Linear adaptive control of a class of SISO nonaffine nonlinear systems

Abstract

This paper addresses the problem of linear adaptive control for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Using the implicit function theory, the existence of an ideal controller which can achieve control objectives is firstly demonstrated. However, this ideal controller cannot be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller using a simple linear controller with the free parameters updated online by a stable adaptation mechanism designed to minimise the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied class of nonaffine systems. We prove that the closed-loop system is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.

Keywords:

• linear adaptive control
• ideal controller
• adaptation mechanism
• nonaffine nonlinear systems

Additional information

Notes on contributors

Ahsene Boubakir

Ahsene Boubakir was born in Jijel, Algeria in 1981. He received the Engineer degree in Automatic control from University of Jijel, Algeria in 2004, MSc degree in Automatic control and robotics from Military Polytechnic School (EMP), Algiers, Algeria in 2007. He is currently pursuing a PhD degree in Automatic Control from National Polytechnic School of Algiers. His research interests include adaptive control, model free control and sliding mode control.

Salim Labiod

Salim Labiod was born in Jijel, Algeria in 1972. He received the Engineer diploma, the PhD degree and the HDR in automatic control from the National Polytechnic School of Algiers in 1995, 2005 and 2007, respectively. He is currently professor at the Faculty of Science and Technology of the University of Jijel, Algeria, and head of the Laboratory of Automatic Control of Jijel (LAJ). His research interests include fuzzy/neural control, nonlinear control and adaptive control.

Fares Boudjema

Fares Boudjema was born in Algiers, Algeria, on 28 March 1962. He received the Engineer degree in Electrical Engineering from the Ecole Nationale Polytechnique, Algiers, Algeria in 1985, the DEA degree, and the Doctorat degree in Automatic Control from the University of Paul Sabatier, Toulouse, France, in 1987, and 1991, respectively. In 1991, he joined the Department of Electrical Engineering at the Ecole Nationale Polytechnique, Algiers, as an Assistant Professor. He was promoted to Associate Professor in 1994, and Professor in 2000. He was the head of the control process laboratory from July 2000 through March 2005. Since March 2010, he has been the head of the automatic control department. His research interests include application of sliding mode control, artificial neural network control, fuzzy control and decentralised control in the field of the Electrical machines, power systems, robotics and UAV.

Franck Plestan

Franck Plestan received the PhD in Automatic Control from the Ecole Centrale de Nantes, France, in 1995. From September 1996 to August 2000, he was with Louis Pasteur University, Strasbourg, France. In September 2000, he joined the Ecole Centrale de Nantes, Nantes, France where he is currently Professor. His research interests include robust control (adaptive/higher order sliding mode), theoretical aspects of nonlinear observer design and control of electromechanical and mechanical systems (pneumatic actuators, biped robots, electrical motors).