The existence of the optimal control of systems with quadratic quantity criterium
Küçük Resim Yok
Tarih
2009
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
Consider optimal control problem in R n with quadratic in control quality criterium: dx dt = f(x, t)B(t)u (1) x(s) = y I(s, y, u) = ?(?, x(?)) + Z ? s [?(t, x(t)) + (N(t)u(t), u(t))] dt ? inf (2) Here t ? [0, T], x ? R n, Q0 = (0, T) × R n, Q is bounded sub domain of Q0 with the boundary ?Q. We assume that : 1) The functions ?(t, x) and ?(t, x) are nonnegative, smoth in their arguments in Q¯, morover, ?? ?x is Lipshitz in x in Q¯ (Q¯ is the closure of Q) 2) f(t, x) is smooth in Q¯ and ?f ?x is Lipshitz in x in Q¯. 3) n × m is dimensional matrix B(t) is smooth in t in Q¯. 4) m × m is dimensional matrix N(t) is positive definite in Q¯. and smooth in t The bellman’s equation of the problem (1) , (2) is ?V ?t + µ f(t, x), ?V ?t ¶ + ?(t, x) ? 1 4 µ B(t)N ?1 (t)B ? (t) ?V ?t , ?V ?t ¶ = 0 With the boundary condition. THEOREM 1. If the hyper surface ?Q is correctly embedded into R n+1, and the conditions (1)-(4) hold , then the boundary value problem (7), (8) has the unique solution in Q, which is continuous together with it’s partial derivative up to the second order.
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Ateiwi, A. M. ve Komashynsk Voladymyrivna, I. (2009). The existence of the optimal control of systems with quadratic quantity criterium. Maltepe Üniversitesi. s. 86.
