A controlled heterogeneous collection of identical items is presented. According to their level of wear and tear, they are divided into a finite number of classes and the partition of the collection is allowed to change with the time. A suitable exchangeability assumption is made, to preserve the property of the items to be identical. The role of the occupation numbers is investigated and a filtering problem is set up, where the observation is the cardinality of a particular class. A control on the dynamics of the items is introduced and the existence of an optimal control is proved. A discrete time approximation for the separated problem, which is a finite dimensional one, is performed. As a consequence, an approximation for the value function is given.
Controlled Hetereogeneous Collection: the Role of Occupation Numbers
TARDELLI, PAOLA
2008-01-01
Abstract
A controlled heterogeneous collection of identical items is presented. According to their level of wear and tear, they are divided into a finite number of classes and the partition of the collection is allowed to change with the time. A suitable exchangeability assumption is made, to preserve the property of the items to be identical. The role of the occupation numbers is investigated and a filtering problem is set up, where the observation is the cardinality of a particular class. A control on the dynamics of the items is introduced and the existence of an optimal control is proved. A discrete time approximation for the separated problem, which is a finite dimensional one, is performed. As a consequence, an approximation for the value function is given.Pubblicazioni consigliate
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