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COMPARATIVE ANALYSIS OF KOLMOGOROV ANN AND PROCESS CHARACTERISTIC INPUT-OUTPUT MODES

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In the past decades, representation models of dynamical processes have been developed via both traditional math-analytical and less traditional computational-intelligence approaches. This challenge to system sciences goes on because essentially involves the mathematical approximation theory. A comparison study based on cybernetic input-output view in the time domain on complex dynamical processes has been carried out. An analytical decomposition representation of complex multi-input-multi-output thermal processes is set relative to the neural-network approximation representations, and shown that theoretical background of both emanates from Kolmogorov’s theorem. The findings provided a new insight as well as highlighted the efficiency and robustness of fairly simple industrial digital controls, designed and implemented in the past, inherited from input-output decomposition model approximation employed.
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REFERENCES

References: 

[1] P. Albertos, A. Sala, and A. Dourado, “Learning Control of Complex Systems”, In Control of Complex Systems, K.J. Aström, P. Albertos, M. Blanke, A. Isidori, W. Schaufelberger, and R. Sanz, Eds., Ch. 6, pp. 123-141. London, UK: Springer-Verlag, 2001.
[2] J. A. Anderson, Introduction to Neural Networks. Cambrigde, MA: MIT Press, 1995.
[3] A. C. P. M. Backx, “Identification of an Industrial Process: A Markov Parameter Approach” Doctoral Thesis., Eindhoven, NL: Eindhoven University of Technology, 1987.
[4] C. Bishop, Neural Networks for Pattern Recognition. Oxford, UK: Clarendon, 1995.
756 Comparative Analysis Of Kolmogorov Ann And Process Characteristic Input-Output Modes
Georgi M. DIMIROVSKI, Yuanwei JING
[5] V. H. Cheng and C. A. Desoer, “Discrete time convolution control systems.” Intl. J. Control, vol. 36, no. 3, pp. 367-407, 1982.
[6] G. Cybenko, “Approximation by superposition of a sigmoidal function.” Maths. Control, Signals & Systems, vol. 2, pp. 303-314, 1989.
[7] N. Deo, Graph Theory with Applications to Engineering and Computer Science. Englewood Cliffs, NJ: Prentice-Hall, 1974.
[8] C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties. New York, NY: Academic Press, 1975.
[9] G. M. Dimirovski, N. E. Gough, and S. Barnett, “Categories in systems and control theory.” Intl. J. Systems Science, vol. 8, no. 9, pp. 1081-1090.
[10] G. M. Dimirovski, S. Barnett, D. N. Kleftouris, and N. E. Gough, “An input-output package for MIMO non-linear control systems” (cited in M.G. Singh’s [Editor-in-Chief] Systems and Control Encyclopedia: Theory, Technology, Applications, Oxford, Pergamon Press, 1987; see vol. 5, pp. 3382-83). In Software for Computer Control, M. Novak, Ed., pp. 265-273. Oxford, UK: Pergamon Press, 1979.
[11] G. M. Dimirovski and N. E. Gough, “Digital modeling and simulation of technological systems by means of k-time sequence matrices.” In Proceedings of the 6th International Symposium on Computer at the University, Paper 605.(1-10). Zagreb, HR: The SRCE and University of Zagreb, 1984.
[12] G. M. Dimirovski and N. E. Gough, “On a structural duality and input-output properties of a class of non-linear multivariable control systems.” Facta Universitatis Series EE, vol. 3, no. 1, pp. 1-9, Jan. 1990.
[13] G. M. Dimirovski, V. P. Deskov, and N. E. Gough, “On the ordering of characteristic input-output modes in MIMO discrete-time systems.” In Mutual Impact of Computing Power and Control Theory, M. Karny and K. Warwick, Eds., pp. 227-234. London, UK: Plenum Publishing, 1993.
[14] G. M. Dimirovski, “Learning identification and design of industrial furnace control systems”, in ESF-COSY Lecture Notes on Iterative Identification and Control Design, P. Albertos and A. Sala, Eds., Ch. III.3, pp. 259-287. Valencia, ES: European Science Foundation and DISA of Universidad Politecnica de Valencia, 2000.
