A generalized indirect adaptive neural networks backstepping control procedure for a class of non-affine nonlinear systems with pure-feedback prototype

This study presents a generalized procedure for designing recurrent neural network enhanced control of time-varying-delayed 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, to deal with some of the challenging issues encountered in such complex nonlinear control systems. Taking consideration of the correctness, rigorousness, and generality of the new development, the Lyapunov stability theory is referred to prove that the closed-loop control system is uniformly ultimately bounded stable and the output of the system is converged to a small neighborhood of the desired trajectory. Two bench mark tests are simulated to demonstrate the effectiveness and efficiency of the procedure. In addition these could be the show cases for potential readers/users to digest and/or apply the procedure to their ad hoc problems.