Optimal boundary control problem for n × n infinite-order parabolic lag system

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

“…For the problem (1)-(4) with the performance function (26) with z Σd ∈ L 2 (Σ) and λ 2 > 0, and with constraint (12), and with adjoint Eqs. (28)- (31), there exists a unique optimal control v * which satisfies the maximum condition (32).…”

“…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.…”

“…The necessary and sufficient conditions of optimality for systems consists of only one equation and for (n × n) systems governed by different types of partial differential equations defined on spaces of functions of infinitely many variables and also for infinite order systems are discussed for example in [25][26][27][28]42,45] in which the argument of [46,47] were used.…”

Time-Optimal Boundary Control of an Infinite Order Parabolic System with Time Lags

“…Various optimization problems associated with the optimal control of distributed parabolic systems with time delays appearing in the boundary conditions were studied recently in (El-Saify, 2005;El-Saify, 2006;Knowles, 1978;Kowalewski, 1988;Kowalewski, 1990a;Kowalewski, 1990b;Kowalewski, 1993;Kowalewski, 1998;Kowalewski, 1999;Kowalewski, 2001;Kowalewski and Duda, 1992;Kowalewski and Krakowiak, 1994;Kowalewski and Krakowiak, 2000;Kowalewski and Krakowiak, 2006;Wang, 1975).…”

“…Finally, in (El-Saify, 2005;El-Saify, 2006), linear quadratic optimal distributed and boundary control problems for n × n second order and n × n infinite order parabolic time-varying lag systems were considered.…”