Contiguity and Dynamic Programming

• Дата: 2007
• Автор: Galperin, E.A.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут проблем моделювання в енергетиці ім. Г.Є. Пухова НАН України 2007
• Назва видання: Электронное моделирование
• Теми: Математические методы и модели
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/101822
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Contiguity and Dynamic Programming / E.A. Galperin // Электронное моделирование. — 2007. — Т. 29, № 6. — С. 23-36. — Бібліогр.: 11 назв. — англ.

Some aspects of the principle of optimality [1, p.83] are considered, and a modification is proposed for the derivation of the main functional equations of dynamic programming to demonstrate that those equations are valid also in the case of non-optimal remaining trajectories under certain contiguity condition that is defined and analyzed in the paper. Control systems with incomplete information or structural limitations on controls do not, in general, satisfy the contiguity condition. Control problems for such systems may have optimal solutions which, however, cannot be obtained by dynamic programming. This fact is shown on example of a widely used engineering system for which optimal trajectories have all its remaining parts non optimal and non contiguous to the optimal trajectories. The paper presents theoretical justification of dynamic programming for contiguous systems without the principle of optimality, and discussion of some problems important for applications.