State and output feedback-based adaptive optimal control of nonlinear continuous-time systems in strict feedback form

This paper focuses on neural network (NN) based adaptive optimal control of nonlinear continuous-time systems in strict feedback form with known dynamics. A single NN is utilized to learn the infinite horizon cost function which is the solution to the Hamilton-Jacobi-Bellman (HJB) equation in continuous-time. 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 in a generic multi input and multi output (MIMO) nonlinear system in strict feedback form with a state feedback approach. Then, the approach is extended to single input and single output (SISO) nonlinear system in strict feedback form by using output feedback via a nonlinear observer. Lyapunov techniques are used to show that all signals are uniformly ultimately bounded (UUB) and that the approximated control signals approach the optimal control inputs with small bounded error. In the absence of NN reconstruction errors, asymptotic convergence to the optimal control input is demonstrated. Finally, a simulation example is provided to validate the theoretical results for the output feedback controller design.