Linear-quadratic optimal control for unknown mean-field stochastic discrete-time system via adaptive dynamic programming approach

We develop an adaptive dynamic programming (ADP) approach to deal with the linear-quadratic (LQ) optimal control problem with unknown discrete-time mean-field stochastic system in this paper. At first, the mean-field stochastic LQ problem is transformed into the deterministic case by system transition. Secondly, a value iteration ADP approach is proposed and convergence proof is also discussed. Once again, in order to achieve the iteration method without any knowledge of the dynamics, back propagation neural network (BPNN) is applied to design model network, critic network and action network to ensure unknown system model, value function and control strategy, respectively. At last, it is demonstrated that the ADP approach is valid through simulation.