ArticleOriginal scientific text
Title
Modulating element method in the identification of a generalized dynamical system
Authors 1, 1
Affiliations
- Department of Mathematics, Naval Academy, 81-919 Gdynia, Poland
Abstract
In this paper the identification of generalized linear dynamical differential systems by the method of modulating elements is presented. The dynamical system is described in the Bittner operational calculus by an abstract linear differential equation with constant coefficients. The presented general method can be used in the identification of stationary continuous dynamical systems with compensating parameters and for certain nonstationary compensating or distributed parameter systems.
Keywords
identification, dynamical system, modulating element, integral, derivative, limit condition, operational calculus
Bibliography
- S. Bellert, On foundations of operational calculus, Bull. Acad. Polon. Sci. Cl. III 9 (1957), 855-858.
- S. Bellert, An attempt at generalizing the theory of linear dynamical systems, Prace Naukowe Polit. Warszaw. Elektronika 19 (1975), 5-29 (in Polish).
- S. Bellert, On the generalization of the theory of linear dynamical systems, in: Proc. Third Internat. Sympos. on Network Theory, Split 1975, 759-769.
- R. Bittner, On certain axiomatics for the operational calculus, Bull. Acad. Polon. Sci. Cl. III 7 (1959), 1-9.
- R. Bittner, Algebraic and analytic properties of solutions of abstract differential equations, Rozprawy Mat. 41 (1964).
- R. Bittner, Operational Calculus in Linear Spaces, PWN, Warszawa, 1974 (in Polish).
- R. Bittner, Operational Calculus in Groups, PWN, Warszawa, 1992 (in Polish).
- Z. Bubnicki, Identification of Controlled Objects, PWN, Warszawa, 1974 (in Polish).
- A. Ditkin and A. P. Prudnikov, Operational Calculus, Vysshaya Shkola, Moscow, 1975 (in Russian).
- Z. Fortuna, B. Macukow and J. Wąsowski, Numerical Methods, WNT, Warszawa, 1982 (in Polish).
- J. Loeb et G. Cahen, Extraction, à partir des enregistrements de mesures, des paramètres dynamiques d'un système, Automatisme, VIII, 12 (1963), 479-486.
- D. G. Luenberger, Optimization by Vector Space Methods, Wiley, New York, 1969.
- E. Mieloszyk, Operational calculus in algebras, Publ. Math. Debrecen 34 (1987), 137-143.
- L. Niemiec and M. Zellma, Identification algorithm for dynamical systems via basic cubic splines, Zeszyty Naukowe AMW 3 (1988), 105-131 (in Polish).
- J. Osiowski (ed.), Stanisław Bellert-Selected Papers, posthumous edition, PWN, Warszawa-Wrocław, 1980 (in Polish).
- D. Przeworska-Rolewicz, Algebraic Analysis, PWN, Warszawa, and Reidel, Dordrecht, 1988.
- M. Shinbrot, On the analysis of linear and nonlinear systems, Trans. ASME 79 (1957), 547-552.
- G. Sieńczewski, Deterministic models of stationary linear systems with right invertible operators and identification of their parameters, Preprint 260, Institute of Mathematics, Polish Academy of Sciences, 1982.
- S. B. Stechkin and Yu. N. Subbotin, Splines in Computational Mathematics, Nauka, Moscow, 1976 (in Russian).
- H. Wysocki, An approach to linear differential dynamical systems via operational calculus, Zeszyty Naukowe WSMW 4 (1983), 37-46 (in Polish).
- H. Wysocki, On an operational calculus with weighting element, Studia Sci. Math. Hungar. 29 (1994), 1-8.
- H. Wysocki and M. Zellma, On an identification method for the generalized dynamic differential system, Postępy Cybernetyki (10) 1 (1987), 5-18.
- H. Wysocki and M. Zellma, Identification of a generalized dynamic system using the modulating element method, Control and Cybernetics 20 (3) (1991), 37-61.
- H. Wysocki and M. Zellma, Identification of a generalized dynamic system by the method of modulating elements, Arch. Control Sci. 28 (3-4) (1993), 201-222.
Pages:
447-467
Main language of publication
English
Received
1993-07-22
Published
1995
Exact and natural sciences