Commande robuste des systèmes non linéaires complexes

This work deals with a fuzzy tracking control design for uncertain nonlinear dynamic system withexternal disturbances and using a TS (Takagi-Sugeno) fuzzy model description. The control is basedon the Super-Twisting algorithm, which is among of second order sliding mode control. Moreover, twoadaptive fuzzy type-2 systems have been introduced to generate the two Super-Twisting signals toavoid both the chattering and the constraint on the knowledge of disturbances and uncertainties upperbounds. These adaptive fuzzy type-2 systems has only one input : the sliding surface, and one output :the optimale values of the control gains, which are hard to compute with the original algorithm.Simulation results are obtained in order to compare the performances of the proposed method tothat given by Levant. Then, we have introduced the integral sliding mode concept to impose inadvance the convergence time and the arrival on the sliding surface. The proposed approaches aregeneralized to the case of multivariable systems. Several results in simulation and in real time usinga benchmark are obtained to validate and to confirm the performances of our contributions.

[1]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

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

[3]  Kevin Guelton,et al.  Output feedback LMI tracking control conditions with H , 2009, Inf. Sci..

[4]  Arie Levant,et al.  Homogeneity approach to high-order sliding mode design , 2005, Autom..

[5]  Jerry M. Mendel,et al.  Enhanced Karnik--Mendel Algorithms , 2009, IEEE Transactions on Fuzzy Systems.

[6]  Bart Kosko,et al.  Fuzzy Systems as Universal Approximators , 1994, IEEE Trans. Computers.

[7]  Jerry M. Mendel,et al.  Examining the continuity of type-1 and interval type-2 fuzzy logic systems , 2010, International Conference on Fuzzy Systems.

[8]  P. J. MacVicar-Whelan.  Fuzzy sets for man-machine interaction , 1976 .

[9]  Li-Xin Wang.  Stable adaptive fuzzy control of nonlinear systems , 1993, IEEE Trans. Fuzzy Syst..

[10]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[11]  Rajani K. Mudi,et al.  A robust self-tuning scheme for PI- and PD-type fuzzy controllers , 1999, IEEE Trans. Fuzzy Syst..

[12]  Yann Morère.  Mise en oeuvre de lois de commande pour les modèles flous de type Takagi-Sugeno , 2001 .

[13]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[14]  José Ragot,et al.  STRUCTURE IDENTIFICATION OF MULTIPLE MODELS WITH OUTPUT ERROR LOCAL MODELS , 2002 .

[15]  Noureddine Manamanni,et al.  Switching Controllers' Synthesis: Combination of a Sliding Mode and H Infinity Control by a Fuzzy Supervisor , 2003, ADHS.

[16]  Jerry M. Mendel,et al.  Type-2 fuzzy logic systems , 1999, IEEE Trans. Fuzzy Syst..

[17]  Benoit Cebron.  Commande de systemes dynamiques hybrides , 2000 .

[18]  Reda Boukezzoula.  Commande floue d'une classe de systèmes non linéaires : application au problème de suivi de trajectoire , 2000 .

[19]  Chin-Wang Tao,et al.  Flexible complexity reduced PID-like fuzzy controllers , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[20]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[21]  Bor-Sen Chen,et al.  Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model , 2001, IEEE Trans. Fuzzy Syst..

[22]  N. N. Karnik,et al.  Introduction to type-2 fuzzy logic systems , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[23]  Antonella Ferrara,et al.  Output tracking control of uncertain nonlinear second-order systems , 1997, Autom..

[24]  Abdelaziz Hamzaoui,et al.  Two Order Sliding Fuzzy Type-2 Control Based on Integral Sliding Mode for MIMO Systems , 2011, EUSFLAT Conf..

[25]  Jerry M. Mendel,et al.  Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems , 2002, IEEE Trans. Fuzzy Syst..

[26]  C. Augé.  UNIVERSITE DE REIMS CHAMPAGNE-ARDENNE , 2006 .

[27]  E. H. Mandami.  Application of Fuzzy Logic to Approximate Reasoning using Linguistic Synthesis , 1977 .

[28]  József Bokor,et al.  Analysis and Control of Nonlinear Process Systems , 2004 .

[29]  Hak-Keung Lam,et al.  Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching , 2009, IEEE Transactions on Fuzzy Systems.

[30]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[31]  Abdelaziz Hamzaoui,et al.  Second-Order Sliding Fuzzy Interval Type-2 Control for an Uncertain System With Real Application , 2012, IEEE Transactions on Fuzzy Systems.

