On the solvability of the problem of the optimal boundary control of thermal processes described by the Volterra integro-differential equations

Subject Optimization
Title On the solvability of the problem of the optimal boundary control of thermal processes described by the Volterra integro-differential equations
Author(s) Akylbek Kerimbekov, Erkeaim Seidakmat kyzy
Keywords Functional, boundary value problem, the optimality condition, nonlinear integral equation, optimal control.
Abstract In this paper we have investigated the problem of tracking, where is required to minimize the functional J[u(t) ]=∫_0^T▒∫_Q▒[V(t,x)-ξ(t,x) ] ^2 dxdt+β∫_0^T▒〖u^2 (t)dt, β>0〗, on the set of solutions of the boundary value problem V_t-AV=λ∫_0^t▒K(t,τ)V(τ,x) dτ+g[t,x], x∈Q⊂R^n, 0