DECENTRALIZED OPTIMAL CONTROL FOR THE MEAN FIELD LQG PROBLEM OF MULTI-AGENT SYSTEMS

摘要

This paper investigates the decentralized optimal control of the linear quadratic Gaussian (LQG) problem in discrete-time stochastic multi-agent systems. The state equations of the subsystems are uncoupled and the individual cost function is coupled with the states of other agents. With the help of state aggregation technique and the mean field structure, we get the decentralized optimal controllers that each agent only uses its own state and an iterative function which may be computed off-line for the optimization of the individual cost function and the social cost function respectively. And then, we prove that as the number of subsystems increases to infinite, the losses of the decentralized controllers and the optimal cost function for the two optimal control problems will go to zero due to the approximation in the optimization. At last, an illustrative example is given.