Finite-time rendezvous algorithms for mobile autonomous agents

This paper focuses on finite-time rendezvous problems. Here finite-time rendezvous refers to agreement on states in finite time within certain communication range. Using semistability theory for discontinuous dynamical systems, we develop a framework for designing finite-time semistable rendezvous protocols for multiagent dynamical systems. Specifically, we present distributed switching static and dynamic output feedback controller architectures for multiagent rendezvous.

[1]  Shankar Sastry,et al.  A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators , 1986, 1986 25th IEEE Conference on Decision and Control.

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

[3]  Dimos V. Dimarogonas,et al.  On the Rendezvous Problem for Multiple Nonholonomic Agents , 2007, IEEE Transactions on Automatic Control.

[4]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[5]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[6]  E. Ryan An Integral Invariance Principle for Differential Inclusions with Applications in Adaptive Control , 1998 .

[7]  Wassim M. Haddad,et al.  Thermodynamics, A Dynamical Systems Approach , 2010 .

[8]  W.M. Haddad,et al.  Semistability theory for differential inclusions with applications to consensus problems in dynamical networks with switching topology , 2008, 2008 American Control Conference.

[9]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

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

[11]  Qing Hui,et al.  Nonlinear dynamical systems and control for large-scale, hybrid, and network systems , 2008 .

[12]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[13]  Brian D. O. Anderson,et al.  The Multi-Agent Rendezvous Problem. Part 1: The Synchronous Case , 2007, SIAM J. Control. Optim..

[14]  Sanjay P. Bhat,et al.  Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks , 2008, IEEE Transactions on Automatic Control.

[15]  Xiwei Liu Distributed nonlinear control algorithms for network consensus , 2010 .

[16]  Brian D. O. Anderson,et al.  The Multi-Agent Rendezvous Problem. Part 2: The Asynchronous Case , 2007, SIAM J. Control. Optim..

[17]  M. Areak,et al.  Passivity as a design tool for group coordination , 2006, 2006 American Control Conference.

[18]  Sanjay P. Bhat,et al.  Semistability, Finite-Time Stability, Differential Inclusions, and Discontinuous Dynamical Systems Having a Continuum of Equilibria , 2009, IEEE Transactions on Automatic Control.

[19]  Dennis S. Bernstein,et al.  Arc-length-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria , 2003, Proceedings of the 2003 American Control Conference, 2003..

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

[21]  Shouchuan Hu Differential equations with discontinuous right-hand sides☆ , 1991 .

[22]  J. Cortés Discontinuous dynamical systems , 2008, IEEE Control Systems.

[23]  W. Haddad,et al.  Nonnegative and Compartmental Dynamical Systems , 2010 .

[24]  A. Bacciotti,et al.  Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions , 1999 .