Brief review of tasks and results of programm of creation of unified geometrical theory of control (UGTC)

• Autorzy: Butkovskiy A. G. , Babichev A. V.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is in very much compressed thesis form to depict the results and problems that were obtained during development of "Unified geometrical theory of control (UGTC)", or "Theory of control structures (TCS)". It is emphasized that UGTC deals with control of structures and symmetries, and a number of structures are considered. Because the UGTC treats the basic concepts of control theory, some main philosophical and methodological principles related to the control science and mathematics are discussed. Concrete theoretical results are given in geometrical form, which permits to show the invariance and generality of these statements. Particularly, the geometrical construction of foliation extends to the synthesis in the control theory as well as to the choice axiom in the set theory, demonstrating an important connection between appropriate problems. Also the problems of axiomatic control theory and control in metric and topological spaces are mentioned. For systems with differential structure the various representations in terms of differential forms, partial differential equations and phase portraits of differential inclusions are considered. The relation between optimality principle and physical variable of energy tensor is determined.

Słowa kluczowe

EN

set theory; partial differential equations; computational geometry; control system synthesis; axiomatic control theory

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2004
• Tom: Vol. 30, no 1
• Strony: 37--42
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Butkovskiy A. G.

• Institute of Control Sciences Russia's Academy of Sciences, Profsoyuznaya 65, Moscow, 117997 Russia

autor

Babichev A. V.

• Institute of Control Sciences Russia's Academy of Sciences, Profsoyuznaya 65, Moscow, 117997 Russia

Bibliografia

• [1] Babichev A. V., Butkovskiy a. G., Pohjolainen S., K edinoj geometricheskoj teorii upravleni (Towards unified geometrical theory of control), Nauka, Moscow 2001, (in Russian).
• [2] Butkovskiy A. G., Distributed Control Systems, Elsevier, New York 1969.
• [3] Butkovskiy A. G., Structural Theory of Distributed Systems, Ellis Horwood Publ., England, 1983
• [4] Butkovskiy A. G., The application of the structural theory of the systems with distributed parameters and feed-back principle to the solutions of the boundary conditions problems for the equations of mathematical physics. Proceedings of 11th International Conference on Systems Sciences System Science XV. Wydawnictwo Politechniki Wrocławskiej, Wroclaw 1992, 21-22.
• [5] Butkovskiy A. G., A geometric theory of control of systems with distributed parameters, Journal of Computer and Systems Sciences International, Vol. 34, No. 5, 1996, 1-40.
• [6] Butkovskiy A. G., Towards geometrization of control. Journal of Computer and System Sciences International, Vol. 36, No. 1, 1997, 23-57.
• [7] Butkovskiy A. G., Control in metric spaces. Automation and Remote Control, Vol. 60, No. 7 part 1, 1999, 914-925.
• [8] Butkovskiy A. G., Control from the angle of the Zermelo axiom of choice, Automation and Remote Control, Vol. 61, No. 7, part 2, 2000, 1231-1234.
• [9] Butkovskiy A. G., Babichev A. V., An axiomatical approach to the structure of control and optimal control, System Science, Vol. 27, No. 1, 2001, 49-58.
• [10] http://www.Butkovskiy.by.ru/