[15] G. M. Dimirovski, A. Dourado, N. E. Gough, B. Ribeiro, M. J. Stankovski, I. H. Ting and E. Tulunay, “On learning control in industrial furnaces and boilers,” in Proceedings of the 2000 IEEE International Symposium on Intelligent Control, P. P. Grumpos, N. T. Kousoulas and M. Polycarpou, Eds., pp. 67-72. Piscataway, NJ: The IEEE and University of Patras, 2000.
[16] G. M. Dimirovski, A. Dourado, E. Ikonenen, U. Koretela, J. Pico, B. Ribeiro, M. J. Stankovski and E. Tulunay, “Learning Control of Thermal Systems”, In Control of Complex Systems, K.J. Aström, P. Albertos, M. Blanke, A. Isidori, W. Schaufelberger, and R. Sanz, Eds., Ch. 14, pp. 317-337. London, UK: Springer-Verlag, 2001.
[17] G.M. Dimirovski and Yuanwei Jing, “Parallels of Kolmogorov Neural Networks and Characteristic Input-Output Modes Decomposition”, DCE-DUI and ICT-NEU Techn. Report IOD-KNN-01/2001, Dogus University Istanbul, TR, and Northeastern University, Shenyang, CN, 2001 (unpublished).
[18] R. C. Dorf, “Analysis and design of control systems by means of time-domain matrices,” Proceedings of Institution of Electrical Engineers, vol. 109 C, pp. 616-626, 1962.
[19] K. Funahashi, “On approximate realization of continuous mappings by neural networks,” Neural Networks, vol. 2, pp. 183-192, 1989.
[20] F. Girosi and T. Pogio, “Representation properties of networks: Kolmogorov’s theorem is irrelevant”, Neural Computation, vol. 1, pp. 465-469, 1989.
[21] N. E. Gough and R. S. Al-Thiga, “Characteristic patterns and vectors of discrete multivariable control systems,” Arabian J. Science & Engineering, vol. 10, no. 3, pp. 253-264, 1985.
[22] N. E. Gough, and M. A. Mirza, “Computation of characteristic weighting patterns of discrete MIMO control systems”, Int. J. Systems Science, vol. 18, no. 10, pp. 1799-1814, Oct. 1987.
[23] N.E. Gough, G. M. Dimirovski, I. H. Ting, and N. Sadaoui, “Robust multivariable control system design for a furnace based on
Comparative Analysis Of Kolmogorov Ann And Process Characteristic Input-Output Modes 757
Georgi M. DIMIROVSKI, Yuanwei JING
characteristic patterns,” In Application of Multivariable System Techniques, R. Whalley, Ed., pp. 145-152. London, UK: The IMeasC and Elsevier Applied Science, 1990.
[24] R. Haber and H. Unbehauen, “Structure identification of nonlinear dynamic systems – a survey of input-output approaches,” Automatica, vol. 26, no. 6, pp. 651-677, Jun. 1990.
[25] F. Harary, R. Z. Norman, and D. Cartwright, Structural Models: An Introduction to the Theory of Directed Graphs. Ney York, NY: J. Wiley, 1965.
[26] S. Haykin, Neural Networks: A Comprehensive Foundation (2nd ed.). New York, NY: Macmillan, 1999.
[27] R. Heht-Nielsen, “Kolmogorov’s mapping neural network existence theorem.” In Proceedings of the IEEE Intl. Joint Conference on Neural Networks, vol. 3, pp. 11-14. New York, NY: The IEEE, 1987.
[28] K. J. Hunt, D. Sbarbaro, R. Zbikowski and P. J. Gawthrop, “Neural networks for control systems – A survey.” Automatica, vol.28, no.6, pp. 1083-1112, 1992.
[29] I. S. Iohvidov, Hankel and Toeplitz Matrices and Applications. Basel, CH: Birkhauser, 1982.
[30] H. Katsuura and D. A. Sprecher, “Computational aspects of Kolmogorov’s theorem.” Neural Networks, vol. 7, pp. 455-461, 1994.
