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Full-Text Articles in Control Theory
Finite Hybrid- And Semi-Markov Chains, Jose L. Menaldi, Maurice Robin
Finite Hybrid- And Semi-Markov Chains, Jose L. Menaldi, Maurice Robin
Mathematics Faculty Research Publications
The ergodic behaviour of finite Markov chains having also instantaneous transition are considered. Some estimates are obtained which complement our previous work [29]. Also, an optimal switching control model for semi-Markov chains is analysed, without any particular assumptions on the recurrent classes.
Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp
Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp
Theses and Dissertations
This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.
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 …