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Full-Text Articles in Dynamic Systems
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.
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 …
Additive Control Of Stochastic Linear Systems With Finite Horizon, Pao-Liu Chow, José-Luis Menaldi, Maurice Robin
Additive Control Of Stochastic Linear Systems With Finite Horizon, Pao-Liu Chow, José-Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
We consider a dynamic system whose state is governed by a linear stochastic differential equation with time-dependent coefficients. The control acts additively on the state of the system. Our objective is to minimize an integral cost which depends upon the evolution of the state and the total variation of the control process. It is proved that the optimal cost is the unique solution of an appropriate free boundary problem in a space-time domain. By using some decomposition arguments, the problems of a two-sided control, i.e. optimal corrections, and the case with constraints on the resources, i.e. finite fuel, can be …