Adaptive neural network observer control for a class of nonlinear strict-feedback systems with unmeasurable states

This article addresses the backstepping control problem of the nonlinear strict-feedback system with an immeasurable state. To eliminate the effect coming from the immeasurable state variable, a new adaptive state observer method is developed for backstepping design by employing a neural network (NN) approximation strategy. As one of the highlighting contributions, the observer method can be performed with the relaxed condition because it does not require the design parameters to satisfy the Hurwitz equation, therefore it can be more easily applied and extended to serve for nonlinear system control than the existing observer methods. Finally, by integrating the observer dynamic into the backstepping design, the adaptive tracking control is achieved. Lastly, the feasibility of the method is proved by both stability theory and computer simulation.