State augmented feedback controller design approach for T-S fuzzy system with complex actuator saturations

The control problem of T-S fuzzy system with actuator amplitude, rate and acceleration saturations is addressed in this paper, where state augmented feedback controller with LMIs (Liner Matrix Inequalities) constraint conditions are proposed. Dynamic decoupling method is applied to fuzzify the input magnitude saturation nonlinearity into several sub-linear systems with fuzzy rules, thus a new T-S fuzzy system with input rate and acceleration saturations can be obtained. Then PDC (parallel distributed compensation) and NPDC (non-PDC) controller are both designed for the new T-S fuzzy system. The first and second order derivatives of input variable are given to obtain an augmented fuzzy system. As the augmented system output variable, the input rate is represented by first order derivative of the input term, the rate saturation constraint is described through norm bounded method. Moreover, the polytopic approach is used to replace the second order derivative of the input term, and a state augmented feedback NPDC controller is designed, the domain of attraction optimization process is also given. Finally, two practical examples are presented to show the effectiveness of proposed method.

[1]  Jianbin Qiu,et al.  A Novel Approach to Reliable Control of Piecewise Affine Systems With Actuator Faults , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Shaocheng Tong,et al.  Output feedback robust stabilization of switched fuzzy systems with time-delay and actuator saturation , 2015, Neurocomputing.

[3]  Shaocheng Tong,et al.  Composite Adaptive Fuzzy Output Feedback Control Design for Uncertain Nonlinear Strict-Feedback Systems With Input Saturation , 2015, IEEE Transactions on Cybernetics.

[4]  Huijun Gao,et al.  Fuzzy-Model-Based Control of an Overhead Crane With Input Delay and Actuator Saturation , 2012, IEEE Transactions on Fuzzy Systems.

[5]  Peng Shi,et al.  Control of Nonlinear Networked Systems With Packet Dropouts: Interval Type-2 Fuzzy Model-Based Approach , 2015, IEEE Transactions on Cybernetics.

[6]  Emilia Fridman,et al.  Stabilisation of neutral systems with saturating control inputs , 2011, Int. J. Syst. Sci..

[7]  Huijun Gao,et al.  Robust Sampled-Data $H_{\infty}$ Control for Vehicle Active Suspension Systems , 2010, IEEE Transactions on Control Systems Technology.

[8]  Yonggang Chen,et al.  Stabilisation for switched linear systems with time-varying delay and input saturation , 2014, Int. J. Syst. Sci..

[9]  Jianbin Qiu,et al.  Static-Output-Feedback ${\mathscr H}_{\bm \infty }$ Control of Continuous-Time T - S Fuzzy Affine Systems Via Piecewise Lyapunov Functions , 2013, IEEE Transactions on Fuzzy Systems.

[10]  Shaocheng Tong,et al.  Adaptive fuzzy output-feedback control for output constrained nonlinear systems in the presence of input saturation , 2014, Fuzzy Sets Syst..

[11]  Hamid Reza Karimi,et al.  New approach to delay-dependent H∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions , 2015, J. Frankl. Inst..

[12]  Salim Labiod,et al.  Static Output Feedback Stabilization of Multiple Models Subject to Actuators Saturation , 2010 .

[13]  Wen-Jer Chang,et al.  Fuzzy control of multiplicative noised nonlinear systems subject to actuator saturation and H∞ performance constraints , 2015, Neurocomputing.

[14]  Jianbin Qiu,et al.  Approaches to T–S Fuzzy-Affine-Model-Based Reliable Output Feedback Control for Nonlinear Itô Stochastic Systems , 2017, IEEE Transactions on Fuzzy Systems.

[15]  Young Hoon Joo,et al.  LMI conditions for local stability and stabilization of continuous-time T-S fuzzy systems , 2015, International Journal of Control, Automation and Systems.

[16]  Huaping Liu,et al.  Piecewise Fuzzy Anti-Windup Dynamic Output Feedback Control of Nonlinear Processes With Amplitude and Rate Actuator Saturations , 2009, IEEE Trans. Fuzzy Syst..

[17]  Jianbin Qiu,et al.  Recent Advances on Fuzzy-Model-Based Nonlinear Networked Control Systems: A Survey , 2016, IEEE Transactions on Industrial Electronics.

[18]  Jianbin Qiu,et al.  Fuzzy-Model-Based Reliable Static Output Feedback $\mathscr{H}_{\infty }$ Control of Nonlinear Hyperbolic PDE Systems , 2016, IEEE Transactions on Fuzzy Systems.

[19]  Salim Labiod,et al.  Robust H∞ static output feedback stabilization of T-S fuzzy systems subject to actuator saturation , 2012 .

