Model Reference Fuzzy Control of Nonlinear Dynamical Systems Using an Optimal Observer

This paper proposes a novel indirect model reference fuzzy control approach for nonlinear systems, expressed in the form of a Takagi Sugeno (TS) fuzzy model based on an optimal observer. In contrast to what is seen in the literature on adaptive observer-based TS fuzzy control systems, the proposed method is capable of tracking a reference signal rather than just regulation. Additionally the proposed algorithm benefits from an adaptation algorithm which estimates the parameters of observer optimally. The stability analysis of the adaptation law and the controller is done using an appropriate Lyapunov function. The proposed method is then simulated on the control of Chua's circuit and it is shown that it is capable of controlling this chaotic system with high performance.

[1]  Yih-Guang Leu,et al.  Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems , 2005, IEEE Trans. Neural Networks.

[2]  Ebrahim H. Mamdani,et al.  A linguistic self-organizing process controller , 1979, Autom..

[3]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[4]  T. John Koo,et al.  Stable model reference adaptive fuzzy control of a class of nonlinear systems , 2001, IEEE Trans. Fuzzy Syst..

[5]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[6]  Hui-Min Yen,et al.  Takagi-Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design , 2011 .

[7]  Yih-Guang Leu,et al.  Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[8]  M. T. Yassen,et al.  Adaptive control and synchronization of a modified Chua's circuit system , 2003, Appl. Math. Comput..

[9]  Jovan D. Boskovic,et al.  An Optimal Control Modification to Model-Reference Adaptive Control for Fast Adaptation , 2008 .

[10]  Yau-Tarng Juang,et al.  Adaptive fuzzy sliding-mode controller of uncertain nonlinear systems. , 2008, ISA transactions.

[11]  Chun-Fei Hsu,et al.  Fuzzy-identification-based adaptive controller design via backstepping approach , 2005, Fuzzy Sets Syst..

[12]  Marcelo C. M. Teixeira,et al.  On relaxed LMI-based designs for fuzzy regulators and fuzzy observers , 2001, 2001 European Control Conference (ECC).

[13]  Martin Kratmüller,et al.  The Adaptive Control of Nonlinear Systems Using the T-S-K Fuzzy Logic , 2009 .

[14]  C.-W. Park,et al.  Adaptive tracking control of flexible joint manipulator based on fuzzy model reference approach , 2003 .

[15]  Peter Liu,et al.  LMI-based fuzzy chaotic synchronization and communications , 2001, IEEE Trans. Fuzzy Syst..

[16]  Chih-Chiang Cheng,et al.  Adaptive sliding mode controller design based on T-S fuzzy system models , 2006, Autom..

[17]  Mignon Park,et al.  An indirect model reference adaptive fuzzy control for SISO Takagi-Sugeno model , 2001, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[18]  Mohammad Ababneh,et al.  Design of digital controllers for uncertain chaotic systems using fuzzy logic , 2009, J. Frankl. Inst..

[19]  Mignon Park,et al.  Adaptive parameter estimator based on T-S fuzzy models and its applications to indirect adaptive fuzzy control design , 2004, Inf. Sci..

[20]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  Martin Kratmüller.  Adaptive Fuzzy Control Design , 2009 .

[22]  Stephen Yurkovich,et al.  Fuzzy Control , 1997 .

[23]  Mignon Park,et al.  Tracking control of a robot manipulator using a direct model reference adaptive fuzzy control , 1999, Proceedings 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human and Environment Friendly Robots with High Intelligence and Emotional Quotients (Cat. No.99CH36289).

[24]  Han Ho Choi,et al.  LMI-Based Nonlinear Fuzzy Observer-Controller Design for Uncertain MIMO Nonlinear Systems , 2007, IEEE Transactions on Fuzzy Systems.

[25]  Youngwan Cho,et al.  A Lyapunov Function Based Direct Model Reference Adaptive Fuzzy Control , 2004, KES.

[26]  Mojtaba Ahmadieh Khanesar,et al.  Direct Model Reference Takagi–Sugeno Fuzzy Control of SISO Nonlinear Systems , 2011, IEEE Transactions on Fuzzy Systems.

[27]  Victor M. Becerra,et al.  Optimal control , 2008, Scholarpedia.

[28]  J. H. Kim,et al.  Indirect model reference adaptive fuzzy control of dynamic fuzzy-state space model , 2001 .