Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach

In this paper, a direct adaptive fuzzy robust control approach is proposed for single input and single output (SISO) strict-feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics and dynamical disturbances. No prior knowledge of the boundary of the nonlinear uncertainties is required. Fuzzy logic systems are used to approximate the intermediate stabilizing functions, and a stable direct adaptive fuzzy backstepping robust control approach is developed by combining the backstepping technique with the fuzzy adaptive control theory. The stability of the closed-loop system and the convergence of the system output are proved based on the small-gain theorem. Simulation studies are conducted to illustrate the effectiveness of the proposed approach.

[1]  Alberto Isidori,et al.  Nonlinear control systems: an introduction (2nd ed.) , 1989 .

[2]  Zhong-Ping Jiang,et al.  Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties , 1998, Autom..

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

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

[5]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

[6]  Bing Chen,et al.  Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes , 2005, IEEE Transactions on Fuzzy Systems.

[7]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[8]  Frank L. Lewis,et al.  Robust backstepping control of a class of nonlinear systems using fuzzy logic , 2000, Inf. Sci..

[9]  Kevin M. Passino,et al.  Stable adaptive control using fuzzy systems and neural networks , 1996, IEEE Trans. Fuzzy Syst..

[10]  J. Corriou.  Chapter 12 – Nonlinear Control , 2017 .

[11]  Sorin G. Gal,et al.  On the defect of additivity of fuzzy measures , 2002, Fuzzy Sets Syst..

[12]  Zhong-Ping Jiang,et al.  A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems , 1996, Autom..

[13]  Bor-Sen Chen,et al.  H∞ tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach , 1996, IEEE Trans. Fuzzy Syst..

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

[15]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

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

[17]  Shaocheng Tong,et al.  Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach , 2007, Fuzzy Sets Syst..

[18]  Zhong-Ping Jiang,et al.  A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics , 1999, IEEE Trans. Autom. Control..

[19]  Changjiu Zhou,et al.  Adaptive fuzzy H/sub /spl infin// stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach , 2005, IEEE Transactions on Fuzzy Systems.

[20]  Bing Chen,et al.  Adaptive Neural Control for a Class of Perturbed Strict-Feedback Nonlinear Time-Delay Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  Tsu-Tian Lee,et al.  Adaptive fuzzy control for strict-feedback canonical nonlinear systems with H infin tracking performance , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[22]  Gang Feng,et al.  Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstepping , 2005, Fuzzy Sets Syst..

[23]  Amar Goléa,et al.  Observer-based adaptive control of robot manipulators: Fuzzy systems approach , 2008, Appl. Soft Comput..

[24]  A. Isidori.  Nonlinear Control Systems , 1985 .

[25]  I. Kanellakopoulos.  Robustification tools for nonlinear control design , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

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

[27]  Z. Qu.  Robust control of nonlinear uncertain systems without generalized matching conditions , 1995, IEEE Trans. Autom. Control..

[28]  Yongming Li,et al.  Adaptive fuzzy backstepping robust control for uncertain nonlinear systems based on small-gain approach , 2010, Fuzzy Sets Syst..

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

[30]  Peng Shi,et al.  Robust Hinfinity output feedback control design for fuzzy dynamic systems with quadratic D stability constraints: An LMI approach , 2006, Inf. Sci..

[31]  Darren M. Dawson,et al.  Integrator backstepping control of a brush DC motor turning a robotic load , 1994, IEEE Trans. Control. Syst. Technol..

[32]  I. Kanellakopoulos,et al.  Adaptive nonlinear control without overparametrization , 1992 .

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

[34]  A. Isidori,et al.  Adaptive control of linearizable systems , 1989 .

[35]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

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

[37]  Bing Chen,et al.  Comments on "Adaptive Fuzzy H∞ Stabilization for Strict-Feedback Canonical Nonlinear Systems Via Backstepping and Small-Gain Approach" , 2009, IEEE Trans. Fuzzy Syst..

[38]  Zhong-Ping Jiang,et al.  A combined backstepping and small-gain approach to adaptive output feedback control , 1999, Autom..

[39]  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..