Abstract
Convergence is often the key liveness property for distributed systems that interact with physical processes. Techniques for proving convergence (asymptotic stability) have been extensively studied by control theorists. In particular, for the asynchronous model of computation Tsitsiklis [8] provides a set of necessary and sufficient conditions for proving stability and convergence under the assumption that each asynchronous operator (state transition function) is applied infinitely often. This paper generalize these results to obtain necessary and sufficient conditions for systems where the infinite sequence of operators is a member of an arbitrary omega regular language. This enables us to apply our theory to distributed systems with changing communication topology, node failures and joins. We illustrate an application of the new set of conditions in verifying the convergence of a simple (continuous) consensus protocol.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blondel, V.D., Hendrickx, J.M., Olshevsky, A., Tsitsiklis, J.N.: Convergence in multiagent coordination consensus and flocking. In: Proceedings of the Joint forty-fourth IEEE Conference on Decision and Control and European Control Conference, pp. 2996–3000 (2005)
Borkar, V., Varaiya, P.: Asymptotic Agreement in Distributed Estimation. IEEE Trans. on Automatic Control 27(3), 650–655 (1982)
Chandy, K.M., Mitra, S., Pilotto, C.: Convergence verification: From shared memory to partially synchronous systems. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 218–232. Springer, Heidelberg (2008)
Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control 48(6), 988–1001 (2003)
Mitra, S., Chandy, K.M.: A formalized theory for verifying stability and convergence of automata in PVS. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 230–245. Springer, Heidelberg (2008)
Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Transactions on Automatic Control 51(3), 401–420 (2006)
Olfati-saber, R., Alex Fax, J., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 2007 (2007)
Tsitsiklis, J.N.: On the stability of asynchronous iterative processes. Mathematical Systems Theory 20(2-3), 137–153 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Prabhakar, P., Mitra, S., Viswanathan, M. (2009). On Convergence of Concurrent Systems under Regular Interactions. In: Bravetti, M., Zavattaro, G. (eds) CONCUR 2009 - Concurrency Theory. CONCUR 2009. Lecture Notes in Computer Science, vol 5710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04081-8_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-04081-8_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04080-1
Online ISBN: 978-3-642-04081-8
eBook Packages: Computer ScienceComputer Science (R0)