- Tytuł:
- Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions
- Autorzy:
-
Mordukhovich, B. S.
Wang, D.
Wang, L. - Powiązania:
- https://bibliotekanauki.pl/articles/969562.pdf
- Data publikacji:
- 2008
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
discrete approximations
optimal control
variational analysis
endpoint constraints
delay-differential inclusions
multivalued initial conditions
extended Euler-Lagrange formalism
generalized differentiation
Banach and Asplund spaces
necessary optimality conditions - Opis:
- This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except for some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the three major parts: (a) constructing a well-posed sequence of discrete-time problems that approximate in an appropriate sense the original continuous-time problem of dynamic optimization; (b) deriving necessary optimality conditions for the approximating discrete-time problems by reducing them to infinite-dimensional problems of mathematical programming and employing then generalized differential calculus; (c) passing finally to the limit in the obtained results for discrete approximations to establish necessary conditions for the given optimal solutions to the original problem. This method is fully realized in the delay-differential systems under consideration.
- Źródło:
-
Control and Cybernetics; 2008, 37, 2; 393-428
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł