Optimal Control Problem for Infinite Order Hyperbolic System with Mixed Control-State Constraints

An optimization problem for infinite order distributed parabolic systems with multiple time-varying lags

“…The optimization problem presented in the paper constitutes a generalization of the optimal boundary control problem of a parabolic systems with Neumann boundary condition involving constant time lag appearing in the state and in the boundary conditions considered in [25][26][27][31][32][33][35][36][37][38][39][40][41][42].…”

“…Using the adjoint Eqs. (28)- (31) in this case, the condition (27) can also be written in the following form…”

“…Case: u ∈ L 2 (Q). We can also consider an analogous optimal control problem where the performance functional is given bŷ (33) where z d ∈ L 2 (Q). From Theorem 3.1 and the Trace Theorem ( [47], vol.…”

“…Making use of the Dubovitskii-Milyutin Theorem in [1][2][3][4][5][6]10,33,34] the necessary and sufficient conditions of optimality for similar systems governed by second order operator with an infinite number of variables and also for infinite order systems were investigated. The interest in the study of this class of operators is stimulated by problems in quantum field theory.…”

Optimality Conditions for Infinite Order Hyperbolic Differential System

“…The optimal control problem of systems governed by different types of operators defined on spaces of functions of an infinite number of variables are initiated and proved, e.g., in [3][4][5][6][7][8], we have obtained the set of inequalities that characterize the optimal control for systems or (n × n)-systems governed by elliptic, parabolic, and hyperbolic equations of infinite number of variables with Dirichlet and Neumann conditions. The questions treated in this paper are related to the above results but in a different direction, by taking the case of operator of infinite order in a finite dimension.…”