Necessary optimality conditions for a smooth discrete optimal control problem with vector-valued objective function. (Russian. English summary) Zbl 1180.49018

Gorokhovik, V. V.; Gorokhovik, S. Ya.; Marinković, B.

Tr. Inst. Mat., Minsk 17, No. 1, 27-40 (2009).

Summary: The paper deals with a nonlinear discrete optimal control problem with a vector-valued objective function of terminal type. For admissible controls which satisfy the additional Lyusternik-type regularity condition, first and second necessary optimality conditions extending such classical optimality conditions as the Euler condition and the nonnegativity of second variation are proved.

MSC:

49K10

Optimality conditions for free problems in two or more independent variables

Keywords:

nonlinear discrete optimal control problem; vector-valued objective function; Lyusternik-type regularity condition; necessary optimality conditions