Online Optimal Control of Continuous-Time Affine Nonlinear Systems

Abstract

In this chapter, optimal control problems of continuous-time affine nonlinear systems are studied using adaptive dynamic programming (ADP) approach. First, an identifier–critic architecture based on ADP methods is presented to derive the approximate optimal control for partially unknown continuous-time nonlinear systems. Based on the ADP approach developed in this chapter, the identifier neural network (NN) and the critic NN are tuned simultaneously. Meanwhile, using recorded and instantaneous data simultaneously for the adaptation of the critic NN, the restrictive persistence of excitation condition is relaxed. Second, an ADP algorithm is developed to obtain the optimal control for continuous-time nonlinear systems with control constraints . By using the present algorithm, a single critic NN is utilized to derive the optimal control. Moreover, unlike in the case of policy iteration, where an initial stabilizing control is indispensable, there is no special requirement imposed on the initial control law.