Nonlinear System Representation

The sections in this article are 1 Input–Output System Representation 2 Nonlinear Differential Algebraic Representation 3 Volterra Representation 4 State-Space Representation 5 Bilinear Representation 6 Narma Representation 7 Fuzzy-Logic Nonlinear Representation 8 Nonlinear Representation Using Neural Networks 9 Model-Free Representation 10 Features of Nonlinear Representations 11 Example 12 Concluding Remarks 13 Acknowledgment

[1]  Sahjendra N. Singh.  A modified algorithm for invertibility in nonlinear systems , 1981 .

[2]  Tommy W. S. Chow,et al.  Blind identification of quadratic nonlinear models using neural networks with higher order cumulants , 2000, IEEE Trans. Ind. Electron..

[3]  Tommy W. S. Chow,et al.  A new method in determining initial weights of feedforward neural networks for training enhancement , 1997, Neurocomputing.

[4]  Chuen-Chien Lee.  FUZZY LOGIC CONTROL SYSTEMS: FUZZY LOGIC CONTROLLER - PART I , 1990 .

[5]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

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

[7]  Tommy W. S. Chow,et al.  A weight initialization method for improving training speed in feedforward neural network , 2000, Neurocomputing.

[8]  J J Hopfield,et al.  Learning algorithms and probability distributions in feed-forward and feed-back networks. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Chuen-Chien Lee,et al.  Fuzzy logic in control systems: fuzzy logic controller. II , 1990, IEEE Trans. Syst. Man Cybern..

[10]  M. Vidyasagar,et al.  Nonlinear systems analysis (2nd ed.) , 1993 .

[11]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[12]  R. de Figueiredo.  The Volterra and Wiener theories of nonlinear systems , 1982, Proceedings of the IEEE.

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

[14]  P. Paraskevopoulos,et al.  A new orthogonal series approach to state space analysis of bilinear systems , 1994, IEEE Trans. Autom. Control..

[15]  David E. Thompson.  Design Analysis: Mathematical Modeling of Nonlinear Systems , 1999 .

[16]  B. H. Wang,et al.  Learning fuzzy logic control: an indirect control approach , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[17]  L. Yang.  Fuzzy Logic with Engineering Applications , 1999 .

[18]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[19]  Yoh-Han Pao,et al.  Stochastic choice of basis functions in adaptive function approximation and the functional-link net , 1995, IEEE Trans. Neural Networks.

[20]  Tommy W. S. Chow,et al.  Functional Approximation of Higher-Order Neural Networks , 1996 .

[21]  I. J. Leontaritis,et al.  Input-output parametric models for non-linear systems Part II: stochastic non-linear systems , 1985 .

[22]  C C Lee,et al.  FUZZY LOGIC IN CONTROL SYSTEM FUZZY LOGIC CONTROLLER-PART II , 1990 .

[23]  George-Othon Glentis,et al.  Efficient algorithms for Volterra system identification , 1999, IEEE Trans. Signal Process..

[24]  A. U. Levin,et al.  Recursive identification using feedforward neural networks , 1995 .

[25]  C. L. Nikias,et al.  Higher-order spectra analysis : a nonlinear signal processing framework , 1993 .

[26]  Julius S. Bendat,et al.  Engineering Applications of Correlation and Spectral Analysis , 1980 .

[27]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[28]  Eduardo D. Sontag,et al.  Realization Theory of Discrete-Time Nonlinear Systems: Part I - The Bounded Case , 1979 .