Function approximation-based sliding mode adaptive control

Abstract

For the position tracking in DC motor with unknown bound time-varying dead zone uncertainties, a novel sliding mode adaptive controller is proposed by means of sliding mode and function approximation technique in this paper. First, control law with an uncertain term and another compensative term is obtained using sliding mode technique, and then the function approximation technique is employed to transform the uncertain term into finite combinations of orthonormal basis functions. The concrete expressions of uncertain term and compensative term can thus be derived based on the Lyapunov design. Actual system control experiments of the sliding adaptive control proposed are given.

Function Approximation Based Control for Non-Square Systems

“…It should be noted thatd i (t) − d i , the error between the parameters and their estimations, is not necessarily asymptotically stable. However, according to (24), we see that the derivative of the Lyapunov function of the closed loop system is negative semi-definite andd i (t) − d i is bounded, which indicates that the update lawsd i (t) finally converge to certain constant values.…”

“…Note that compared with the adaptive control problem for a system with parametric uncertainty, it is challenging for a system with time-varying uncertainty where traditional techniques such as the model reference adaptive control (MRAC) are not feasible. To tackle this problem, we adopt the function approximation technique (FAT) based adaptive control [21]- [24]. Compared with the traditional MRAC, the advantage of the FAT-based control is in the representation of the time-varying uncertainties by a set of given basis functions weighted by a set of unknown constant parameters.…”

“…We construct the algorithm based on the function approximation technique, inspired by its application on the adaptive control [21]- [24]. The main idea of the construction of the control law is as follows.…”

Function Approximation-based Sliding Mode Adaptive Control for Time-varying Uncertain Nonlinear Systems

“…J. Wu et al, 2007;Fang et al, 2006;Chiang et al, 2007). These research problems are hotspot in the control realm, and some results have been obtained through years of hard work of researchers Chen & Huang, 2005;Huang & Liao, 2006;Liang et al, 2008). These research works adopt a common technique named function approximation technique (FAT) despite of their different design methods.…”

On Motion Planning and Control for Partially Differentially Flat Systems

“…To address both the stability and the adaptiveness, in this paper, we propose an function approximation technique (FAT)-based method inspired by its application to adaptive control problems. 2,3,6,10,30,31 It is model-free, and thus feasible for a wide class of systems and robust to uncertainties. On the other hand, compared with the soft computing techniques, the stability of the FAT-based method can be proved.…”