State and Output Feedback Control of Interval Type-2 Fuzzy Systems With Mismatched Membership Functions

This paper is concerned with the problems of state and output feedback control for interval type-2 (IT2) fuzzy systems with mismatched membership functions. The IT2 fuzzy model and the IT2 state and output feedback controllers do not share the same membership functions. A novel performance index, which is expressed as an extended dissipativity performance, is introduced to be a generalization of H∞, L2-L∞, passive, and dissipativity performances indexes. First, the IT2 Takagi-Sugeno fuzzy model and the controllers are constructed by considering the mismatched membership functions. Second, on the basis of Lyapunov stability theory, the IT2 fuzzy state and output feedback controllers are designed, respectively, to guarantee that the closed-loop system is asymptotically stable with extended dissipativity performance. The existence conditions of the two kinds of controllers are obtained in terms of convex optimization problems, which can be solved by standard software. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.

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

[2]  Chin-Teng Lin,et al.  Neural-Network-Based Fuzzy Logic Control and Decision System , 1991, IEEE Trans. Computers.

[3]  C. S. George Lee,et al.  Reinforcement structure/parameter learning for neural-network-based fuzzy logic control systems , 1994, IEEE Trans. Fuzzy Syst..

[4]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[5]  K. Grigoriadis,et al.  Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[6]  Bernhard Maschke,et al.  Dissipative Systems Analysis and Control , 2000 .

[7]  Oscar Castillo,et al.  A New Method for Adaptive Control of Non-Linear Plants Using Type-2 Fuzzy Logic and Neural Networks , 2002, International Journal of General Systems.

[8]  Jingcheng Wang,et al.  Delay-dependent dissipative control for linear time-delay systems , 2002, J. Frankl. Inst..

[9]  Dongrui Wu,et al.  A type-2 fuzzy logic controller for the liquid-level process , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[10]  Hani Hagras,et al.  A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots , 2004, IEEE Transactions on Fuzzy Systems.

[11]  G. Feng,et al.  A Survey on Analysis and Design of Model-Based Fuzzy Control Systems , 2006, IEEE Transactions on Fuzzy Systems.

[12]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[13]  H. Hagras,et al.  Type-2 FLCs: A New Generation of Fuzzy Controllers , 2007, IEEE Computational Intelligence Magazine.

[14]  Oscar Montiel,et al.  Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic , 2007, Inf. Sci..

[15]  Oscar Castillo,et al.  Type-2 Fuzzy Logic , 2007 .

[16]  F. M. Callier,et al.  Dissipative Systems Analysis and Control: Theory and Applications (2nd Edition)-[Book review; B. Brogliato, R. Lozano, B. Maschke] , 2007, IEEE Transactions on Automatic Control.

[17]  Hak-Keung Lam,et al.  Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Hak-Keung Lam,et al.  Stability analysis of discrete-time fuzzy-model-based control systems with time delay: Time delay-independent approach , 2008, Fuzzy Sets Syst..

[19]  Shaocheng Tong,et al.  A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control , 2009, IEEE Transactions on Fuzzy Systems.

[20]  Chia-Feng Juang,et al.  Reinforcement Interval Type-2 Fuzzy Controller Design by Online Rule Generation and Q-Value-Aided Ant Colony Optimization , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  Hani Hagras,et al.  Interval Type-2 Fuzzy Logic Congestion Control for Video Streaming Across IP Networks , 2009, IEEE Transactions on Fuzzy Systems.

[22]  Xiaoping Liu,et al.  Robust Hinfinity control of Takagi-Sugeno fuzzy systems with state and input time delays , 2009, Fuzzy Sets Syst..

[23]  Shengyuan Xu,et al.  Passivity Analysis of Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[24]  Yun Chen,et al.  New delay-dependent L2-L∞ filter design for stochastic time-delay systems , 2009, Signal Process..

[25]  Ricardo Martínez-Soto,et al.  Optimization of Interval Type-2 Fuzzy Logic Controllers for a Perturbed Autonomous Wheeled Mobile Robot Using Genetic Algorithms , 2009, Soft Computing for Hybrid Intelligent Systems.

[26]  Honghai Liu,et al.  An Interval Fuzzy Controller for Vehicle Active Suspension Systems , 2010, IEEE Transactions on Intelligent Transportation Systems.

[27]  Hassan Nouri,et al.  Noninteracting Adaptive Control of PMSM Using Interval Type-2 Fuzzy Logic Systems , 2011, IEEE Transactions on Fuzzy Systems.

[28]  Jianbin Qiu,et al.  Asynchronous Output-Feedback Control of Networked Nonlinear Systems With Multiple Packet Dropouts: T–S Fuzzy Affine Model-Based Approach , 2011, IEEE Transactions on Fuzzy Systems.

[29]  Ligang Wu,et al.  A New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Time-Varying Delay Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  James Lam,et al.  α-Dissipativity analysis of singular time-delay systems , 2011, Autom..

[31]  Oscar Castillo,et al.  Type-2 Fuzzy Logic Systems , 2012 .

[32]  Yeong-Hwa Chang,et al.  Fuzzy Sliding-Mode Formation Control for Multirobot Systems: Design and Implementation , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[33]  Peng Shi,et al.  Fuzzy-Model-Based Fault-Tolerant Design for Nonlinear Stochastic Systems Against Simultaneous Sensor and Actuator Faults , 2013, IEEE Transactions on Fuzzy Systems.

[34]  Yeong-Hwa Chang,et al.  T-S Fuzzy Model-Based Adaptive Dynamic Surface Control for Ball and Beam System , 2013, IEEE Transactions on Industrial Electronics.

[35]  Shengyuan Xu,et al.  Filtering of Markovian Jump Delay Systems Based on a New Performance Index , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[36]  Zhiguang Feng,et al.  Reliable Dissipative Control for Singular Markovian Systems , 2013 .

[37]  Chia-Feng Juang,et al.  An Interval Type-2 Neural Fuzzy Chip With On-Chip Incremental Learning Ability for Time-Varying Data Sequence Prediction and System Control , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[38]  Kaspar Althoefer,et al.  Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching , 2014, IEEE Transactions on Industrial Electronics.

[39]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .