Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions

• Autorzy: Mordukhovich B. S. , Wang D. , Wang L.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

optimal control; variational analysis; endpoint constraints; delay-differential inclusions; multivalued initial conditions; extended Euler-Lagrange formalism; discrete approximations; generalized differentiation; Banach and Asplund spaces; necessary optimality conditions

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2008
• Tom: Vol. 37, no 2
• Strony: 393--428
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Mordukhovich B. S.

autor

Wang D.

autor

Wang L.

• Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA,

Bibliografia

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