Paper Info
Title
Random convex programs for distributed multi-agent consensus
Abstract
We consider convex optimization problems with N randomly drawn convex constraints. Previous work has shown that the tails of the distribution of the probability that the optimal solution subject to these constraints will violate the next random constraint, can be bounded by a binomial distribution. In this paper we extend these results to the violation probability of convex combinations of optimal solutions of optimization problems with random constraints and different cost objectives. This extension has interesting applications to distributed multi-agent consensus algorithms in which the decision vectors of the agents are subject to random constraints and the agents' goal is to achieve consensus on a common value of the decision vector that satisfies the constraints. We give explicit bounds on the tails of the probability that the agents' decision vectors at an arbitrary iteration of the consensus protocol violate further constraint realizations. In a numerical experiment we apply these results to a model predictive control problem in which the agents aim to achieve consensus on a control sequence subject to random terminal constraints.
Year
Venue
Keywords
2013
Control Conference
binomial distribution,constraint satisfaction problems,convex programming,distributed control,multi-robot systems,predictive control,random processes,agent decision vector,agent goal,consensus protocol,constraint realization,constraint satisfaction,control sequence,convex optimization problem,cost objectives,distributed multiagent consensus algorithm,model predictive control problem,numerical experiment,probability distribution,random constraint,random convex programs,random terminal constraint,randomly drawn convex constraints,violation probability,robustness,stochastic processes,uncertainty,optimization,topology,convex functions,vectors
Field
DocType
Citations 
Binomial distribution,Mathematical optimization,Nonlinear programming,Stochastic process,Constraint satisfaction problem,Proper convex function,Convex optimization,Optimization problem,Mathematics,Bounded function
Conference
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Giuseppe Carlo Calafiore122623.82
Daniel Lyons2111.63