Design of Fast Variable Structure Adaptive Fuzzy Control for Nonlinear State-Delay Systems with Uncertainty

Abstract

In this study, a new fast variable structure adaptive fuzzy controller is presented for nonlinear state-delay systems which are subjected to external disturbances and uncertainties. The undesirable chattering and singularity of the variable structure scheme are eliminated by using a novel fast robust high-precision continuous nonsingular control law which is able to accelerate the finite-time convergence both in reaching and sliding phases of the motion. A fuzzy logic system with a neural network adaptive law is used to approximate the dynamics of the nonlinear system containing the current state and the delayed state. The superiority of the proposed fuzzy neural network in online adjusting the weights of the network is the fast convergence rate of the approximation error to the optimum value in a very short time. The stability of the closed-loop system is proved by using an extended finite-time Lyapunov criterion such that the convergence of the position tracking error, velocity tracking error, and the estimation error to the bounded region is guaranteed in a very short time. Two second-order uncertain nonlinear simulation examples with external disturbances are given to evaluate the efficacy of the proposed control technique. The simulation results show that faster and high-precision tracking performance is obtained compared with the existing recent works focused on robust control of nonlinear state-delay systems with uncertainties.

KEYWORDS:

• Adaptive control
• Continuous
• Finite-time
• Fuzzy neural network
• Nonsingular
• State-delay
• Variable structure scheme

ACKNOWLEDGEMENTS

The authors would like to thank the anonymous reviewers and Associate Editor for their valuable comments and suggestions to improve the original manuscript.

Additional information

Notes on contributors

M. Montazeri

Maryam Montazeri received the BSc and MSc degree in electrical engineering from Islamic Azad University, Najafabad Branch, Isfahan, Iran. She is currently working toward the PhD degree in electrical engineering in Islamic Azad University of Najafabad Branch. Her research interests include adaptive and robust control and control of neuromusculoskeletal system using functional electrical stimulation. Email: [email protected]

M. R. Yousefi

Mohammad Reza Yousefi received the BSc degree in electrical engineering from Islamic Azad University, Najafabad Branch, Isfahan, Iran, and the MSc and PhD degrees in biomedical engineering from the K N Toosi University of Technology, Tehran, Iran, in 2001, 2004 and 2014, respectively. His current research interests include wavelet galerkin method, finite element method, and biomedical instrumentation. Email: [email protected]

K. Shojaei

Khoshnam Shojaei was born in Esfahan, Iran, on March 8, 1981. He received his BSc, MSc and PhD degree with distinction in electrical engineering from Iran University of Science and Technology (IUST) in 2004, 2007 and 2011, respectively. Currently, he is an associate professor in Najafabad Branch, Islamic Azad University, Iran. His research areas are the adaptive control of nonlinear systems, control of autonomous robots including land, air and ocean vehicles, navigation of mobile robots and multi-agent systems.

G. Shahgholian

Ghazanfar Shahgholian received his BSc degrees in electrical engineering from Isfahan University of Technology (IUT), Esfahan, Iran, in 1992. He received the MSc and PhD degrees in electrical engineering from University of Tabriz, Tabriz, Iran in 1994 and Islamic Azad University, Science and Research Branch, Tehran, Iran, in 2006, respectively. He is now an associate professor at Department of Electrical Engineering, Faculty of Engineering, Islamic Azad University – Najaf Abad Branch, Esfahan. His teaching and research interests include application of control theory to power system dynamics, power electronics and power system simulation. Email: [email protected]