Passive Fuzzy Control Design for a Class of Nonlinear Distributed Parameter Systems with Time-varying Delay

This paper is devoted to studying the issue of passive fuzzy controller design for a class of nonlinear distributed parameter systems represented by semi-linear parabolic partial differential equations. The main objective of this paper is to develop two kinds of fuzzy controllers, one is static output feedback controller (SOFC), the other is dynamic output feedback controller (DOFC), which can guarantee both the stability and passivity of the designed closed-loop system. For the purpose of achieving the anticipated target, in this paper, the semi-linear parabolic PDE systems are assumed to be exactly represented by a Takagi-Sugeno (T-S) fuzzy parabolic PDE model. Furthermore, two examples are given to demonstrate the effectiveness of the controller design scheme.

[1]  Guanrong Chen,et al.  Fuzzy impulsive control of chaotic systems based on TS fuzzy model , 2009 .

[2]  Jianbin Qiu,et al.  A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Fuzzy Systems.

[3]  Yao Yu,et al.  Mixed H2/H∞ fuzzy proportional-spatial integral control design for a class of nonlinear distributed parameter systems , 2017, Fuzzy Sets Syst..

[4]  Diyi Chen,et al.  Application of Takagi–Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization , 2013 .

[5]  Anton S. Shiriaev,et al.  The notion of V-detectability and stabilization of invariant sets of nonlinear systems☆ , 2000 .

[6]  Mrdjan J. Jankovic,et al.  Constructive Nonlinear Control , 2011 .

[7]  Huai-Ning Wu,et al.  Some extended Wirtinger's inequalities and distributed proportional-spatial integral control of distributed parameter systems with multi-time delays , 2015, J. Frankl. Inst..

[8]  Huijun Gao,et al.  Stabilization of Nonlinear Systems Under Variable Sampling: A Fuzzy Control Approach , 2007, IEEE Transactions on Fuzzy Systems.

[9]  Han-Xiong Li,et al.  Fuzzy Boundary Control Design for a Class of Nonlinear Parabolic Distributed Parameter Systems , 2014, IEEE Transactions on Fuzzy Systems.

[10]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .

[11]  Wen-Jer Chang,et al.  Fuzzy Control for Discrete Passive Affine T-S Fuzzy Systems with Observer Feedback , 2007, ICIC.

[12]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[13]  Ju H. Park,et al.  Further Results on Stabilization of Chaotic Systems Based on Fuzzy Memory Sampled-Data Control , 2018, IEEE Transactions on Fuzzy Systems.

[14]  W. Zheng,et al.  On Passivity analysis of fuzzy time-varying delayed systems , 2009, 2009 7th Asian Control Conference.

[15]  Wei Lin,et al.  Robust passivity and feedback design for minimum-phase nonlinear systems with structural uncertainty , 1999, Autom..

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

[17]  Enric Fossas,et al.  Feedback passivity of nonlinear discrete-time systems with direct input-output link, , 2004, Autom..

[18]  Huijun Gao,et al.  LMI-based H∞ synchronization of second-order neutral master-slave systems using delayed output feedback control , 2009 .

[19]  Wen‐Jer Chang,et al.  Delay dependent passive fuzzy control design for synchronous generator with multiplicative noise , 2008, 2008 SICE Annual Conference.

[20]  Huai-Ning Wu,et al.  Fuzzy Control for Nonlinear Time-Delay Distributed Parameter Systems Under Spatially Point Measurements , 2019, IEEE Transactions on Fuzzy Systems.

[21]  Tingwen Huang,et al.  Analysis and Control of Output Synchronization for Complex Dynamical Networks , 2018 .

[22]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[23]  Han-Xiong Li,et al.  Exponential Stabilization for a Class of Nonlinear Parabolic PDE Systems via Fuzzy Control Approach , 2012, IEEE Transactions on Fuzzy Systems.

[24]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[25]  Yang Liu,et al.  A New Fuzzy Impulsive Control of Chaotic Systems Based on T–S Fuzzy Model , 2011, IEEE Transactions on Fuzzy Systems.

[26]  Lei Guo,et al.  Passivity and Stability Analysis of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions , 2011, IEEE Transactions on Neural Networks.

[27]  Euntai Kim,et al.  New approaches to relaxed quadratic stability condition of fuzzy control systems , 2000, IEEE Trans. Fuzzy Syst..