A Self-tuning Optimal Controller for Affine Nonlinear Continuous-time Systems with Unknown Internal Dynamics

This paper presents a novel neural network (NN) based self-tuning controller for the optimal regulation of affine nonlinear continuous-time systems. Knowledge of the internal system dynamics is not required whereas the control coefficient matrix is considered to be available. The proposed nonlinear optimal regulator tunes itself in order to simultaneously learn the optimal control input, optimal cost function, and the system internal dynamics using a single NN. A novel NN weight tuning algorithm is derived which ensures the internal system dynamics are learned while simultaneously minimizing a predefined cost function. An initial stabilizing controller is not required. Lyapunov methods are used to show that all signals are uniformly ultimately bounded (UUB). In the absence of NN reconstruction errors, the approximated control input is shown to converge to the optimal control asymptotically for the regulator design, and simulation results illustrate the effectiveness of the approach.