Optimal consensus control of discrete-time stochastic multi-agent systems

This paper is concerned with the optimal consensus control of discrete-time multi-agent systems with multiplicative noise. The sufficient condition for the existence of a parameterized generalized algebraic Riccati equation (ARE) is first developed. Then, the sufficient condition on the control gain, the communication topology graph, and the critical value of the parameterized generalized ARE's parameter for mean square consensus are derived. Finally, the explicit control strategy is given to to guarantee consensus and minimize the performance index simultaneously.