Nonlinear system identification using neural state space models, applicable to robust control design

REFERENCES

• BILLINGS , S. A. , JAMALUDDIN , H. B. , and CHEN , S. , 1992 , Properties of neural networks with applications to modelling non-linear dynamical systems . International Journal of Control , 55 , 193 – 224 .
   Web of Science ®Google Scholar
• BOYD , S. , and BARRATT , C. , 1991 , Linear Controller Design, Limits of Performance ( Engle wood Cliffs , NJ : Prentice-Hall )
   Google Scholar
• CHEN , S. , BILLINGS , S. , and GRANT , P. , 1990a , Nonlinear system identification using neural networks . International Journal of Control , 51 , 1191 – 1214 .
   Web of Science ®Google Scholar
• CHEN , S. , COWAN, C, BILLINGS , S. , and GRANT , P. , 1990b , Parallel recursive prediction error algorithm for training layered neural networks . International Journal of Control , 51 , 1215 – 1228 .
   Web of Science ®Google Scholar
• CYBENKO , G. , 1989 , Approximations by superpositions of a'sigmoidal function . Mathematics of Control, Signals and Systems , 2 , 183 – 192 .
   Google Scholar
• DAHLEH , M. A. , and KHAMMASH , M. H. , 1993 , Controller design for plants with structured uncertainty . Automatica , 29 , 37 – 56 .
   Web of Science ®Google Scholar
• DE MOOR , B. , VAN OVERSCHEE , P. , and SUYKENS , J. , 1991 , Subspace algorithms for system identification and stochastic realization . Proceedings of the International Symposium Recent Advances in Mathematical Theory of Systems, Control, Networks and Signal Processing , Kobe , Japan , pp. 589 – 595 .
   Google Scholar
• DOYLE , J. , PACKARD , A. , and ZHOU , K. , 1991 , Review of LFTs, LMIs, and μ . Proceedings of the 30th Conference on Decision and Control , Brighton , U.K. , pp. 1227 – 1232 .
   Google Scholar
• FLETCHER , R. , 1987 , Practical Methods of Optimization , second edition , ( Chichester , U.K. Wiley ).
   Google Scholar
• FUNAHASHI , K.-I. , 1989 , On the approximate realization of continuous mappings by neural networks . Neural Networks , 2 , 183 – 192 .
   Web of Science ®Google Scholar
• GILL , P. E. , MURRAY , W. , and WRIGHT , M. H. , 1981 , Practical Optimization ( London , U.K. Academic Press ).
   Google Scholar
• GOODWIN , G. , and SIN , K. , 1984 , Adaptive Filtering, Prediction and Control ( Englewood Cliffs , NJ : Prentice-Hall ).
   Google Scholar
• HAMMERSTROM , D. , 1993 , Working with neural networks . IEEE Spectrum , July, 46 – 53 .
   Web of Science ®Google Scholar
• HORNIK , K. , STINCHCOMBE , M. , and WHITE , H. , 1989 , Multilayer feedforward networks are universal approximators . Neural Networks , 2 , 359 – 366 .
   Web of Science ®Google Scholar
• HUNT , K. J. , SBARBARO , D. , ZBIKOWSKI , R. , and GAWTHROP , P. J. , 1992 , Neural networks for control systems-a survey . Automatica , 28 , 1083 – 1112 .
   Web of Science ®Google Scholar
• LESHNO , M. , Lin , V. Y. , PINKUS , A. , and SCHOCKEN , S. , 1993 , Multilayer feedforward networks with a nonpolynomial activation function can approximate any function . Neural Networks , 6 , 861 – 867 .
   Web of Science ®Google Scholar
• LJUNG , L. , 1979 , Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems . IEEE Transactions on Automatic Control , 24 , 36 – 50 ; 1987, System Identification Theory for the User (Englewood Cliffs, NJ Prentice-Hall) .
   Web of Science ®Google Scholar
• MACIEJOWSKI , J. M. , 1989 , Multivariable Feedback Design ( Addison-Wesley ).
   Google Scholar
• MATLAB. , 1992 , Optimization Toolbox User's Guide , MathWorks, Inc., Version 4.1.
   Google Scholar
• NARENDRA , K. S. , and PARTHASARATHY , K. , 1990 , Identification and control of dynamical systems using neural networks . IEEE Transactions on Neural Networks , 1 , 4 – 27 ; 1991, Gradient methods for the optimization of dynamical systems containing neural networks. IEEE Transactions on Neural Networks, 2, 252–262 .
   PubMedGoogle Scholar
• PACKARD , A. , and DOYLE , J. , 1993 , The complex structured singular value . Automatica , 29 , 71 – 109 .
   Web of Science ®Google Scholar
• RUMELHART , D. , HINTON , C , WILLIAMS , R. , 1986, Learning representations by back-propagating errors. Nature , 323 , 533–536.
   Web of Science ®Google Scholar
• SMITH , R. S. , DOYLE , J. , 1992 , Model validation a connection between robust control and identification . IEEE Transactions on Automatic Control , 37 , 942 – 952 .
   Web of Science ®Google Scholar
• STEINBUCH , M. , TERLOUW , J. , BOSGRA , O. , and SMIT , S. , 1992 , Uncertainty modelling and structured singular-value computation applied to an electromechanical system . Proceedings of the institution of Electrical Engineers , Pt D , 139 , 301 – 307 .
   Google Scholar
• SUYKENS , J. , DE MOOR , B. and VANDEWALLE , J. , 1993 , Neural network models as linear systems with bounded uncertainty, applicable to robust controller design . International Symposium on Nonlinear Theory and its Applications , Honolulu Hawaii , pp. 419 – 422 .
   Google Scholar
• VAN OVERSCHEE , P. , DE MOOR , B. , 1994 , N4S1D subspace algorithms for the identification of combined deterministic-stochastic systems . Automatica , 30 , 75 – 93 .
   Web of Science ®Google Scholar
• ZURADA , J. M. , 1992 , Introduction to Artificial Neural Systems ( New York West Publishing ).
   Google Scholar