[20]  Chengzhi Yuan,et al.  Switching control of linear systems subject to asymmetric actuator saturation , 2015, Int. J. Control.

[21]  Jianbin Qiu,et al.  Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay , 2015 .

[22]  C-C Ku,et al.  Fuzzy Controller Design Subject to Actuator Saturation for Dynamic Ship Positioning Systems with Multiplicative Noises , 2010 .

[23]  Jianbin Qiu,et al.  Nonsynchronized Robust Filtering Design for Continuous-Time T–S Fuzzy Affine Dynamic Systems Based on Piecewise Lyapunov Functions , 2013, IEEE Transactions on Cybernetics.

[24]  Xiaojun Ban,et al.  LMI based control of a class of uncertain nonlinear systems with input rate saturation , 2014, 2014 International Conference on Mechatronics and Control (ICMC).

[25]  Yuechao Ma,et al.  Observer-based H∞ guaranteed cost control for uncertain singular time-delay systems with input saturation , 2016 .

[26]  PooGyeon Park,et al.  Special issue on time-delay systems and their applications , 2016 .

[27]  Jun Zhao,et al.  Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems , 2013, Syst. Control. Lett..

[28]  Ji-Chang Lo,et al.  Existence of Similarity Transformation Converting BMIs to LMIs , 2007, IEEE Transactions on Fuzzy Systems.

[29]  Hamid Reza Karimi,et al.  New results on H∞ dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information , 2014 .

[30]  Saleh Mobayen,et al.  An LMI-based robust tracker for uncertain linear systems with multiple time-varying delays using optimal composite nonlinear feedback technique , 2015 .

[31]  Li Li,et al.  Robust stabilization of T-S fuzzy discrete systems with actuator saturation via PDC and non-PDC law , 2015, Neurocomputing.

[32]  Sophie Tarbouriech,et al.  Local stabilization of linear systems under amplitude and rate saturating actuators , 2003, IEEE Trans. Autom. Control..

[33]  Zongli Lin,et al.  Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation , 2003, IEEE Trans. Fuzzy Syst..

[34]  Saleh Mobayen,et al.  Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback , 2014 .

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

[36]  Yong-Yan Cao,et al.  PARAMETER‐DEPENDENT LYAPUNOV FUNCTION APPROACH TO STABILITY ANALYSIS AND DESIGN FOR POLYTOPIC SYSTEMS WITH INPUT SATURATION , 2007 .

[37]  Chian-Song Chiu.  A Dynamic Decoupling Approach to Robust T–S Fuzzy Model-Based Control , 2014, IEEE Transactions on Fuzzy Systems.

[38]  Jianbin Qiu,et al.  A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[39]  Goshaidas Ray,et al.  Improved delay-dependent stabilization of time-delay systems with actuator saturation , 2014 .

[40]  Yun Zou,et al.  Finite-time stabilization of switched linear systems with nonlinear saturating actuators , 2014, J. Frankl. Inst..

[41]  Peter Liu,et al.  LMI-based fuzzy chaotic synchronization and communications , 2001, IEEE Trans. Fuzzy Syst..

[42]  Thor I. Fossen,et al.  Handbook of Marine Craft Hydrodynamics and Motion Control: Fossen/Handbook of Marine Craft Hydrodynamics and Motion Control , 2011 .

[43]  Guang-Ren Duan,et al.  Gain Scheduled Control of Linear Systems Subject to Actuator Saturation With Application to Spacecraft Rendezvous , 2014, IEEE Transactions on Control Systems Technology.

[44]  Xuan Li,et al.  Robust fuzzy-scheduling control for nonlinear systems subject to actuator saturation via delta operator approach , 2014, Inf. Sci..

[45]  Thor I. Fossen,et al.  Handbook of Marine Craft Hydrodynamics and Motion Control , 2011 .

[46]  Hamid Reza Karimi,et al.  Fuzzy control for Electric Power Steering System with assist motor current input constraints , 2015, J. Frankl. Inst..

[47]  Hamid Reza Karimi,et al.  Adaptive Output-Feedback Controller Design for Switched Nonlinear Stochastic Systems With a Modified Average Dwell-Time Method , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[48]  Hak-Keung Lam,et al.  Fuzzy Sampled-Data Control for Uncertain Vehicle Suspension Systems , 2014, IEEE Transactions on Cybernetics.

[49]  Dong Yue,et al.  Control Synthesis of Discrete-Time T–S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach , 2016, IEEE Transactions on Cybernetics.

[50]  Yong-Nong Chang,et al.  Robust anti-windup controller design of time-delay fuzzy systems with actuator saturations , 2011, Inf. Sci..