- Tytuł:
- Finite-dimensional representations of the value functions of some optimal control problems
- Autorzy:
- Mirica, S.
- Powiązania:
- https://bibliotekanauki.pl/articles/206207.pdf
- Data publikacji:
- 2002
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
funkcja brzegowa
funkcja wartości
regularność
sterowanie optymalne
twierdzenie weryfikacji
generalized characteristic flow
generalized Hamiltonian flow
marginal function
optimal control
regularity
value function
verification theorem - Opis:
- 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.
- Źródło:
-
Control and Cybernetics; 2002, 31, 3; 779-801
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł