Necessary conditions of second order optimality for systems with three-point boundary conditions
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
In this report the object of investigation is an optimal control problem in systems of nonlinear first order ordinary differential equations with three-point boundary conditions: x? = f(x, u, t), x(t) ? R n , t ? T = [t0, t1], (1) Ax(t0) + Bx(t1) + Dx(t2) = c, t1 ? (t0, t2), (2) Here f ? R n is continuous by collection of variables together with its partial derivatives with respect to x and u up to the second order inclusive, A, B, D ? R n×n, c ? R n×1 are constant matrices. It is supposed that control action satisfy restriction u(t) ? V, t ? T , where V is a convex compact set from R r . The goal of optimal control problem is optimization of the functional: J(u) = ?(x(t0), x(t2)) (3) defined on the solutions of boundary problem (1)-(2) at admissible controls where it is supposed that function ?(x, y) is continuous by x and y up to the second order inclusive. The formula of the second order increment of functional (3) is calculated. On the basis of control variations there are obtained new necessary conditions of optimality for quasi-singular controls for systems which are described by a set of differential equations with three-point boundary conditions.
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Sharifov, Y. A. ve Djabrailov, S. I. (2009). Necessary conditions of second order optimality for systems with three-point boundary conditions. Maltepe Üniversitesi. s. 386.
