ИССЛЕДОВАНИЕ УСТОЙЧИВОСТИ СИСТЕМЫ УПРАВЛЕНИЯ МЕТОДОМ ДЕКОМПОЗИЦИИ ВЕКТОРНОГО ПОЛЯ

S N Chukanov; D V Ulianov

Authors

S. N. Chukanov Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of RAS
D. V. Ulianov Omsk State Technical University

Keywords:

vector field decomposition, control system, Lyapunov function, Hodge-Helmholtz decomposition, operator of homotopy

Abstract

A method of decomposing the vector field of a dynamical system based on the homotopy operator development is proposed in this paper. The decomposition of the vector field of multi-parameter dynamical system is considered. The invariants are constructed for components of vector field decomposition. The method of decomposition of the dynamical system vector field is applied to develop Lyapunov functions for control systems.

Author Biographies

S. N. Chukanov, Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of RAS

DSc in Engineering, Professor

D. V. Ulianov, Omsk State Technical University

Post-graduate

References

Saffman P. G. Vortex dynamics. – Cambridge University Press. – 1992. – 312 p.

Chukanov S. N. Definitions of invariants for n-dimensional traced vector fields of dynamic systems // Pattern Recognition and Image Analysis. – Vol. 19. – No 2. – 2009. – P. 303–305.

Красовский Н. Н. Некоторые задачи теории устойчивости движения. – М : ГИФМЛ, 1959. – 211 с.

Зубов В. И. Устойчивость движения (методы Ляпунова и их применение). – М. : Высш. шк., 1984. – 232 с.

Multimedia tools for communicating mathematics / ed. K. Polthier, J. Rodrigues. – Springer-Verlag, 2002. – P. 241–264.

Арнольд В. И. Математические методы классической механики. – М. : Эдиториал УРСС, 2006. – 416 с.

Edelen D. G. B. Applied Exterior Calculus. – John Wiley&Sons, Inc., 1985. – 472 p.

Wang Y., Lia Ch., Cheng D. Generalized Hamiltonian realization of time-invariant nonlinear systems // Automatica. – 2003. – Vol. 39. – P. 1437–1443.

Balachandran A. P., Marmo G., Skagerstam B. S., Stern A. Classical topology and quantum states. – World Scientific, 1991. – 356 p.

Сейдж Э. П., Уайт Ч. С. Оптимальное управление системами. – М. : Радио и связь, 1982. – 392 c.

Jurdjevic V., Quinn J. F. Controllability and Stability // Journal of Differential Equations. – 1978. – Vol. 28. – P. 381–389.

Hudon N., Hoffner K., Guay M. Equivalence to Dissipative Hamiltonian Realization. In: Proceedings of the 47-th Conference on Decision and Control, Cancun, Mexico, 2008. – P. 3163–3168.

Cheng D., Shen T., Tarn T. J. Pseudo-hamiltonian realization and its application // Communications in information and systems. – 2002. – Vol. 2. – No. 2. – P. 91–120.