A class of non-affine nonlinear systems adaptive neural networks backstepping control with pure-feedback prototype

This study presents a generalized procedure for designing recurrent neural network enhanced control of time delay nonlinear dynamic systems with non-affine triangle structure and pure-feedback prototype. Under the framework, recurrent neural network is developed to accommodate the on-line approximation, which the weights of the neural network are iteratively and adaptively updated through system state vector. Based on the neural network online approximation model, an indirect adaptive neural network controller is designed by means of dynamic compensation. Indirect control procedure and virtual control law are chosen to deal with the problems encountered in the design of such complex nonlinear control systems. Taking consideration of the correctness, rigorousness, and generality of the new development, Lyapunov stability theory is referred to prove the closed-loop control system uniformly ultimately bounded stable and the output of the system is converged to a small neighborhood of the desired trajectory. A bench mark test is simulated to demonstrate the effectiveness and efficiency of the procedure and furthermore it could be a show case for potential readers/users to digest and/or apply the procedure to their ad hoc problems.