Time-varying output-based Takagi–Sugeno fuzzy controller of uncertain nonlinear systems

Abstract

This paper proves the ultimately boundedness analysis for the trajectory tracking problem between the states of an uncertain nonlinear system represented by a Takagi–Sugeno (T–S) system and a given set of desired trajectories. The design of an output feedback controller includes a weighted contribution of the models included in the T–S design. The proposed T–S fuzzy estimates the state variables based on the output information, exclusively. The output-based controller design uses a time-dependent Lyapunov function yielding the characterisation of ultimate boundedness for the trajectory tracking error. Sufficient conditions are obtained to ensure the existence of positive-definite solutions for two coupled time-varying matrix Riccati equations, which are needed to solve the tracking problem. A simplified scheme determines the gains for the feedback controller and observer. The proposed control law solves the trajectory tracking of an autonomous underwater vehicle. In this case, numerical solutions show that the controller forced the convergence of the tracking error after 2.0 seconds. An alternative control design approach based on linear matrix inequalities (LMI) is used for comparison purposes. The suggested controller forces a faster convergence of the tracking error than the LMI-based one and provides a smaller ultimate bound.

Keywords:

• Trajectory tracking
• T–S fuzzy control
• state observer
• Riccati differential equation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Instituto Politécnico Nacional [grant number SIP20201286].

Notes on contributors

Jorge Cervantes

Jorge Cervantes received the B.S. degree from ESIME-IPN in 2003. In 2011, he earned the M.S. degree from the Automatic Control Department from CINVESTAV-IPN where now he is Ph.D. candidate. His current researching interests are underwater robotics, artificial neural networks and fuzzy systems.

Wen Yu

Wen Yu received the B.S. degree on Electrical Engineering from Tsinghua University, Beijing, China in 1990 and the M.S. and Ph.D. degrees, both in Electrical Engineering, from Northeastern University, Shenyang, China, in 1992 and 1995, respectively. From 1995 to 1996, he served as a Lecturer in the Department of Automatic Control at Northeastern University, Shenyang, China. Since 1996, he has been with the CINVESTAV-IPN where he is currently a Professor with the Departamento de Control Automatico. From 2002 to 2003, he held research positions with the Instituto Mexicano del Petroleo. He was a Senior Visiting Research Fellow with Queen’s University Belfast, Belfast, U.K., from 2006 to 2007, and a Visiting Associate Professor with the University of California, Santa Cruz, from 2009 to 2010. He also holds a visiting professorship at Northeastern University in China from 2006. Dr. Wen Yu serves as an associate editor of Neurocomputing and Journal of Intelligent and Fuzzy Systems. He is a member of the Mexican Academy of Sciences.

Sergio Salazar

Sergio Salazar was born in Tlaxcala Mexico. In1994 Dr Salazar received the Master in Electrical Engineering CINVESTAV, Mexico and the Ph.D. in Automatic Control, HEUDIASYC UTC France in 2004. He made two Postdoctoral periods at UTC, Compiegne France in 2005 and the Postdoctoral positional CINVESTAV, Mexico in 2006. Since 2010, he served as Professor-Researcher at UMI 3175 LAFMIA CINVESTAV-CNRS. He has published 12 articles in international referred journals.

Isaac Chairez

Isaac Chairez received the B.S degree on Biomedical Engineering from UPIBI, IPN, Mexico in 2002 and the M.S. and Ph.D. degrees both in Automatic Control from the CINVESTAV, IPN in 2004 and 2007, respectively. Since 2008, he is a full-time professor at the Bioprocesses Department in UPIBI, IPN. He has served as editor in chief of the Mexican Journal on Biomedical Engineering and as associate editor in for the International Journal of Dynamics and Control. He has published around 130 papers in different international journals. His current research activities include Artificial Neural Networks, Fuzzy Systems, Sliding Mode Control and their applications in different scientific and technological fields.