Curvatures of single-input control systems

• Autorzy: Jakubczyk B.
• Języki publikacji: EN

Abstrakty

EN

We introduce invariants of control-affine systems which we call curvatures. They are defined by the drift and the control distribution, given by the system. The curvatures allow us to analyse the variational equation along a given trajectory, as well as existence of conjugate points.

Słowa kluczowe

EN

control system; curvature; invariants; variational equation; conjugate point

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 4B
• Strony: 1375--1391
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Jakubczyk B.

• Institute of Mathematics, Polish Academy of Sciences, 00-956 Warsaw, Śniadeckich 8, Poland,

Bibliografia

• AGRACHEV A. A. and SACHKOV, Yu.L. (2004) Control Theory from the Geometric Viewpoint. Springer- Verlag, New York.
• BONNARD, B. and CHYBA, M. (2003) Singular Trajectories and their Role in Control Theory. Mathématiques & Applications 40, Springer- Verlag, New York.
• BONNARD, B. and KUPKA, I. (1993) Théorie des sigularités de l’application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal. Forum Math. 5, 11-159.
• HARTMAN, P. (1964) Ordinary Differential Equations. John Wiley & Sons, New York.
• JAKUBCZYK, B. and KRYŃSKI, W. (2009) Vector fields with distributions and geometry of ODE’s (preprint).
• KRYŃSKI W. (2008) Equivalence problems for tangent distributions and ordinary differential equations. PhD Thesis, Institute of Mathematics, Polish Academy of Sciences, Warszawa (in Polish).