Optimal control for nonlinear continuous systems by adaptive dynamic programming based on fuzzy basis functions

In this study, we resolve the optimal control problem for nonlinear continuous systems with unknown internal dynamics using policy iteration (PI)-based fuzzy adaptive dynamic programming, where the cost functional is approximated by fuzzy basis functions (FBFs), which are convenient for solving the nonlinear Hamilton-Jacobi-Bellman equation. The cost functional is described in a discrete form and the weighted residuals method in the least squares sense is then employed to update the weights of the FBFs using the PI algorithm. The iteration process terminates when the weights converge and the optimal controller can then be obtained in a simple manner. It should be noted that FBFs are used widely in real applications due to their satisfactory performance at approximating the nonlinear functional. A numerical example is given to illustrate the effectiveness of our method.