[32]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[33]  Kazuo Tanaka,et al.  Trajectory stabilization of a model car via fuzzy control , 1995 .

[34]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[35]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[36]  Jerry M. Mendel,et al.  On the Stability of Interval Type-2 TSK Fuzzy Logic Control Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[38]  Jean-Pierre Barbot,et al.  Sliding Mode Control In Engineering , 2002 .

[39]  Jerry M. Mendel,et al.  Interval type-2 fuzzy logic systems , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[40]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[41]  Bor-Sen Chen,et al.  Mixed H2/H∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach , 2000, IEEE Trans. Fuzzy Syst..

[42]  Vadim I. Utkin,et al.  A control engineer's guide to sliding mode control , 1999, IEEE Trans. Control. Syst. Technol..

[43]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[44]  Abdelaziz Hamzaoui,et al.  State observer based robust adaptive fuzzy controller for nonlinear uncertain and perturbed systems , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[45]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control - design and stability analysis , 1994 .

[46]  Franck Plestan,et al.  High-Order Sliding-Mode Controllers of an Electropneumatic Actuator: Application to an Aeronautic Benchmark , 2009, IEEE Transactions on Control Systems Technology.

[47]  Refractor.  Uncertainty , 2001, The Lancet.

[48]  J. Mendel.  Fuzzy logic systems for engineering: a tutorial , 1995, Proc. IEEE.

[49]  Avrie Levent,et al.  Robust exact differentiation via sliding mode technique , 1998, Autom..

[50]  Franck Plestan,et al.  Higher order sliding mode control based on integral sliding mode , 2007, Autom..

[51]  Renhou Li,et al.  Stability analysis and systematic design of fuzzy control systems , 2001, Fuzzy Sets Syst..

[52]  Jerry M. Mendel,et al.  Connection admission control in ATM networks using survey-based type-2 fuzzy logic systems , 2000, IEEE Trans. Syst. Man Cybern. Part C.

[53]  Jerry M. Mendel,et al.  Type-2 fuzzy sets and systems: an overview , 2007, IEEE Computational Intelligence Magazine.

[54]  Kazuo Tanaka,et al.  Parallel Distributed Compensation Based Stabilization of A 3-DOF RC Helicopter: A Tensor Product Transformation Based Approach , 2009, J. Adv. Comput. Intell. Intell. Informatics.

[55]  Antonella Ferrara,et al.  On second order sliding mode controllers , 1998 .

[56]  Type-2 Fuzzy Sets : Some Questions and Answers , 2001 .

[57]  由希 辻.  Representation , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[58]  S. Laghrouche,et al.  Multivariable practical higher order sliding mode control , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[59]  Akira Ichikawa,et al.  Application of limit fuzzy controllers to stability analysis , 1992 .

[60]  Arie Levant,et al.  Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence , 2001, IEEE Trans. Autom. Control..

[61]  Kheireddine Chafaa,et al.  Indirect adaptive interval type-2 fuzzy control for nonlinear systems , 2007, Int. J. Model. Identif. Control..

[62]  A. Levant.  Sliding order and sliding accuracy in sliding mode control , 1993 .

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

[64]  Farid Sheikholeslam,et al.  Stability analysis and design of fuzzy control systems , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[65]  Mohammed M'Saad,et al.  Direct adaptive control subject to input amplitude constraint , 2000, IEEE Trans. Autom. Control..

[66]  Ebrahim Mamdani,et al.  Applications of fuzzy algorithms for control of a simple dynamic plant , 1974 .

[67]  Mehdi Roopaei,et al.  Adaptive fuzzy sliding mode control scheme for uncertain systems , 2009 .

[68]  Yuri B. Shtessel,et al.  Smooth second-order sliding modes: Missile guidance application , 2007, Autom..

[69]  Jerry M. Mendel,et al.  A quantitative comparison of interval type-2 and type-1 fuzzy logic systems: First results , 2010, International Conference on Fuzzy Systems.

[70]  Franck Plestan,et al.  A new algorithm for high‐order sliding mode control , 2008 .

[71]  Vincent Bregeault.  Quelques contributions à la théorie de la commande par modes glissants , 2010 .

[72]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[73]  Leonid M. Fridman,et al.  Second-order sliding-mode observer for mechanical systems , 2005, IEEE Transactions on Automatic Control.

[74]  Yao Tian,et al.  Fuzzy PID Control for Intelligent Smartcar System with CCD Camera , 2011 .

