Adaptive neural network-based optimal control of nonlinear continuous-time systems in strict-feedback form

This paper focuses on neural network (NN) based optimal control of nonlinear continuous-time systems in strict-feedback form when the system dynamics are known by using an adaptive backstepping approach. A single NN-based adaptive approach is designed to learn the solution of the infinite horizon continuous-time Hamilton-Jacobi-Bellman (HJB) equation while the corresponding optimal control input that minimizes the HJB equation is calculated in a forward-in-time manner without using value and policy iterations. First, the optimal control problem is solved for a generic multi-input and multi-output nonlinear system with a state feedback approach. Then the approach is extended to a single-input and single-output nonlinear system by using output feedback via a nonlinear observer. Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signals approach the optimal control inputs with small bounded error both for the state and output feedback-based controller designs. In the absence of NN reconstruction errors, asymptotic convergence to the optimal control is demonstrated. Finally, simulation examples are provided to validate the theoretical results. Copyright (c) 2013 John Wiley & Sons, Ltd.