Neural Network-Based Exponential Stability of Affine Nonlinear Systems by Event-Triggered Approach

In this paper, the event-triggered approach is considered as the implementation of exponential stability for a class of nonlinear systems with an asymptotic control input which is generated by an neural network-based feedback network. Under additional mild assumptions, we first rigorously conduct discussion on the transformation between affine nonlinear systems and linear systems via some existing results. Subsequently, we present a novel weight update law for the feedback neural network (NN) so as to achieve the process of finding the optimal weight matrix. Afterward, we derive an appropriate condition using the Lyapunov-Krasovskii method, that guarantees the practical convergence of the closed-loop system toward an equilibrium point (zero point) and is used to design relevant coefficients for the event-triggering scheme. Finally, a numerical example substantiates the achievement of exponential stability and the reduction of loss of the closed-loop system.