Optimal Mean-square Consensus for Discrete-Time Linear Systems with Random Input Gains

This paper studies the optimal consensus problem for linear multi-agent systems with random input gains, which means there exists a random white noise imposed on the control input of each follower agent. An optimal state feedback control protocol based on linear quadratic regulation (LQR) optimal control theory is constructed for each follower agent, such that the mean-square consensus can be achieved. We also show that these control protocols guarantee the global optimality consensus. A numerical example is provided to validate the theoretical result.