Adaptive critic design based robust neural network control for a class of continuous-time nonaffine nonlinear system

A novel adaptive critic design (ACD) based robust neural network (NN) controller is proposed for a class of continuous-time nonaffine nonlinear system in this paper. Although studies about ACD-based NN controller have been made on nonlinear systems, little is known about the more complicate nonaffine nonlinear systems. Because the nonlinear functions of nonaffine nonlinear systems are implicit functions with respect to the control, existing ACD methods can not been applied directly. Instead of approximating the nonaffine nonlinear function, we proposed that an action NN is employed to approximate the derived unknown uncertain term. Additionally, a robust term is developed to attenuate the NN reconstruction errors. Moreover, novel tuning laws for the weights of action NN and critic NN and the adaptive parameter are derived to guarantee the uniformly ultimate boundedness of all signals of the closed-loop system by Lyapunov method. By developing a novel Lyapunov function candidate and using adaptive bounding technique, no a prior knowledge of bounds of the time derivative of the control effectiveness term, the NN ideal weights of action NN and critic NN and the reconstruction errors is required. Simulation results demonstrate the effectiveness of the approach.