Learning Optimal Control Policy for Unknown Discrete-Time Systems

This brief studies the optimal control policy learning problem for discrete-time linear systems. A data-driven model-free algorithm is proposed by using the data matrices of the augmented system state and the increasing of the discount factor. The control gains generated by the proposed algorithm are proven to converge to the optimal one. Compared with the existing work, our model-free algorithm avoids the dependence on initial stabilizing control policy and the use of Kronecker product. Some numerical examples are provided to illustrate the proposed algorithm and analysis results.