Continuous-Time Time-Varying Policy Iteration

A novel policy iteration algorithm, called the continuous-time time-varying (CTTV) policy iteration algorithm, is presented in this paper to obtain the optimal control laws for infinite horizon CTTV nonlinear systems. The adaptive dynamic programming (ADP) technique is utilized to obtain the iterative control laws for the optimization of the performance index function. The properties of the CTTV policy iteration algorithm are analyzed. Monotonicity, convergence, and optimality of the iterative value function have been analyzed, and the iterative value function can be proven to monotonically converge to the optimal solution of the Hamilton-Jacobi-Bellman (HJB) equation. Furthermore, the iterative control law is guaranteed to be admissible to stabilize the nonlinear systems. In the implementation of the presented CTTV policy algorithm, the approximate iterative control laws and iterative value function are obtained by neural networks. Finally, the numerical results are given to verify the effectiveness of the presented method.