Symmetries of control systems

• Autorzy: Alexey V. Samokhin
• Języki publikacji: EN

Abstrakty

EN

Symmetries of the control systems of the form $u_t = f(t,u,v)$, $u ∈ ℝ^n$, $v ∈ ℝ^m$ are studied. Some general results concerning point symmetries are obtained. Examples are provided.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 337-342

Daty

wydano

1996

Twórcy

autor

Alexey V. Samokhin

• Moscow State Technical University of Civil Aviation, 6a Pulkovskaya St., Moscow 125838, Russia

Bibliografia

• [1] P. H. M. Kersten, The general symmetry algebra structure of the underdetermined equation $u_x=(v_xx)^2$, J. Math. Phys. 32 (1991), 2043-2050.
• [2] I. M. Anderson, N. Kamran and P. Olver, Interior, exterior and generalized symmetries, preprint, 1990.
• [3] A. P. Krishenko, personal communication.
• [4] Y. N. Pavlovskiĭ and G. N. Yakovenko, Groups admitted by dynamical systems, in: Optimization Methods and their Applications, Nauka, Novosibirsk, 1982, 155-189 (in Russian).
• [5] G. N. Yakovenko, Solving a control system using symmetries, in: Applied Mechanics and Control Processes, MFTI, Moscow, 1991, 17-31 (in Russian).
• [6] G. N. Yakovenko, Symmetries by state in control systems, MFTI, Moscow, 1992, 155-176 (in Russian).
• [7] J. W. Grizzle and S. I. Marcua, The structure of nonlinear control systems possessing symmetries, IEEE Trans. Automat. Control 30 (1985), 248-257.
• [8] A. J. van der Schaft, Symmetries and conservation laws for Hamiltonian systems with inputs and outputs: A generalization of Noether's theorem, Systems Control Lett. 1 (1981), 108-115.