On abnormal extremals for Lagrange variational problems. (English) Zbl 0826.49012

Agrachev, A. A.; Sarychev, A. V.

J. Math. Syst. Estim. Control 5, No. 1, 127-130 (1995).

Summary: Abnormal extremals for the problem of relative extremum and the Lagrange problem of the calculus of variations are studied. Legendre-Jacobi-type necessary/sufficient minimality conditions for abnormal extremum are derived and Morse-type index and nullity theorems for abnormal extremals of the Lagrange problem are established.
[Full electronic manuscript (published January 1, 1995) = 32 pp, 350,492 bytes. Retrieval Code: 99949].

MSC:

49K15	Optimality conditions for problems involving ordinary differential equations
90C30	Nonlinear programming
93B05	Controllability
93B29	Differential-geometric methods in systems theory (MSC2000)

Keywords:

abnormal extremals; index theorems; Lagrange problem; minimality conditions; nullity theorems