Optimal control of parabolic equation with an infinite number of variables for non-standard functional and time delay

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

“…The parabolic operator ∂/∂t + A(t) in the state equation (1) is an infinite order parabolic operator and A(t) [24] and (Gali andEl-Saify, 1982, 1983) and [34] is given by:…”

“…A fundamental study of such problems is given by [48] and was next developed by [29,49]. It was also intensively investigated by [7][8][9][11][12][13]25,26,30,[34][35][36][37][38][39][40][41][42][43][44][45], in which linear quadratic problem for parabolic systems with time delays given in the different form (constant, time delays, time-varying delays, time delays given in the integral form, etc.) were presented.…”

“…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.…”

Time-Optimal Control of Infinite Order Distributed Parabolic Systems Involving Multiple Time-Varying Lags

“…A fundamental study of such problems is given by (26) and was next developed by (15) and (27). It was also intensively investigated by (19; 20), (21), (22), (18) and (17) in which linear quadratic problem for parabolic systems with time delays given in the different form (constant time delays, time-varying delays, time delays given in the integral form, etc.) were presented.…”

Optimality of the boundary control for n×n parabolic lag system

“…The necessary and sufficient conditions of optimality for systems (n × n systems) governed by different types of partial differential operators defined on spaces of functions of infinitely many variables are discussed in [2][3][4][5][6][7][8][9][10][11][12]. The interest in the study of this class of operators is stimulated by problems in quantum field theory [1].…”