Hybrid adaptive control based on a Hopfield dynamic neural network for nonlinear dynamical systems

In this paper, we propose a hybrid adaptive control scheme based on Hopfield-based dynamic neural network (HACHNN) for SISO nonlinear systems. An auxiliary direct adaptive controller is proposed to ensure the stability in the time-interval of when an indirect adaptive controller is failed because of ĝ(x)→0. The weights of the Hopfield-based dynamic neural network are on-line tuned by the adaptive laws derived in the sense of Lyapunov theorem, so that the stability of the closed-loop system can be guaranteed, and all signals in the closed-loop system are bounded. The designed structure of the Hopfield-based dynamic neural network maintains the tracking performance of the control scheme, and it also makes the practical implementation much easier.