Phase portraits of planar control-affine systems

• Autorzy: Jakubczyk B. , Respondek W.
• Języki publikacji: EN

Abstrakty

EN

We study nonlinear control systems in the plane, affine with respect to control. We introduce two sets of feedback equivariants forming a phase portrait PP and a parameterized phase portrait PPP of the system. The phase portrait PP consists of an equilibrium set E, a critical set C (parameterized, for PPP), an optimality index, a canonical foliation and a drift direction. We show that under weak generic assumptions the phase portraits determine, locally, the feedback and orbital feedback equivalence class of a system. The basic role is played by the critical set C and the critical vector field on C. We also study local classification problems for systems and their families.

Słowa kluczowe

EN

control system; family of control systems; invariants; phase portrait; critical trajectories; feedback equivalence; bifurcation

PL

system sterowania; niezmiennik; trajektoria krytyczna; bifurkacja

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2005
• Tom: Vol. 34, no 3
• Strony: 819--847
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Jakubczyk B.

• Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warsaw

autor

Respondek W.

• Laboratoire de Mathematiques INSA de Rouen Pl. Emile Blondel, 76131 Mont Saint Aignan, France

Bibliografia

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