Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

Abstract

This paper presents a robust sliding mode controller for a class of unknown nonlinear discretetime systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.

Barrier Function-Based Adaptive Neuro Network Sliding Mode Vibration Control for Flexible Double-Clamped Beams With Input Saturation

“…Furthermore, based on Assumption 1 and Assumption 2, and choose parameters c 1 , c 2 , k a , k b satisfying c 1 > 0, c 2 > 0 and 2k a −k 2 b > 1, then we haveV 1 (t) ≤ −µ 1 V 1 +C 1 , while 1 and s in the double-clamped beam system are guaranteed to be uniformly ultimately bounded. We can rewritten the Lyapunov function V 1 (t) by integrating the inequality (38) as follows,…”

“…Based on the adaptive neural network, an adaptive sliding mode controller is proposed to track the trajectory for nonholonomic wheeled mobile robots, which effectively solve the problem of model uncertainties and external disturbances [37]. To eliminate the chattering and achieve robustness simultaneously, in [38], a robust sliding mode control is designed with the neural network, with which the nonlinear dynamic system stability is ensured. Compared with the traditional neural network, the RBF neural network has a simple structure, fast learning algorithm, and better approximation capabilities [39].…”

Robust adaptive sliding mode control for discrete singular systems with randomly occurring mixed time-delays under uncertain occurrence probabilities

“…Compared with the normal systems, the research on the synthesis problems of singular systems are relatively complicated since the resultant closed-loop systems are required to satisfy not only stability but also regularity as well as causality at the same time. Recently, the analysis and synthesis problems of singular systems have turned into a hot issue involving various modelling ways, such as Gierer-Meinhardt design a discontinuous control law to force the state trajectories onto the neighbourhood of pre-selected sliding surface (Goyal et al, 2015;Roy & Kar, 2017). Notice that the SMC has strong robustness and fast response for matched external disturbances and model uncertainties (Basin et al, 2012;Hu, Zhang, Kao, et al, 2019;Hu, Zhang, Yu, et al, 2019).…”

Vibration Reduction of the Nonlinearly Tufted Carpet Yarn by a Modified Sliding Mode Control Method

“…To control the yarn vibration, a reasonable controller is needed. At present, there are many control methods for nonlinear systems, such as neural network control [3][4][5], sliding mode control [6][7][8][9], adaptive control [10,11], and so on. Among them, sliding mode control has many advantages, such as quick response, online monitoring, simple realization, and strong anti-interference ability.…”