Finite-dimensional representations of the value functions of some optimal control problems

• Autorzy: Mirica S.
• Języki publikacji: EN

Abstrakty

EN

In this survey we analyze the possibility of obtaining information on regularity and irregularity properties of the value functions of some optimal control problems from their more precise description as marginal functions of finite-dimensional type, in terms of certain "generalized characteristic flows" which, in turn, may be constructed using either necessary optimality conditions (PMP-Pontryagin's Minimum Principle), whenever applicable, or suitable extensions of Cauchy's Method of Characteristics for the associated Hamilton-Jacobi-Bellman equation. This type of representation, which may be justified either by the application of PMP "combined" with existence theorems or by the application of a suitable verification theorem of Dynamic Programming type, not only facilitates numerical computation of the value function but also may allow identification of its discontinuity points, non-differentiability points, propagation of singularities, etc. ; this approach is illustrated with three significant examples from classical Calculus of Variations.

Słowa kluczowe

EN

generalized characteristic flow; generalized Hamiltonian flow; marginal function; optimal control; regularity; value function; verification theorem

PL

funkcja brzegowa; funkcja wartości; regularność; sterowanie optymalne; twierdzenie weryfikacji

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2002
• Tom: Vol. 31, no 3
• Strony: 779--801
• Opis fizyczny: Bibliogr. 15 poz.,

Twórcy

autor

Mirica S.