A time/space separation based 3D fuzzy modeling approach for nonlinear spatially distributed systems

Spatially distributed systems (SDSs) are usually infinite-dimensional spatio-temporal systems with unknown nonlinearities. Therefore, to model such systems is difficult. In real applications, a low-dimensional model is required. In this paper, a time/space separation based 3D fuzzy modeling approach is proposed for unknown nonlinear SDSs using input-output data measurement. The main characteristics of this approach is that time/space separation and time/space reconstruction are fused into a novel 3D fuzzy system. The modeling methodology includes two stages. The first stage is 3D fuzzy structure modeling which is based on Mamdani fuzzy rules. The consequent sets of 3D fuzzy rules consist of spatial basis functions estimated by Karhunen-Love decomposition. The antecedent sets of 3D fuzzy rules are used to construct temporal coefficients. Going through 3D fuzzy rule inference, each rule realizes time/space synthesis. The second stage is parameter identification of 3D fuzzy system using particle swarm optimization algorithm. After an operation of defuzzification, the output of the 3D fuzzy system can reconstruct the spatio-temporal dynamics of the system. The model is suitable for the prediction and control design of the SDS since it is of low-dimension and simple nonlinear structure. The simulation and experiment are presented to show the effectiveness of the proposed modeling approach.

[1]  Shaoyuan Li,et al.  Embedded Interval Type-2 T-S Fuzzy Time/Space Separation Modeling Approach for Nonlinear Distributed Parameter System , 2011 .

[2]  Yuanqing Xia,et al.  Fault Detection for T–S Fuzzy Discrete Systems in Finite-Frequency Domain , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  E. Zafiriou,et al.  Model reduction for optimization of rapid thermal chemical vapor deposition systems , 1998 .

[4]  Panagiotis D. Christofides,et al.  Nonlinear and Robust Control of Pde Systems , 2001 .

[5]  Shaoyuan Li,et al.  SVR Learning-Based Spatiotemporal Fuzzy Logic Controller for Nonlinear Spatially Distributed Dynamic Systems , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[6]  W. Schiesser.  The Numerical Method of Lines: Integration of Partial Differential Equations , 1991 .

[7]  W. Ray,et al.  Identification and control of distributed parameter systems by means of the singular value decomposition , 1995 .

[8]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[9]  Shaoyuan Li,et al.  Analytical Study and Stability Design of a 3-D Fuzzy Logic Controller for Spatially Distributed Dynamic Systems , 2008, IEEE Transactions on Fuzzy Systems.

[10]  P. Christofides,et al.  Finite-dimensional approximation and control of non-linear parabolic PDE systems , 2000 .

[11]  Shaoyuan Li,et al.  A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes , 2014, Appl. Soft Comput..

[12]  Hao Ying,et al.  Fuzzy Control and Modeling: Analytical Foundations and Applications , 2000 .

[13]  Abdelhamid Rabhi,et al.  Detection of impending vehicle rollover with road bank angle consideration using a robust fuzzy observer , 2015, Int. J. Autom. Comput..

[14]  Han-Xiong Li,et al.  Hybrid Karhunen-Loeve/neural modelling for a class of distributed parameter systems , 2008, Int. J. Intell. Syst. Technol. Appl..

[15]  Stephen A. Billings,et al.  Identification of finite dimensional models of infinite dimensional dynamical systems , 2002, Autom..

[16]  Stephen A. Billings,et al.  State-Space Reconstruction and Spatio-Temporal Prediction of Lattice Dynamical Systems , 2007, IEEE Transactions on Automatic Control.

[17]  J. Zarei,et al.  Unknown Input Observer Design for Interval Type-2 T–S Fuzzy Systems With Immeasurable Premise Variables , 2017, IEEE Transactions on Cybernetics.

[18]  Chenkun Qi,et al.  A spatio-temporal Volterra modeling approach for a class of distributed industrial processes , 2009 .

[19]  Shaoyuan Li,et al.  Model-based predictive control for spatially-distributed systems using dimensional reduction models , 2011, Int. J. Autom. Comput..

[20]  Ghazal Montaseri,et al.  Predictive control of uncertain nonlinear parabolic PDE systems using a Galerkin/neural-network-based model , 2012 .

[21]  Shaoyuan Li,et al.  A Three-Dimensional Fuzzy Control Methodology for a Class of Distributed Parameter Systems , 2007, IEEE Transactions on Fuzzy Systems.

[22]  Jianbin Qiu,et al.  Unknown Input Observer Design for Interval Type-2 T-S Fuzzy Systems With Immeasurable Premise Variables , 2017, IEEE Trans. Cybern..

[23]  Qingyun Wang,et al.  Adaptive fuzzy synchronization for a class of chaotic systems with unknown nonlinearities and disturbances , 2012, Nonlinear Dynamics.

[24]  Chenkun Qi,et al.  A LS-SVM modeling approach for nonlinear distributed parameter processes , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[25]  Imad Benacer,et al.  Extracting parameters of OFET before and after threshold voltage using genetic algorithms , 2016, Int. J. Autom. Comput..

[26]  Fuzhang Zhao,et al.  Optimized Algorithm for Particle Swarm Optimization , 2016 .

[27]  Raymond A. Adomaitis.  RTCVD Model Reduction: A Collocation on Empirical Eigenfunctions Approach , 1995 .

[28]  Li Shao-yuan.  Time-space ARX modeling and predictive control for distributed parameter system , 2011 .

[29]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[30]  Huaicheng Yan,et al.  Hybrid neural network predictor for distributed parameter system based on nonlinear dimension reduction , 2016, Neurocomputing.

[31]  Chenkun Qi,et al.  A time/space separation-based Hammerstein modeling approach for nonlinear distributed parameter processes , 2009, Comput. Chem. Eng..

[32]  P. Christofides,et al.  Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes , 2002 .

[33]  Chenkun Qi,et al.  A Karhunen-Loève Decomposition-Based Wiener Modeling Approach for Nonlinear Distributed Parameter Processes , 2008 .

[34]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[35]  Karlene A. Hoo,et al.  System identification and model-based control for distributed parameter systems , 2004, Comput. Chem. Eng..

[36]  XU Yun-yan.  Hammerstein model for distributed parameter system of micro-cantilever in atomic-force microscope , 2015 .

[37]  Parlitz,et al.  Prediction of spatiotemporal time series based on reconstructed local states , 2000, Physical review letters.

[38]  Chenkun Qi,et al.  Modeling of distributed parameter systems for applications—A synthesized review from time–space separation , 2010 .