On robust synchronization of heterogeneous linear multi-agent systems with static couplings

This paper addresses cooperative control problems in heterogeneous groups of linear dynamical agents that are coupled by diffusive links. We study networks with parameter uncertainties, resulting in heterogeneous agent dynamics, and we analyze the robustness of their output synchronization. The networks under consideration consist of non-identical double-integrators and harmonic oscillators. The geometric approach to linear control theory reveals structural requirements for non-trivial output synchronization in such networks. Furthermore, a clock synchronization problem and a circular motion coordination problem are discussed as applications corresponding to these two network types. The results are illustrated by numerical simulations.

[1]  Frank L. Lewis,et al.  Lyapunov, Adaptive, and Optimal Design Techniques for Cooperative Systems on Directed Communication Graphs , 2012, IEEE Transactions on Industrial Electronics.

[2]  P. Dorato,et al.  Static output feedback: a survey , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[3]  Ella M. Atkins,et al.  Distributed multi‐vehicle coordinated control via local information exchange , 2007 .

[4]  Ali Saberi,et al.  Output synchronization for heterogeneous networks of non-introspective agents , 2012, Autom..

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

[6]  Frank Allgöwer,et al.  On topology and dynamics of consensus among linear high-order agents , 2011, Int. J. Syst. Sci..

[7]  Leslie Hogben,et al.  Combinatorial Matrix Theory , 2013 .

[8]  Ulf T. Jönsson,et al.  A framework for robust synchronization in heterogeneous multi-agent networks , 2011, IEEE Conference on Decision and Control and European Control Conference.

[9]  Florian Dörfler,et al.  Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators , 2009, Proceedings of the 2010 American Control Conference.

[10]  Wei Ren,et al.  Synchronization of coupled harmonic oscillators with local interaction , 2008, Autom..

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

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

[13]  Karl Henrik Johansson,et al.  Static Diffusive Couplings in Heterogeneous Linear Networks , 2012 .

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

[15]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[16]  Tamer Basar.  An Invariance Principle in the Theory of Stability , 2001 .

[17]  Frank Allgöwer,et al.  A constructive approach to Synchronization using relative information , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[18]  Ruggero Carli,et al.  Optimal Synchronization for Networks of Noisy Double Integrators , 2011, IEEE Transactions on Automatic Control.

[19]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[20]  吉澤 太郎.  An Invariance Principle in the Theory of Stability (常微分方程式及び函数微分方程式研究会報告集) , 1968 .

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

[22]  F. Allgöwer,et al.  An Internal Model Principle for Consensus in Heterogeneous Linear Multi-Agent Systems , 2009 .

[23]  Jan Lunze,et al.  Synchronization of Heterogeneous Agents , 2012, IEEE Transactions on Automatic Control.

[24]  Ruggero Carli,et al.  Robust synchronization of networks of heterogeneous double-integrators , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[25]  Peter Wieland,et al.  From Static to Dynamic Couplings in Consensus and Synchronization among Identical and Non-Identical Systems , 2010 .