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Full-Text Articles in Physical Sciences and Mathematics
Discrete-Time Hybrid Control In Borel Spaces: Average Cost Optimality Criterion, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau, Maurice Robin
Discrete-Time Hybrid Control In Borel Spaces: Average Cost Optimality Criterion, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau, Maurice Robin
Mathematics Faculty Research Publications
This paper addresses an optimal hybrid control problem in discrete-time with Borel state and action spaces. By hybrid we mean that the evolution of the state of the system may undergo deep changes according to structural modifications of the dynamic. Such modifications occur either by the position of the state or by means of the controller's actions. The optimality criterion is of a long-run ratio-average (or ratio-ergodic) type. We provide the existence of optimal average policies for this hybrid control problem by analyzing an associated dynamic programming equation. We also show that this problem can be translated into a standard …
Discrete-Time Hybrid Control In Borel Spaces, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau
Discrete-Time Hybrid Control In Borel Spaces, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau
Mathematics Faculty Research Publications
A discrete-time hybrid control model with Borel state and action spaces is introduced. In this type of models, the dynamic of the system is composed by two sub-dynamics affecting the evolution of the state; one is of a standard-type that runs almost every time and another is of a special-type that is active under special circumstances. The controller is able to use two different type of actions, each of them is applied to each of the two sub-dynamics, and the activations of these sub-dynamics are possible according to an activation rule that can be handled by the controller. The aim …