Mean-Square Output Consensus of Heterogeneous Multi-Agent Systems with Multiplicative Noises in Dynamics and Measurements

This paper studies the output consensus problem of heterogeneous linear stochastic multiagent systems with multiplicative noises in system parameters and measurements, where the system noise in each agent is allowed to be different. By employing stochastic output regulation theory and the stochastic Lyapunov function approach, a composite controller embedded with stochastic output regulator equations (SOREs) and a stochastic dynamic compensator is designed to achieve the mean-square output consensus of the multi-agent systems. To implement the consensus algorithm, a sufficient condition for feasible solutions of the SOREs is first established in terms of Lyapunov and Selvester equations. Then the time-varying SOREs are approximated by the Euler-Maruyama method combined with an a-posteriori partial estimation of the increments of the Brownian motion. A numerical example illustrates the theoretical results.