Event-Based Neural Network Approximation and Control of Uncertain Nonlinear Continuous-Time Systems

This paper presents a novel event-based adaptive control of uncertain nonlinear continuous-time systems. An adaptive model by using two linearly parameterized neural networks (NNs) is designed to approximate the unknown internal dynamics of the nonlinear system with event sampled state vector. The estimated state vector and the dynamics from the adaptive model are subsequently used to design the control law. Novel NN weight update laws are proposed in the context of event-based availability of state vector wherein the NN weights are updated once at every aperiodic sampling instant unlike the traditional periodically sampled adaptive NN based control. A positive lower bound on the inter-sample times is shown. The boundedness of the NN weight estimation errors and system state vector are demonstrated by representing the event sampled closed-loop system as a nonlinear impulsive dynamical system and by using an adaptive trigger condition. Finally, simulation results are included to show the performance of the proposed approach.