Adaptive NN control for a class of strict-feedback nonlinear systems

An adaptive neural network control (ANNC) is proposed for a class of strict-feedback uncertain nonlinear systems with both unknown system nonlinearities and unknown virtual control gain nonlinearities. The continuous function separation technique and RBF neural network are introduced to model system nonlinearities. A systematic procedure for synthesis of ANNC is developed by combining the backstep- ping technique and Lyapunov stability theory. An important feature of the proposed algorithm is that the order of dynamic compensator of ANNC is only identical to the order n of controlled system, such that it can reduce the computation load and makes particularly suitable for parallel processing in actual implementation. In addition, the resulted closed-loop system is proven to be semi-global uniform ultimate bound and the possible controller singularity problem can be removed. Finally, numerical simulation example are presented to illustrate the tracking performance of the proposed algorithm. Index Terms-Uncertain nonlinear systems, neural networks, adaptive control, backstepping technique.