Optimal control of n × n parabolic system involving time lag

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

“…If h(t) = h = constant, i.e., system with constant time lag [7], then the n × n system (4) becomes ∀1 i n,…”

“…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].…”

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

“…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.…”

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.…”