Randomized optimal consensus of multi-agent systems
2012 (English)In: Automatica, ISSN 0005-1098, Vol. 48, no 12, 3018-3030 p.Article in journal (Refereed) Published
In this paper, we formulate and solve a randomized optimal consensus problem for multi-agent systems with stochastically time-varying interconnection topology. The considered multi-agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min(z is an element of Rd) Sigma(n)(i=1) f(i)(z), in which the optimal solution set of objective function f(i) can only be observed by agent i itself. At each time step, simply determined by a Bernoulli trial, each agent independently and randomly chooses either taking an average among its neighbor set, or projecting onto the optimal solution set of its own optimization component. Both directed and bidirectional communication graphs are studied. Connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions. The convergence analysis is carried out using convex analysis. We compare the randomized algorithm with the deterministic one via a numerical example. The results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade-off between following its neighbors or sticking to its own opinion at each time step.
Place, publisher, year, edition, pages
2012. Vol. 48, no 12, 3018-3030 p.
Multi-agent systems, Optimal consensus, Set convergence, Distributed optimization, Randomized algorithms
IdentifiersURN: urn:nbn:se:kth:diva-85510DOI: 10.1016/j.automatica.2012.08.018ISI: 000312286800003OAI: oai:DiVA.org:kth-85510DiVA: diva2:499944
FunderKnut and Alice Wallenberg FoundationSwedish Research CouncilICT - The Next Generation
QC 201301102012-02-132012-02-132013-04-11Bibliographically approved