A New Approach to Finite-Horizon Optimal Control for Discrete-Time Affine Nonlinear Systems via a Pseudolinear Method

In this article, a new time-varying adaptivedynamic programming (ADP) algorithm is developed to solve finite-horizon optimal control problems for a class of discrete-time affine nonlinear systems. Inspired by the pseudolinear method, the nonlinear system can be approximated by a series of time-varying linear systems. In each iteration of the time-varying ADP algorithm, the optimal control law for the time-varying linear system is obtained. For an arbitrary initial state, it is proven that states of the time-varying linear systems converge to the states of discrete-time affine nonlinear systems. It is also shown that the iterative value functions and the iterative control laws converge to the optimal value function and the optimal control law, respectively. Finally, numerical results are presented to verify the effectiveness of the present method.