Design of a fuzzy adaptive controller for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and unknown control direction

This paper aims at investigating the fuzzy adaptive control design for uncertain multivariable systems with unknown actuator nonlinearities and unknown control direction that possibly exhibit time-delay. The actuator nonlinearities involve dead-zone or backlash-like hysteresis, while the control direction is closely related to the sign of the control gain matrix. Two fuzzy adaptive controllers are proposed to deal with such an issue. The design of the first controller is mainly carried out in the free time-delay case, while the second control design is performed assuming that the system exhibits time-varying delays. Of practical interest, the adaptive compensation of the effects of the actuator nonlinearities requires neither the knowledge of their parameters nor the construction of their inverse. Furthermore, the lack of knowledge of the control direction is handled by incorporating in the control law a Nussbaum-type function. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.

[1]  Chaio-Shiung Chen,et al.  Dynamic structure adaptive neural fuzzy control for MIMO uncertain nonlinear systems , 2009, Inf. Sci..

[2]  Bing Chen,et al.  Direct adaptive fuzzy control for nonlinear systems with time-varying delays , 2010, Inf. Sci..

[3]  Shaocheng Tong,et al.  A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems , 2003, IEEE Trans. Fuzzy Syst..

[4]  Tianping Zhang,et al.  Adaptive Fuzzy Control for a Class of MIMO Nonlinear Systems with Unknown Dead-zones , 2007 .

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

[6]  Gang Tao,et al.  Adaptive control of plants with unknown dead-zones , 1994 .

[7]  Ying Zhang,et al.  Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity , 2006, IEEE Transactions on Automatic Control.

[8]  Paolo Nistri,et al.  Mathematical Models for Hysteresis , 1993, SIAM Rev..

[9]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[10]  M. Krasnosel’skiǐ,et al.  Systems with Hysteresis , 1989 .

[11]  P. Kokotovic,et al.  Continuous-time adaptive control of systems with unknown backlash , 1995, IEEE Trans. Autom. Control..

[12]  Shaocheng Tong,et al.  Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties , 2009, Inf. Sci..

[13]  Jing Zhou,et al.  Robust Adaptive Output Control of Uncertain Nonlinear Plants With Unknown Backlash Nonlinearity , 2007, IEEE Transactions on Automatic Control.

[14]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[15]  Jun Oh Jang,et al.  A deadzone compensator of a DC motor system using fuzzy logic control , 2001, IEEE Trans. Syst. Man Cybern. Syst..

[16]  Gang Tao,et al.  Discrete-time adaptive control of systems with unknown deadzones , 1995 .

[17]  E. Bai,et al.  Convergence results for an adaptive dead zone inverse , 1998 .

[18]  Kevin M. Passino,et al.  Stable multi-input multi-output adaptive fuzzy/neural control , 1999, IEEE Trans. Fuzzy Syst..

[19]  C. Su,et al.  Model reference adaptive control of continuous-time systems with an unknown input dead-zone , 2003 .

[20]  Shuzhi Sam Ge,et al.  Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

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

[22]  Shaocheng Tong,et al.  Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach , 2010, Inf. Sci..

[23]  Liu Hsu,et al.  Lyapunov-based adaptive control of MIMO systems , 2003, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

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

[25]  Shuzhi Sam Ge,et al.  Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs , 2007, Autom..

[26]  Edwin K. P. Chong,et al.  A two-layered fuzzy logic controller for systems with deadzones , 1994, IEEE Trans. Ind. Electron..

[27]  Kok Kiong Tan,et al.  A novel predictive and iterative learning control algorithm , 2003 .

[28]  Jean-Pierre Richard,et al.  Stability of some linear systems with delays , 1999, IEEE Trans. Autom. Control..

[29]  Yeong-Chan Chang,et al.  Robust tracking control for nonlinear MIMO systems via fuzzy approaches , 2000, Autom..

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

[31]  Masahiro Oya,et al.  Stable adaptive fuzzy control of nonlinear systems preceded by unknown backlash-like hysteresis , 2003, IEEE Trans. Fuzzy Syst..

[32]  Liu Hsu,et al.  Lyapunov/Passivity-Based Adaptive Control of Relative Degree Two MIMO Systems With an Application to Visual Servoing , 2006, IEEE Transactions on Automatic Control.

