Randomized optimal consensus of multiagent systems based on a novel intermittent projected subgradient algorithm

Abstract

SummaryIn this article, a novel intermittent projected subgradient algorithm is presented to solve the randomized optimal consensus problem for heterogeneous multiagent systems with time‐varying communication topologies. The multiagent systems achieve the consensus meanwhile minimizing the global objective function via the proposed algorithm, where fi(x) is the convex objective function of agent i itself. Due to the common Bernoulli distribution adopted in the existing random optimization algorithm without considering the different computing capability of each agent. An individual projection probability is assigned for each agent based on computing capabilities so that either making projection or taking average is chosen according to the above probability which can effectively avoid overload for some agents with lower computing capabilities and improve the reliability of the overall systems. A new sufficient step‐size condition is given to ensure all agents converge to the optimal solution with probability one. Finally, a numerical example is also given to validate the proposed method.