Adaptive neural dynamic surface sliding mode control for uncertain nonlinear systems with unknown input saturation

Qiang Chen,Xuemei Ren,Linlin Shi,Yurong Nan

doi:10.1177/1729881416657750

Abstract

In this article, an adaptive neural dynamic surface sliding mode control scheme is proposed for uncertain nonlinear systems with unknown input saturation. The non-smooth input saturation nonlinearity is firstly approximated by a smooth non-affine function, which can be further transformed into an affine form according to the mean value theorem. Then, one simple sigmoid neural network is employed to approximate the uncertain nonlinearity including the input saturation, and the approximation error is estimated using an adaptive learning law. Virtual controls are designed in each step by combing the dynamic surface control and integral sliding mode technique, and thus the problem of complexity explosion inherent in the conventional backstepping method is avoided. With the proposed control scheme, no prior knowledge is required on the bound of input saturation, and comparative simulations are given to illustrate the effectiveness and superior performance.

Highlights

In many practical dynamic systems, lots of nonlinear and uncertain characteristics are encountered, such as saturation, hysteresis, dead zone, and so on.[1,2,3] Input saturation is well known as one of the most common non-smooth input nonlinearities
Much attention has been paid to controllers design for nonlinear systems with input saturation.[4,5,6,7,8]
In the study by Gao and Selmic,[4] Chen et al.[5] and Chen et al.,[6] significant results have been obtained for controlling saturated nonlinear systems with the bounds of input saturation being known or estimated in prior

Summary

Introduction

In many practical dynamic systems, lots of nonlinear and uncertain characteristics are encountered, such as saturation, hysteresis, dead zone, and so on.[1,2,3] Input saturation is well known as one of the most common non-smooth input nonlinearities. Motivated by the aforementioned discussion, this article develops a new neural dynamic surface SMC scheme for a class of uncertain nonlinear systems with unknown input saturation. ; n, are continuously differentiable to n-order with respect to the state variables xi and the input v(u) Since the unknown functions fi, i 1⁄4 1; . To proceed the design procedure, the control function bnðxn; vanÞ in equation (12) is assumed to be positive and bounded satisfying 0 < b1 < bnðxn; van Þ < b2, where b1 and b2 are positive constants. We will incorporate the DSC and integral sliding mode techniques into a NN-based adaptive control design scheme for the nth-order system described by equation (12). Consider the nonlinear system (12) with unknown input saturation (14), the integral sliding mode surface (21), control law (45), and adaptive learning laws (46). For any positive number Z where a0 and Z are positive constants and jBiþ1j Miþ[1]

As and

Findings

Conclusion