Finite horizon optimal control of non-linear discrete-time switched systems using adaptive dynamic programming with ε-error bound

In this paper, we aim to solve the finite-horizon optimal control problem for a class of non-linear discrete-time switched systems using adaptive dynamic programming(ADP) algorithm. A new ε-optimal control scheme based on the iterative ADP algorithm is presented which makes the value function converge iteratively to the greatest lower bound of all value function indices within an error according to ε within finite time. Two neural networks are used as parametric structures to implement the iterative ADP algorithm with ε-error bound, which aim at approximating the value function and the control policy, respectively. And then, the optimal control policy is obtained. Finally, a simulation example is included to illustrate the applicability of the proposed method.