A partial policy iteration ADP algorithm for nonlinear neuro-optimal control with discounted total reward

Abstract

This paper constructs a partial policy iteration adaptive dynamic programming (ADP) algorithm to solve the optimal control problem of nonlinear systems with discounted total reward. Compared with traditional policy iteration ADP algorithm, the approach updates the iterative control law only in a local region of the global system state space. With the benefit of this feature, the overall computational burden at each iteration for processing units can be significantly reduced. Hence, this feature enables our algorithm to be successfully executed on low-performance devices such as smartphones, smartwatches and the Internet of Things (IoT) objects. We provide the convergency analysis to show that the generated sequence of value functions is monotonically nonincreasing and can finally reach a local optimum. In addition, the corresponding local policy space is developed theoretically for the first time. Besides, when the sequence of the local system state spaces is chosen properly, we prove that the developed algorithm is capable of finding the global optimal performance index function for the nonlinear systems. Finally, we present a numerical simulation to demonstrate the effectiveness of the proposed algorithm.