Consensus stability analysis of optimal control for stochastic multi-agent system

Abstract

This paper investigates distributed optimal control and stochastic consensus stability problems for high-order stochastic multi-agent system over randomly switching topologies and stochastic communication noise. The switching is governed by a time-homogeneous Markov process, whose state corresponds to a possible interaction topology among agents. The influence factors such as Markovian switching topologies and stochastic communication noise on the optimal solution of the high-order stochastic multi-agent system under distributed optimal control is considered. Based on the stochastic optimal control dynamic programming principle, the distributed optimal controller is designed for the high-order stochastic multi-agent with Markovian switching topologies and stochastic communication noises. Then the consensus stability of the high-order stochastic multi-agent system with Markovian switching topologies and stochastic communication noises is analyzed under the distributed optimal control algorithm. Finally the numerical example is included to illustrate the theoretical analysis.