Neural Network Control based Stabilization of Nonlinear Systems in Arbitrary Time

Abstract

Neural network (NN) control approach is an efficient method to approximate unknown nonlinear functions in dynamical systems ensuring uniform ultimate boundedness of the closed loop system. Nevertheless, the problem of arbitrary time uniform boundedness is unsolved in most of the existing results. In this paper, we implement neural network control scheme to show that the states of the nonlinear system and the NN weighted error converge to the compact set in arbitrary time and are semi-globally uniformly ultimately bounded guaranteeing the existence of the compact set. Specifically, it is ensured that after this arbitrary time, valid estimation of the unknown function is achieved as the states remain in existing compact set. We implement this methodology on first-order and second-order systems. In the end, we provide academic and practical examples with simulations to show the efficacy of the mathematical results. © 2021 IEEE.