Indirect adaptive fuzzy control of nonlinear descriptor systems

Abstract This paper focuses on indirect adaptive fuzzy control of nonlinear descriptor systems described by both uncertain algebraic and differential equations aiming to guarantee asymptotic tracking of a regular and impulse-free descriptor reference model. The proposed controller exploits the universal approximation capability of Takagi–Sugeno–Kang (TSK) fuzzy models for the identification of the unknown system dynamics. More specifically, it is assumed that only the system order is known while all the dynamical equations of the system are completely unknown. In the proposed method, the asymptotic tracking of the reference model is guaranteed by suitable adaptation laws for the parameters of the TSK fuzzy model. Simulation results are presented to demonstrate the effectiveness of the proposed method.

[1]  Daniel W. C. Ho,et al.  Sliding mode control of singular stochastic hybrid systems , 2010, Autom..

[2]  Xian Zhang,et al.  Fuzzy-Model-Based ${{\cal D}}$-Stability and Nonfragile Control for Discrete-Time Descriptor Systems With Multiple Delays , 2014, IEEE Transactions on Fuzzy Systems.

[3]  Robert Babuška,et al.  COMPOSITE ADAPTIVE FUZZY CONTROL , 2005 .

[4]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[5]  Alberto Isidori,et al.  Robust Output Regulation for a Class of Linear Differential-Algebraic Systems , 2018, IEEE Control Systems Letters.

[6]  Shaocheng Tong,et al.  Adaptive Fuzzy Decentralized Control for Large-Scale Nonlinear Systems With Time-Varying Delays and Unknown High-Frequency Gain Sign , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Masaki Inoue,et al.  State-space H∞ controller design for descriptor systems , 2015, Autom..

[8]  Yan Wang,et al.  Robust Fuzzy Control of a Class of Nonlinear Descriptor Systems with , 2004 .

[9]  A. Laub,et al.  The linear-quadratic optimal regulator for descriptor systems , 1987 .

[10]  João Yoshiyuki Ishihara,et al.  On the Lyapunov theorem for singular systems , 2002, IEEE Trans. Autom. Control..

[11]  Mei Fang.  Delay-dependent Robust H∞ Control for Uncertain Singular Systems with State Delay , 2009 .

[12]  Bijnan Bandyopadhyay,et al.  Robust nonovershooting tracking controller for descriptor systems , 2018, Eur. J. Control.

[13]  Guang-Hong Yang,et al.  A New Sensor Fault Isolation Method for T–S Fuzzy Systems , 2017, IEEE Transactions on Cybernetics.

[14]  Kazuo Tanaka,et al.  Fuzzy descriptor systems and nonlinear model following control , 2000, IEEE Trans. Fuzzy Syst..

[15]  Xiaoping Liu.  Asymptotic output tracking of nonlinear differential-algebraic control systems , 1998, Autom..

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

[17]  Yonggui Kao,et al.  Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances , 2017, Autom..

[18]  Mohsen Razzaghi,et al.  Optimal control of singular systems VIA legendre series , 1998, Int. J. Comput. Math..

[19]  Salim Labiod,et al.  Direct adaptive fuzzy control for a class of MIMO nonlinear systems , 2007, Int. J. Syst. Sci..

[20]  F. Lewis.  A survey of linear singular systems , 1986 .

[22]  Anuradha M. Annaswamy,et al.  Adaptive control of continuous time systems with convex/concave parametrization , 1998, Autom..

[23]  Saeed Gazor,et al.  Hybrid adaptive fuzzy identification and control of nonlinear systems , 2002, IEEE Trans. Fuzzy Syst..

[24]  Ju H. Park,et al.  Reliable dissipative control for Markov jump systems using an event-triggered sampling information scheme , 2017 .

[25]  C. L. Philip Chen,et al.  Robust Adaptive Fuzzy Control of Nonlinear Systems with Unknown and Time‐Varying Saturation , 2015 .

[26]  Jinde Cao,et al.  Network-Based Quantized Control for Fuzzy Singularly Perturbed Semi-Markov Jump Systems and its Application , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Yuanguo Zhu,et al.  Stability and optimal control for uncertain continuous-time singular systems , 2017, Eur. J. Control.

[28]  Youyi Wang,et al.  Output Feedback Fuzzy Controller Design With Local Nonlinear Feedback Laws for Discrete-Time Nonlinear Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[29]  Shaocheng Tong,et al.  Observer-based adaptive fuzzy control for SISO nonlinear systems , 2004, Fuzzy Sets Syst..

[30]  Hongbin Zhang,et al.  Mixed H∞ and passive control for a class of nonlinear switched systems with average dwell time via hybrid control approach , 2018, J. Frankl. Inst..

[31]  J. Abdul Samath,et al.  Optimal control for nonlinear singular systems with quadratic performance using neural networks , 2007, Appl. Math. Comput..

[32]  Shengyuan Xu,et al.  Slow State Variables Feedback Stabilization for Semi-Markov Jump Systems With Singular Perturbations , 2018, IEEE Transactions on Automatic Control.

[33]  Euntai Kim,et al.  Output feedback tracking control of robot manipulators with model uncertainty via adaptive fuzzy logic , 2004, IEEE Trans. Fuzzy Syst..

[34]  Victor Sreeram,et al.  Fuzzy-Model-Based Nonfragile Control for Nonlinear Singularly Perturbed Systems With Semi-Markov Jump Parameters , 2018, IEEE Transactions on Fuzzy Systems.

[35]  Ali Akbarzadeh Kalat,et al.  Observer-based robust composite adaptive fuzzy control by uncertainty estimation for a class of nonlinear systems , 2017, Neurocomputing.

[36]  Huaguang Zhang,et al.  Stability Analysis of T–S Fuzzy Control Systems by Using Set Theory , 2015, IEEE Transactions on Fuzzy Systems.

[37]  Shaocheng Tong,et al.  Adaptive fuzzy decentralized control fora class of large-scale nonlinear systems , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[38]  Ju H. Park,et al.  Reliable passive control for singular systems with time-varying delays , 2013 .

[39]  Ali Akbarzadeh Kalat,et al.  Radial Pole Paths SVSC for Linear Time Invariant Multi Input Systems with Constrained Inputs , 2020 .

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

[41]  Michel Basset,et al.  State Feedback Fuzzy Adaptive Control for Active Shimmy Damping , 2011, Eur. J. Control.

[42]  Ali Akbarzadeh Kalat,et al.  Soft Variable Structure Control of Linear Systems via Desired Pole Paths , 2018, Inf. Technol. Control..

[43]  Heydar Toossian Shandiz,et al.  Adaptive feedback control for linear singular systems , 2014 .

[44]  Guang-Hong Yang,et al.  Reliable State Feedback Control of T–S Fuzzy Systems With Sensor Faults , 2015, IEEE Transactions on Fuzzy Systems.