Structures, Fields and Methods of Identification of Nonlinear Static Systems in the Conditions of Uncertainty

Author(s)
Nikolay Karabutov

ABSTRACT

The field of structures on set of secants is offered and methods of its construction for various classes of one-valued nonlinearities of static systems are considered. The analysis of structural properties of system is fulfilled on specially generated set of data. Representation on which modification it is possible to judge to nonlinear structure of static systems is introduced. It is shown, that structures of nonlinear static systems have a special V-point. The adaptive algorithm of an estimation of structure of nonlinearity on a class poly-nomial function is offered.

The field of structures on set of secants is offered and methods of its construction for various classes of one-valued nonlinearities of static systems are considered. The analysis of structural properties of system is fulfilled on specially generated set of data. Representation on which modification it is possible to judge to nonlinear structure of static systems is introduced. It is shown, that structures of nonlinear static systems have a special V-point. The adaptive algorithm of an estimation of structure of nonlinearity on a class poly-nomial function is offered.

Cite this paper

nullN. Karabutov, "Structures, Fields and Methods of Identification of Nonlinear Static Systems in the Conditions of Uncertainty,"*Intelligent Control and Automation*, Vol. 1 No. 2, 2010, pp. 59-67. doi: 10.4236/ica.2010.12007.

nullN. Karabutov, "Structures, Fields and Methods of Identification of Nonlinear Static Systems in the Conditions of Uncertainty,"

References

[1] N. S. Rajbman and V. M. Chadeev, “Building of models of processes of manufacture,” Energy, Moscow, 1975.

[2] L. Ljung, “System Identification: Theory for User,” Prentice-Hall, Englewood Cliffs, New Jersey, 1987.

[3] Е. К. Berndt, В. Н. Hall, R. E. Hall, and J. A. Hausman, “Estimation and Inference in Nonlinear Structural Models,” Annals of Economic and Social Measurement, Vol. 3, No. 4, 1974, pp. 653-665.

[4] J. Madár, J. Abonyi and F. Szeifert, “Genetic Programming for the Identification of Nonlinear Input?Output Models,” Industrial & Engineering Chemistry Research, Vol. 44, No. 9, 2005, pp. 3178-3186.

[5] B. McKay, M. Willis, D. Searson, and G.Montague, “Non-Linear Continuum Regression Using Genetic Programming,” 2005. http://www.staff.ncl.ac.uk/d.p.searson/ docs/NLCR_GP3.pdf

[6] L. Ljung, “System Identification: Nonlinear Models,” Berkeley, 2005.

[7] G. R. Liu, “Nonlinear identification and control. A Neural Network Approach,” Springer-Verlag, London, 2001.

[8] M. Norgaard, O. Ravn, N. K. Poulsen and L. K. Hansen, “Neural Networks for Modelling and Control of Dynamic Systems: A Practitioner’s Handbook,” Springer-Verlag, London, 2001.

[9] G. W. Irwin, K. Warwick and K. J. Hunt, Eds., “Neural Network Applications in Control,” The Institution of Electrical Engineers, London, 1995.

[10] G. Dreyfus, “Neural Networks: Methodology and Applications,” Springer-Verlag, Berlin, Heidelberg, 2005.

[11] N. Sundararajan, P. Saratchandran and Y. W. Lu, “Radial Basis Function Neural Networks with Sequential Learning: MRAN and its Applications,” World Scientific Publishing Co, Singapore, 1999.

[12] E. Righeto, L. H. M. Grassi and J. A. Pereira, “Nonlinear Plant Identification by Wavelets,” ABCM Symposium Series in Mechatronics, Vol. 1, 2004, pp. 392-398.

[13] T. Sato, and M. Sato, “Structural Identification Using Neural Network and Kalman Filter Algorithms,” Structural Engineer/Earthquake Engineer, JSCE, Vol. 14, No. 1, 1997, pp. 23s -32s.

[14] S. F. Masri, J. P. Caffrey, T. K. Caughey, A. W Smyth and A. G. Chassiakos, “Direct Identification of the State Equation in Complex Nonlinear Systems,” ICTAM04- Complex Nonlinear Systems, 2003, pp. 1-2.

[15] L.A. Aguirre, M. F. S. Barroso, R. R. Saldanha and E. M. A. M. Mendes, “Imposing Steady-State Performance on Identified Nonlinear Polynomial Models by Means of Constrained Parameter Estimation,” IЕЕE Proceedings of Control Theory and Applications, Vol. 151, No. 2, 2004, pp. 174-179.

[16] V. M. Chadeev and V. B. Ilyushin, “Identification Technique Concerning a Priori Information on Plant Parameters,” Proceedings of the V International Conference “System Identification and Control Problems” SICPRO’06, Institute of Control Sciences, Moscow, 30 January-2 February 2006, pp. 1091-1105.

[17] S. M. Spottswood, “Identification of Nonlinear Parameters from Experimental Data for Reduced Order Models,” University of Cincinnati, Cincinnati, 2006.

[18] M. Espinoza, J.A.K. Suykens and B. De Moor, “Kernel Based Partially Linear Models and Nonlinear Identification,” IEEE Transactions on Automatic Control, Vol. 50, No. 10, 2005, pp. 1602-1606.

[19] D. Graupe, “Identification of Systems,” Robert E. Krieger Publishing Co., Huntington, New York, 1976.

