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 |