Design of an adaptive fuzzy sliding mode control for uncertain discrete-time nonlinear systems based on noisy measurements

Abstract

This paper presents the design of an adaptive fuzzy sliding mode control (AFSMC) for uncertain discrete-time nonlinear dynamic systems. The dynamic systems are described by a discrete-time state equation with nonlinear uncertainties, and the uncertainties include the modelling errors and the external disturbances to be unknown but nonlinear with the bounded properties. The states are measured by the restriction of measurement sensors and the contamination with independent measurement noises. The nonlinear uncertainties are approximated by using the fuzzy IF-THEN rules based on the universal approximation theorem, and the approximation error is compensated by adding an adaptive complementary term to the proposed AFSMC. The fuzzy inference approach based on the extended single input rule modules is proposed to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are obtained by using the weighted least squares estimator and its simplified one. It is proved that under some conditions the estimation errors will remain in the vicinity of zero as time increases, and the states are ultimately bounded subject to the proposed AFSMC. The effectiveness of the proposed method is indicated through the simulation experiment of a simple numerical system.

Keywords:

• adaptive fuzzy sliding mode control
• uncertain discrete-time nonlinear dynamic system
• fuzzy IF-THEN rules
• single input rule modules
• universal approximation theorem
• weighted least squares estimator
• adaptive complementary term

Additional information

Notes on contributors

Toshio Yoshimura

Toshio Yoshimura is a professor emeritus of the University of Tokushima, Japan. He was graduated from Faculty of Engineering, the University of Tokushima in 1963, and received his PhD degree from Kyoto University in 1974. He was a professor from 1982 to 2006 in Faculty of Engineering, the University of Tokushima, and has been appointed as dean in the faculty from 2001 through 2003. His research includes the adaptive, fuzzy and sliding mode controls of mechanical systems, the active suspensions for passenger cars, and integrated steering and suspension controls for vehicle systems. He received the Paper Award in 1975 and was recommended as the Honorary Member in 2006 from the JSME.