Finite-Time Consensus for Switching Network Topologies with Disturbances

Abstract In this paper we investigate the properties of a decentralized consensus algorithm for a network of continuous-time integrators subject to unknown-but-bounded time-varying disturbances. The proposed consensus algorithm is based on a discontinuous local interaction rule. Under certain restrictions on the switching topology, it is proven that after a finite transient time the agents achieve an approximated consensus condition by attenuating the destabilizing effect of the disturbances. This main result is complemented by an additional result establishing the achievement of consensus under different requirements on the switching communication topology. In particular, we provide a convergence result that encompasses situations in which the time varying graph is always disconnected. Lyapunov analyses are carried out to support the suggested algorithms and results. Simulative tests considering, as case study, the synchronization problem for a network of clocks are illustrated and commented on to validate the developed analysis.

[1]  Andrea Garulli,et al.  Analysis of consensus protocols with bounded measurement errors , 2011, Syst. Control. Lett..

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

[3]  Paolo Frasca,et al.  Continuous-time quantized consensus: Convergence of Krasovskii solutions , 2011, Syst. Control. Lett..

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

[5]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[6]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1987, SIGGRAPH.

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

[8]  Christopher Edwards,et al.  A discontinuous protocol design for finite-time average consensus , 2010, 2010 IEEE International Conference on Control Applications.

[9]  Alessandro Pisano,et al.  Sliding mode control: A survey with applications in math , 2011, Math. Comput. Simul..

[10]  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.

[11]  Long Wang,et al.  Finite-Time Consensus Problems for Networks of Dynamic Agents , 2007, IEEE Transactions on Automatic Control.

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

[13]  Baris Fidan,et al.  Aggregation, Foraging, and Formation Control of Swarms with Non-Holonomic Agents Using Potential Functions and Sliding Mode Techniques ∗† , 2007 .

[14]  CortéSJorge.  Finite-time convergent gradient flows with applications to network consensus , 2006 .

[15]  B. Paden,et al.  Lyapunov stability theory of nonsmooth systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[16]  J. Toner,et al.  Flocks, herds, and schools: A quantitative theory of flocking , 1998, cond-mat/9804180.

[17]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[18]  Zhihong Man,et al.  Robust Finite-Time Consensus Tracking Algorithm for Multirobot Systems , 2009, IEEE/ASME Transactions on Mechatronics.

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

[20]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[21]  Laura Giarré,et al.  Consensus for Networks with Unknown but Bounded Disturbances , 2009, SIAM J. Control. Optim..

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

[23]  Debasish Ghose,et al.  Sliding mode control-based algorithms for consensus in connected swarms , 2011, Int. J. Control.

[24]  Alessandro Giua,et al.  Finite-Time Consensus based Clock Synchronization by Discontinuous Control , 2012, ADHS.

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