internal model principle is necessary and sufficient for linear output synchronization , 2011, Autom..

[2]  Murat Arcak,et al.  Passivity as a Design Tool for Group Coordination , 2007, IEEE Transactions on Automatic Control.

[3]  Pogromskiy.  Cooperative oscillatory behavior of mutually coupled dynamical systems , 2005 .

[4]  John T. Wen,et al.  Cooperative Control Design - A Systematic, Passivity-Based Approach , 2011, Communications and control engineering.

[5]  Lorenzo Marconi,et al.  Incremental passivity and output regulation , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[6]  M.W. Spong,et al.  Output Synchronization of Nonlinear Systems with Time Delay in Communication , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[7]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[8]  A. Y. Pogromski,et al.  Passivity based design of synchronizing systems , 1998 .

[9]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2009, Autom..

[10]  John T. Wen,et al.  Passivity As a Design Tool for Cooperative Control , 2011 .

[11]  Nathan van de Wouw,et al.  Controlled synchronization via nonlinear integral coupling , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[12]  G.-B. Stan,et al.  Output synchronization in networks of cyclic biochemical oscillators , 2007, 2007 American Control Conference.

[13]  Romeo Ortega,et al.  Synchronization of Networks of Nonidentical Euler-Lagrange Systems With Uncertain Parameters and Communication Delays , 2011, IEEE Transactions on Automatic Control.

[14]  Rodolphe Sepulchre,et al.  Analysis of Interconnected Oscillators by Dissipativity Theory , 2007, IEEE Transactions on Automatic Control.

[15]  Rodolphe Sepulchre,et al.  Global State Synchronization in Networks of Cyclic Feedback Systems , 2012, IEEE Transactions on Automatic Control.

[16]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[17]  Henk Nijmeijer,et al.  Synchronization in Networks of Diffusively Time-Delay Coupled (Semi-)Passive Systems , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.