# On the solvability of the problem of the distributed optimal control of oscillation processes described by the Fredholm integro-differential equations

Subject | Optimization |

Title | On the solvability of the problem of the distributed optimal control of oscillation processes described by the Fredholm integro-differential equations |

Author(s) | Akylbek Kerimbekov, Elmira Abdyldaeva |

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▒〖∫_Q▒p^2 [t,x,u(t,x) ]dxdt〗,
β>0,
on the set of solutions of the boundary value problem
V_tt-AV=λ∫_0^T▒K(t,τ)V(τ,x) dτ+f[t,x,u(t,x) ], x∈Q⊂R^n,0 |