Necessary conditions for infinite-dimensional control problems

Fattorini, H.O.; Frankowska, Halina

Fattorini, H.O.; Frankowska, Halina (1991), Necessary conditions for infinite-dimensional control problems, Mathematics of Control, Signals, and Systems, 4, 1, p. 41-67. http://dx.doi.org/10.1007/BF02551380

Type

Article accepté pour publication ou publié

Date

1991

Journal name

Mathematics of Control, Signals, and Systems

Volume

Number

Publisher

Springer

Pages

41-67

Abstract (EN)

We consider infinite-dimensional nonlinear programming problems which consist of minimizing a functionf 0(u) under a target set constraint. We obtain necessary conditions for minima that reduce to the Kuhn-Tucker conditions in the finite-dimensional case. Among other applications of these necessary conditions and related results, we derive Pontryagin’s maximum principle for a class of control systems described by semilinear equations in Hilbert space and study convergence properties of sequences of near-optimal controls for these systems.

Subjects / Keywords

Lagrange multiplier rule; Kuhn-Tucker conditions; Maximum principle; Optimal controls; Approximately optimal controls