[20] M. A. Ajzerman, “About One Problem, a Concerning Stability ‘in Big’ Dynamic Systems,” Successes of Mathematical Sciences, Vol. 4, 1949, pp. 186-188.

[21] N. N. Karabutov, “Structural System Identification: Information Structure Analysis,” URSS/Izd. Dom “Librokom”, Moscow, 2009.

[22] N. N. Karabutov, “Selection of the Structure of a Model in Processing the Results of Measurements in Control Systems,” Measurement Techniques, Vol. 51, No. 9, 2008, pp. 960-966.

[23] N. N. Karabutov, “Structure Field Construction for Nonlinear Static Systems Based on Measurement Data Processing,” Measurement Techniques, Vol. 52, No. 12, 2009, pp. 1281-1288.

[1] N. S. Rajbman and V. M. Chadeev, “Building of models of processes of manufacture,” Energy, Moscow, 1975.

[2] L. Ljung, “System Identification: Theory for User,” Prentice-Hall, Englewood Cliffs, New Jersey, 1987.

[3] Е. К. Berndt, В. Н. Hall, R. E. Hall, and J. A. Hausman, “Estimation and Inference in Nonlinear Structural Models,” Annals of Economic and Social Measurement, Vol. 3, No. 4, 1974, pp. 653-665.

[4] J. Madár, J. Abonyi and F. Szeifert, “Genetic Programming for the Identification of Nonlinear Input?Output Models,” Industrial & Engineering Chemistry Research, Vol. 44, No. 9, 2005, pp. 3178-3186.

[5] B. McKay, M. Willis, D. Searson, and G.Montague, “Non-Linear Continuum Regression Using Genetic Programming,” 2005. http://www.staff.ncl.ac.uk/d.p.searson/ docs/NLCR_GP3.pdf

[6] L. Ljung, “System Identification: Nonlinear Models,” Berkeley, 2005.

[7] G. R. Liu, “Nonlinear identification and control. A Neural Network Approach,” Springer-Verlag, London, 2001.

[8] M. Norgaard, O. Ravn, N. K. Poulsen and L. K. Hansen, “Neural Networks for Modelling and Control of Dynamic Systems: A Practitioner’s Handbook,” Springer-Verlag, London, 2001.

[9] G. W. Irwin, K. Warwick and K. J. Hunt, Eds., “Neural Network Applications in Control,” The Institution of Electrical Engineers, London, 1995.

[10] G. Dreyfus, “Neural Networks: Methodology and Applications,” Springer-Verlag, Berlin, Heidelberg, 2005.

[11] N. Sundararajan, P. Saratchandran and Y. W. Lu, “Radial Basis Function Neural Networks with Sequential Learning: MRAN and its Applications,” World Scientific Publishing Co, Singapore, 1999.

[12] E. Righeto, L. H. M. Grassi and J. A. Pereira, “Nonlinear Plant Identification by Wavelets,” ABCM Symposium Series in Mechatronics, Vol. 1, 2004, pp. 392-398.

[13] T. Sato, and M. Sato, “Structural Identification Using Neural Network and Kalman Filter Algorithms,” Structural Engineer/Earthquake Engineer, JSCE, Vol. 14, No. 1, 1997, pp. 23s -32s.

[14] S. F. Masri, J. P. Caffrey, T. K. Caughey, A. W Smyth and A. G. Chassiakos, “Direct Identification of the State Equation in Complex Nonlinear Systems,” ICTAM04- Complex Nonlinear Systems, 2003, pp. 1-2.

[15] L.A. Aguirre, M. F. S. Barroso, R. R. Saldanha and E. M. A. M. Mendes, “Imposing Steady-State Performance on Identified Nonlinear Polynomial Models by Means of Constrained Parameter Estimation,” IЕЕE Proceedings of Control Theory and Applications, Vol. 151, No. 2, 2004, pp. 174-179.

[16] V. M. Chadeev and V. B. Ilyushin, “Identification Technique Concerning a Priori Information on Plant Parameters,” Proceedings of the V International Conference “System Identification and Control Problems” SICPRO’06, Institute of Control Sciences, Moscow, 30 January-2 February 2006, pp. 1091-1105.

[17] S. M. Spottswood, “Identification of Nonlinear Parameters from Experimental Data for Reduced Order Models,” University of Cincinnati, Cincinnati, 2006.

[18] M. Espinoza, J.A.K. Suykens and B. De Moor, “Kernel Based Partially Linear Models and Nonlinear Identification,” IEEE Transactions on Automatic Control, Vol. 50, No. 10, 2005, pp. 1602-1606.

[19] D. Graupe, “Identification of Systems,” Robert E. Krieger Publishing Co., Huntington, New York, 1976.

[20] M. A. Ajzerman, “About One Problem, a Concerning Stability ‘in Big’ Dynamic Systems,” Successes of Mathematical Sciences, Vol. 4, 1949, pp. 186-188.

[21] N. N. Karabutov, “Structural System Identification: Information Structure Analysis,” URSS/Izd. Dom “Librokom”, Moscow, 2009.

[22] N. N. Karabutov, “Selection of the Structure of a Model in Processing the Results of Measurements in Control Systems,” Measurement Techniques, Vol. 51, No. 9, 2008, pp. 960-966.

[23] N. N. Karabutov, “Structure Field Construction for Nonlinear Static Systems Based on Measurement Data Processing,” Measurement Techniques, Vol. 52, No. 12, 2009, pp. 1281-1288.