[75]  K. Tang,et al.  Comparing fuzzy logic with classical controller designs , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[76]  Komi Gasso.  Identification des systèmes dynamiques non-linéaires : approche multi-modèle , 2000 .

[77]  Jerry M. Mendel,et al.  AN ARCHITECTURE FOR MAKING JUDGMENTS USING COMPUTING WITH WORDS , 2002 .

[78]  Jaime A. Moreno,et al.  A Lyapunov approach to second-order sliding mode controllers and observers , 2008, 2008 47th IEEE Conference on Decision and Control.

[79]  R. H. Cannon,et al.  Dynamics of Physical Systems , 1967 .

[80]  Abdelaziz Hamzaoui,et al.  MIMO second order sliding mode fuzzy type-2 control , 2010, 2010 IEEE International Conference on Systems, Man and Cybernetics.

[81]  Christopher Edwards,et al.  Advances in variable structure and sliding mode control , 2006 .

[82]  Kevin Guelton,et al.  Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi-Sugeno systems - A descriptor redundancy approach , 2009, Fuzzy Sets Syst..

[83]  Witold Pedrycz,et al.  Type-2 Fuzzy Logic: Theory and Applications , 2007, 2007 IEEE International Conference on Granular Computing (GRC 2007).

[84]  K. Furuta.  Sliding mode control of a discrete system , 1990 .

[85]  Sylvie Galichet,et al.  Fuzzy controllers: synthesis and equivalences , 1995, IEEE Trans. Fuzzy Syst..

[86]  Jean-Mathias Spiewak.  Contribution à la coordination de flottille de véhicules sous-marins autonomes , 2007 .

[87]  J. Buckley.  Fuzzy controller: further limit theorems for linear control rules , 1990 .

[88]  Xinghuo Yu,et al.  Terminal sliding mode control design for uncertain dynamic systems , 1998 .

[89]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[90]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[91]  Ke Zeng,et al.  A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators , 2000, IEEE Trans. Fuzzy Syst..

[92]  Jerry M. Mendel,et al.  Operations on type-2 fuzzy sets , 2001, Fuzzy Sets Syst..

[93]  W. Baumann,et al.  Feedback control of nonlinear systems by extended linearization , 1986 .

[94]  Y. Stepanenko,et al.  Adaptive control of a class of nonlinear systems with fuzzy logic , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[95]  B. Mansouri.  Contribution à la synthèse de lois de commandes en poursuite de trajectoire pour les systèmes flous de type Takagi Sugeno incertains , 2005 .

[96]  E. H. Mamdani,et al.  Advances in the linguistic synthesis of fuzzy controllers , 1976 .

[97]  W.-S. Lin,et al.  Robust adaptive sliding mode control using fuzzy modelling for a class of uncertain MIMO nonlinear systems , 2002 .

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

[99]  Ahmad B. Rad,et al.  Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems , 2009, Simul. Model. Pract. Theory.

[100]  Abdelaziz Hamzaoui,et al.  Type-2 fuzzy sliding mode control without reaching phase for nonlinear system , 2011, Eng. Appl. Artif. Intell..

[101]  Alexis Girin,et al.  Contribution à la commande non linéaire d'un système électropneumatique pour une utilisation aéronautique: application sur un benchmark dédié , 2007 .

[102]  Jerry M. Mendel,et al.  Type-2 fuzzy logic systems: type-reduction , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[103]  Tzuu-Hseng S. Li,et al.  Design of interval type-2 fuzzy sliding-mode controller , 2008, Inf. Sci..

[104]  Z. Rekasius,et al.  An alternate approach to the fixed terminal point regulator problem , 1964 .

[105]  Kazuo Tanaka,et al.  Parallel distributed compensation of nonlinear systems by Takagi-Sugeno fuzzy model , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[106]  Zhihong Man,et al.  Design of fuzzy sliding-mode control systems , 1998, Fuzzy Sets Syst..

[107]  Abdelaziz Hamzaoui,et al.  Higher order sliding fuzzy type-2 interval control for SISO uncertain nonlinear systems , 2011, 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011).

[108]  B. Pasik-Duncan,et al.  Adaptive Control , 1996, IEEE Control Systems.

[109]  Kamel Guesmi,et al.  Systematic design approach of fuzzy PID stabilizer for DC–DC converters , 2008 .

[110]  Kazuo Tanaka,et al.  Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs , 1998, IEEE Trans. Fuzzy Syst..

[111]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.