Authors N.P. Voronova, S.M. Kovalev A.N. Shabelnikov
Month, Year 06, 2016 @en
Index UDC 519.71
Abstract Conventional approaches to the control of complex dynamical objects in uncertainties are based on analytical models presented in form of differential and difference equations. However, the construction of analytical models is impossible for semi-formalized objects, when various non-factors are occurred. Because of this fact, intelligent models based on human expert knowledges are most preferable ones. Among these models, fuzzy dynamical systems play an important role. The paper presents a decision of general tasks connected with identification, prediction and estimation of states for fuzzy dynamical systems describing the behavior of semi-formalized dynamical objects. A new approach to statement estimation and parameter identification for fuzzy dynamical systems is considered. The basis of the considered approach is adaptive network model of the computation of fuzzy prior and posterior estimates of system’s state variables taking place in consequent time steps. Optimization of the model parameters is taking into account in the approach as well. Proposed technique for parameter identification has the set of fundamentally new properties. Among them, possibility of integration into a system of empirical expert knowledges, higher level of potential accuracy of identification based on possibility of utilizing the generalized fuzzy criteria of optimality and real-time identification of model parameters (because of small number of iterations required for optimal states estimation) are highlighted. An example of optimal parameter estimation for fuzzy dynamical system is considered and experimental results are presented. Experimental verification shows that estimates of identified parameters found based on developed simplex algorithm are not deviated from real values more than by 10% in many cases for wide variety of fuzzy dynamical systems.

Download PDF

Keywords Fuzzy dynamical system; conditional membership function; prior fuzzy distribution; posterior fuzzy distribution; adaptive network model; parametric identification
References 1. Grop D. Metody identifikatsii sistem [The methods for system identification]. Moscow: Mir, 1979, 302 p.
2. L'yung L. Identifikatsiya sistem. Teoriya dlya pol'zovatelya [System identification. Theory for user]. Moscow: Nauka, 1991, 432 p.
3. Pashchenko F.F. Vvedenie v sostoyatel'nye metody modelirovaniya sistem. Identifikatsiya nelineynykh system [Introduction to wealthy methods of system modeling. Autentification of nonlinear systems]. Moscow: Finansy i statistika, 2007, 288 p.
4. Ronghua Guo. Interacting Multiple Model Particle-type Filtering Approaches to Ground Target Tracking, Journal of Computers, 2008, Vol. 3, No. 7, pp. 23-30.
5. Pospelov D.A. Logiko-lingvisticheskie modeli v sistemakh upravleniya [Logical-linguistic models in control systems]. Moscow: Energoiz-dat, 1981, 230 p.
6. Gordon N.J., Salmond D.J., Smith A.F.M. Novel approach to nonlinear/non-Gaussian Bayesian state estimation, IEE Proceedings-F, 1993, Vol. 140, No. 2, pp. 107-113.
7. Doucet A., Godsill S., Andrieu C. On sequential Monte-Carlo sampling methods for Bayesian filtering, Statistics and Computing, 2000, Vol. 10, No. 3, pp. 197-208.
8. Shteynberg Sh.E. Identifikatsiya v sistemakh upravleniya [Identification in control systems]. Moscow: Energoatmoizdat, 1987, 80 p.
9. Kudinov Yu.I., Kudinov I.Yu., Suslova S.A. Nechetkie modeli dinamicheskikh protsessov [Fuzzy models of dynamical processes]. Moscow: Nauchnaya kniga, 2007, 183 p.
10. Kovalev S.M. Intellektual'nye modeli analiza vremennykh ryadov na osnove nechetko-dinamicheskikh sistem [Intelligent models for time-series analysis based on Fuzzy Dynamical Systems], Trudy Mezhdunar. nauchn.-tekhn. Konferentsiy “Intellektual'nye sistemy” (AIS’06) i “Intellektual'nye SAPR” (CAD-2006): Nauchnoe izdanie v 3-kh t. T. 1 [Proceedings of the International scientific and technical Conferences “Intellectual systems” (AIS’06) and “Intelligent CAD” (CAD-2006): Scientific publication in 3 vol. Vol. 1. Moscow: Fizmatlit, 2006, pp. 93-99.
11. Altunin A.E., Semukhin M.V. Modeli i algoritmy prinyatiya resheniy v nechetkikh usloviyakh [Models and algorithms of decision-making in fuzzy conditions]. Tyumen': Izd-vo TGU, 2000, 352 p.
12. Prikladnye nechetkie sistemy [Applied fuzzy systems]: translated from Japanese K. Asai, D. Vatada, S. Ivai i dr., under ed. T. Terano, K. Asai, M. Sugeno. Moscow: Mir, 1993, 368 p.
13. Petrov B.N., Ulanov G.M., Gol'denblat I.I., Ul'yanov S.V. Teoriya modeley v protsessakh upravleniya [The theory of models in control processes]. Moscow: Nauka, 1978, 216 p.
14. Lyu B. Teoriya i praktika neopredelennogo programmirovaniya [Theory and practice of uncertain programming]: translation from English. – B. BINOM: Laboratoriya znaniy, 2014, 416 p.
15. Zade L.A. Ponyatie lingvisticheskoy peremennoy i ego primenenie k prinyatiyu priblizhennykh resheniy [The concept of a linguistic variable and its application to making approximate-located solutions]. Moscow: Mir, 1976, 165 p.
16. Werbos P.J. Beyond regression: New tools for prediction and analysis in the behavioral sciences. Ph.D. thesis, Harvard University, Cambridge, MA, 1974.
17. Nelder J.A. and Mead R. A simplex method for function minimization, Computer Journal, 1965, Vol. 7, pp. 308-313.
18. Kovalev S.M., Kucherenko P.A., Sokolov S.V. Intellektual'naya obrabotka temporal'nykh dannykh na osnove gibridnykh nechetko-stokhasticheskikh modeley [Intelligent processing of temporal data based on hybrid fuzzy stochastic models], Avtomatika i vychislitel'naya tekhnika [Automation and Computer Engineering], 2015, No. 1, pp. 5-17.
19. Sugeno M. Yasukawa T. A fuzzy-logic-based approach to qualitative modeling, IEEE. Transactions on Fuzzy Systems, 1993, Vol. No. 1, pp. 7-31.
20. Emel'yanov V.V., Kureychik V.V., Kureychik V.M. Teoriya i praktika evolyutsionnogo modelirovaniya [Theory and practice of evolutionary modeling]. Moscow: Fizmatlit, 2003, 432 p.

Comments are closed.