UDK 005; 519.7; 303.732
AUTOMATIC LINEAR DIFFERENTIAL EQUATION IDENTIFICATION IN ANALYTICAL FORM
I. S. Ryzhikov
Siberian State Aerospace University named after academician M. F. Reshetnev 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660014, Russian Federation Е-mail: ryzhikov-88@yandex.ru
In this study a multi-agent evolutionary strategies algorithms system is considered in application to linear dynamic system identification problem solving. The proposed approach is based on previous results of designing the universal simultaneous parameters and structure identification technique that uses the observations of system output and input. Every agent is model-based and has an aim to find an extremum for agent’s criterion. The solution of the problem is symbolic and can be automatically found for the small samples and noised data.
evolutionary strategies, multi-agent system, identification, structure and parameters, differential equation.
References
  1.  Astreon K. J., Bohlin T. Numerical Identification of Linear Dynamic Systems from Normal Operating Records. Technical paper. IBM Nordic Laboratory, Lidingo, Sweden: 38 p., 1967.
  2. Medvedev A. V. Identification and control for linear dynamic system of unknown order. Optimization Techniques IFIP Technical Conference. Berlin – Heidelberg – New York: Springer-Verlag, p. 48–56, 1975.
  3.  Zoteev V. Parametrical identification of linear dynamical system on the basis of stochastic difference equations. Matem. Mod. 2008. Vol. 20, no. 9, p. 120–128.
  4. Passino K. M., Yurkovich S. Fuzzy control. Addison Wesley Longman, Inc. 1998. 502 p.
  5.  Tan Y., Dong R., Chien H., He H. Neural networks based identification of hysteresis in human meridian systems. Int. Journal of Applied Mathematics and Computer Science. 2012. Vol. 22, no. 3, p. 685–694.
  6.  Jovanovic O., Identification of Dynamic System Using Neural Network // Architecture and Civil Engineering. 1997. Vol. 1, no. 4, p. 525–532.
  7.  Cao H., Kang L., Chen Y., Yu J. Evolutionary modeling of systems of ordinary differential equations with genetic programming. Genetic Programming and Evolvable Machines1 (40) p. 309–337, 2000.
  8.  Parmar G., Prasad R., Mukherjee S. Order reduction of linear dynamic systems using stability equation method and GA. International Journal of computer and Infornation Engeneering 1:1, 2007.
  9.  Reimer M., Rudzicz F. Identifying articulatory goals from kinematic data using principal differential analysis. Proceedings of Interspeech 2010, Makuhari Japan. 2010. P. 1608–1611.
  10.  Mineiro P., Movell J. R., Williams R. J. Modeling path distributions using partially observable diffusion networks: a Monte-Carlo approach. Technica lReport CogSci.UCSD-99.01, Department of Cognitive Science, UCSD, SanDiego, 1999.
  11.  Saerens M. Viterbi algorithm for acoustic vectors generated by a linear stochastic differential equation. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Detroit, 1995, p. 233–236.
  12. Schwefel Hans-Paul Evolution and Optimum Seeking : New York: Wiley & Sons., 1995.
  13.  Ryzhikov I., Semenkin E. Evolutionary Strategies Algorithm Based Approaches for the Linear Dynamic System Identification. Adaptive and Natural Computing Algorithms, Springer: p. 477–483, 2013.
  14.  Ryzhikov I., Semenkin E. Modified Evolutionary Strategies Algorithm in Linear Dynamic System Identification. ICINCO (1): p. 618-621, 2012.
  15.  Ryzhikov I., Semenkin E. The Application of Evolutionary Algorithm for the Linear Dynamic System Modelling. SIMULTECH: p. 234–237, 2012.

Ryzhikov Ivam Sergeevich – postgraduate student of the Department of System analysis and operation research, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: ryzhikov-88@yandex.ru