[33]  Liu Hsu,et al.  Lyapunov/passivity-based adaptive control of relative degree two MIMO systems with an application to visual servoing , 2006 .

[34]  Yihui Jin,et al.  Stable adaptive control of backlash nonlinear system with bounded disturbances , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

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

[36]  Yan-Jun Liu,et al.  Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems , 2007, Inf. Sci..

[37]  S. Ge,et al.  Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[38]  Keng Peng Tee,et al.  Approximation-based control of nonlinear MIMO time-delay systems , 2007, Autom..

[39]  Gang Tao,et al.  Discrete-time adaptive control of plants with unknown output dead-zones , 1995, Autom..

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

[41]  Chun-Yi Su,et al.  Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis , 2000, IEEE Trans. Autom. Control..

[42]  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.

[43]  Ying Zhang,et al.  Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis , 2004, IEEE Trans. Autom. Control..

[44]  Jer-Guang Hsieh,et al.  On the stability of uncertain systems with multiple time-varying delays , 1997, IEEE Trans. Autom. Control..

[45]  Farshad Khorrami,et al.  Adaptive control of systems with backlash hysteresis at the input , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[46]  Changjiu Zhou,et al.  Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach , 2005, Inf. Sci..

[47]  Vladimir L. Kharitonov,et al.  Lyapunov‐Krasovskii functionals for additional dynamics , 2003 .

[48]  Amar Goléa,et al.  Stable indirect fuzzy adaptive control , 2003, Fuzzy Sets Syst..

[49]  I. Mayergoyz The Classical Preisach Model of Hysteresis , 1991 .

[50]  Shuzhi Sam Ge,et al.  Adaptive neural network control of nonlinear systems with unknown time delays , 2003, IEEE Trans. Autom. Control..

[51]  A. Boulkroune,et al.  Adaptive fuzzy control for MIMO nonlinear systems with unknown dead-zone , 2008, 2008 4th International IEEE Conference Intelligent Systems.

[52]  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).

[53]  M.S. de Queiroz,et al.  Adaptive control for a class of MIMO nonlinear systems with non-symmetric input matrix , 2004, Proceedings of the 2004 IEEE International Conference on Control Applications, 2004..

[54]  Xudong Ye,et al.  Adaptive nonlinear output-feedback control with unknown high-frequency gain sign , 2001, IEEE Trans. Autom. Control..

[55]  R. Nussbaum Some remarks on a conjecture in parameter adaptive control , 1983 .

[56]  Frank L. Lewis,et al.  Deadzone compensation in motion control systems using adaptive fuzzy logic control , 1999, IEEE Trans. Control. Syst. Technol..

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

[58]  Tzuu-Hseng S. Li,et al.  EP-based kinematic control and adaptive fuzzy sliding-mode dynamic control for wheeled mobile robots , 2009, Inf. Sci..

[59]  K. Narendra,et al.  A new adaptive law for robust adaptation without persistent excitation , 1987 .

[60]  Bing Chen,et al.  Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients , 2008, Inf. Sci..

[61]  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).

[62]  Frank L. Lewis,et al.  Deadzone compensation in motion control systems using neural networks , 2000, IEEE Trans. Autom. Control..

[63]  Gang Tao,et al.  Adaptive control of plants with unknown hystereses , 1995 .

[64]  Abdesselem Boulkroune,et al.  General adaptive observer-based fuzzy control of uncertain nonaffine systems , 2006 .

[65]  Er-Wei Bai Adaptive Dead Zone Inverses for Possibly Nonlinear Control Systems , 2001 .

[66]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Tracking Control of MIMO Nonlinear Uncertain Systems , 2007, IEEE Transactions on Fuzzy Systems.

[67]  Xin-Ping Guan,et al.  Observer-based adaptive control for uncertain time-delay systems , 2006, Inf. Sci..

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

[69]  Frank L. Lewis,et al.  Adaptive Control of Nonsmooth Dynamic Systems , 2001 .

[70]  Jing Zhou,et al.  Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis , 2007, Autom..

[71]  H. Chekireb,et al.  DIRECT ADAPTIVE FUZZY CONTROL OF NONLINEAR SYSTEM CLASS WITH APPLICATIONS , 2003 .

[72]  Chun-Yi Su,et al.  Robust adaptive control of a class of nonlinear systems with unknown dead-zone , 2004, Autom..