[31] A. N. Kolmogorov, “On the representation of continuous functions of several variables by superposition of continuous functions of a smaller number of variables” (in Russian). Dokladi Akademii Nauk SSSR, vol. 108, pp. 358-359, 1956.
[32] A. N. Kolmogorov, “On the representation of continuous functions of several variables by superposition of continuous functions of one variable and the addition” (in Russian). Dokladi Akademii Nauk SSSR, vol. 114, pp. 953-956, 1957.
[33] A. N. Kolmogorov and S.V. Fomin, Elements of the Theory of Functions and Functional Analysis (in Russian). Moscow, RUS: Nauka, 1968.
[34] V. Kurkova, “Komlogorov’s theorem is relevant.” Neural Computation, vol. 3, pp. 617-622, 1991.
[35] V. Kurkova, “Komlogorov’s theorem and multi-layer neural networks.” Neural Networks, vol. 5, pp. 501-506, 1992.
[36] J. N. Lin and R. Unbehauen, “On the realization of Kolmogorov’s theorem.” Neural Computation, vol. 5, pp.18-20, 1993.
[37] L. Ljung and T. Soederstoerm, Theory and Practice of Recursive Identification. Cambridge, MA: The MIT Press, 1993.
[38] L. Ljung, System Identification: Theory for the User (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall, 1999.
[39] G. G. Lorentz, Approximation of Functions. New York, NY: Holt, Reinhart & Winston, 1966.
[40] T. Poggio and F. Girrosi, “Networks for approximation and learning.” Proceedings of the IEEE, vol. 78, pp. 1481-1497, 1990.
[41] M. B. Priestly, Non-linear and Non-stationary Time Series Analysis. London, UK: Academic Press, 1988.
[42] W. Rudin, Principles of Mathematical Analysis (3rd ed.). Auckland: McGraw- Hill, 1976.
[43] D. A. Sprecher, “On the structure of continuous functions of several variables.” Trans. American Mathematical Society, vol. 115, pp. 340-355, 1965.
[44] D. A. Sprecher, “A numerical implementation of Kolmogorov’s superposition II.” Neural Networks, vol. 10, pp. 447-457, 1997.
[45] M. J. Stankovski, Non-Conventional Control of Industrial Energy Conversion Processes in Complex Heating Furnaces (Doctoral Thesis; Supervisor G.M. Dimirovski). Skopje, MK: SS Cyril and Methodius University, 1997.
[46] M. H. Stone, “The generalized Weierstrass approximation theorem.” Mathematics Magazine, vol. 21, pp. 167-184, 237-254, 1948.
[47] H. S. Tsien, Engineering Cybernetics. New York, NY: Mc-Graw-Hill, 1950.
[48] P. J. Werbos, “Backpropagation through time: What it does and how to do it.” IEEE Proceedings, vol. 78, pp. 1550-1560, 1990.
[49] B. Widrow and M. A. Lehr, “Thirty years of adaptive neural networks: Perceptron, madaline, and back-propagation.” Proceedings of the IEEE, vol. 78, pp. 1415-1442, 1990.
758 Comparative Analysis Of Kolmogorov Ann And Process Characteristic Input-Output Modes
Georgi M. DIMIROVSKI, Yuanwei JING
[50] A. N. Whitehead and B. Russell, Principia Mathematica (2nd ed.). Cambridge, UK: Cambridge University Press, 1927.
[51] H. White, Artificial Neural Networks. Cambridge, MA: Blackwell, 1992.
[52] N. Wiener, Cybernetics: Or Control and Communication in the Animal and the Machine (2nd ed.), New York, NY: J. Wiley, 1961.
[53] L. A. Zadeh and E. Polak Systems Theory, New York, NY: Academic Press, 1969.
[54] L. A. Zadeh, “Fuzzy sets and systems”. In Proceedings of the Symposium on System Theory, pp. 29-37. Brooklyn, NY: Polytechnic Institute, 1965.
[55] L. A. Zadeh, “Fuzzy logic, neural networks and soft computing,” Comm. ACM, vol. 37, pp. 77-84, Mar. 1994.

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