Fuzzy state-feedback control of uncertain nonlinear MIMO systems

In this research, we suggest a new fuzzy adaptive state-feedback control strategy for unknown nonlinear multivariable systems for which the input-gains matrix is not necessarily symmetric and is characterized by non-zero leading principle minors. A linearly parameterized fuzzy system is used to appropriately model the uncertainties. When designing our control scheme and studying the stability analysis, a decomposition property of the input-gain matrix is employed. A proportional-integral (PI) adaptation law is suggested to enhance the adaptive parameter convergence. An appropriate Lyapunov function is exploited to study the stability of the corresponding closed-loop control system as well as to derive the adaptation laws. Numerical simulations and a detailed comparison study are given to evaluate the efficiency of our suggested control methodology.

[1]  P. Olver.  Nonlinear Systems , 2013 .

[2]  Abdesselem Boulkroune,et al.  Design of a fuzzy adaptive controller for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and unknown control direction , 2010, Inf. Sci..

[3]  A. Boulkroune,et al.  Adaptive fuzzy control of MIMO nonlinear systems with unknown hysteresis and control gain matrix sign , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[4]  Abdesselem Boulkroune,et al.  How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems , 2008, Fuzzy Sets Syst..

[5]  Abdelaziz Hamzaoui,et al.  An Improved robust Adaptive Fuzzy controller for MIMO Systems , 2006, Control. Intell. Syst..

[6]  Chen Bin,et al.  Fuzzy adaptive output feedback control for MIMO nonlinear systems , 2005, Fuzzy Sets Syst..

[7]  Abdesselem Boulkroune,et al.  Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction , 2010, Fuzzy Sets Syst..

[8]  A. Golea,et al.  Fuzzy adaptive control of multivariable nonlinear systems , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[9]  A. Morse.  A gain matrix decomposition and some of its applications , 1993 .

[10]  A. Behal,et al.  Adaptive output feedback control for a class of MIMO nonlinear systems , 2006, 2006 American Control Conference.

[11]  Tong Shaocheng,et al.  Fuzzy adaptive output tracking control of nonlinear systems , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[12]  Antonin Vitecek,et al.  Control of mechanical systems with uncertainties , 2016, 2016 17th International Carpathian Control Conference (ICCC).

[13]  Abdesselem Boulkroune,et al.  Fuzzy approximation-based indirect adaptive controller for multi-input multi-output non-affine systems with unknown control direction , 2012 .

[14]  Jian Chen,et al.  A continuous asymptotic tracking control strategy for uncertain nonlinear systems , 2004, IEEE Transactions on Automatic Control.

[15]  Salim Labiod,et al.  Adaptive fuzzy control of a class of MIMO nonlinear systems , 2005, Fuzzy Sets Syst..

[16]  Shaocheng Tong,et al.  Fuzzy adaptive sliding-mode control for MIMO nonlinear systems , 2003, IEEE Trans. Fuzzy Syst..