Neural learning control of general Brunovsky systems with a novel exponential stability theorem

In this paper, a deterministic learning of general Brunovsky systems from adaptive neural control is investigated, in which the affine terms are unknown functions of system states. To address the parameter convergence issue in a nonlinear adaptive control systems, a novel exponential stability theorem is developed and can be further applied to more multiple-variable systems as well as to the time-delay systems. Firstly, the exponential stability of the states of the closed-loop nominal systems is obtained. Then, the exponential convergence of the neural weight is achieved as long as the corresponding persistent excitation (PE) condition is satisfied. The uncertain dynamics of the systems is learned and stored in a constant weight neural network, which can be implemented to control the systems. The simulation demonstrates the effectiveness of the approach.