Extremal problems for distributed parabolic systems with boundary conditions involving time-varying lags

Extremal problems for parabolic systems with time-varying lags are presented. An optimal boundary control problem for distributed parabolic systems with boundary conditions involving time-varying lags is solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.