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An optimality system for finite average Markov decision chains under risk-aversion

Alfredo Alanís-Durán, Rolando Cavazos-Cadena (2012)

Kybernetika

This work concerns controlled Markov chains with finite state space and compact action sets. The decision maker is risk-averse with constant risk-sensitivity, and the performance of a control policy is measured by the long-run average cost criterion. Under standard continuity-compactness conditions, it is shown that the (possibly non-constant) optimal value function is characterized by a system of optimality equations which allows to obtain an optimal stationary policy. Also, it is shown that the...

Analyse de sensibilité d’un problème de contrôle optimal bilinéaire

Jean-Marc Clérin (2012)

Annales mathématiques Blaise Pascal

Dans cet article, nous étudions la sensibilité d’un problème de contrôle optimal de type bilinéaire. Le coût est différentiable, quadratique et strictement convexe. Le système est gouverné par un opérateur parabolique du quatrième ordre et présente une perturbation additive dans l’équation d’état, ainsi qu’une partie bilinéaire, relativement au contrôle u et à l’état z , de la forme ( u · ∇ ) z . Sous des conditions de petitesse de l’état initial et de la perturbation, nous exploitons les propriétés de régularité...

Analysis of a time optimal control problem related to the management of a bioreactor

Lino J. Alvarez-Vázquez, Francisco J. Fernández, Aurea Martínez (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence of,...

Analysis of a time optimal control problem related to the management of a bioreactor***

Lino J. Alvarez-Vázquez, Francisco J. Fernández, Aurea Martínez (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence of,...

Anisotropic functions : a genericity result with crystallographic implications

Victor J. Mizel, Alexander J. Zaslavski (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In the 1950’s and 1960’s surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...

Anisotropic functions: a genericity result with crystallographic implications

Victor J. Mizel, Alexander J. Zaslavski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In the 1950's and 1960's surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...

Application of the optimal control theory to the wastewater elimination problem.

Lino José Alvarez-Vázquez, Alfredo Bermúdez, Aurea Martínez, Carmen Rodríguez, Miguel Ernesto Vázquez-Méndez (2002)

RACSAM

The main goal of this paper is to show some applications of the optimal control theory to the wastewater elimination problem. Firstly, we deal with the numerical simulation of a given situation. We present a suitable mathematical model, propose a method to solve it and show the numerical results for a realistic situation in the ría of Arousa (Spain). Secondly, in the same framework of wastewater elimination problem, we pose two economic-environmental problems which can be formulated as constrained...

Approximate maximum principle for discrete approximations of optimal control systems with nonsmooth objectives and endpoint constraints

Boris S. Mordukhovich, Ilya Shvartsman (2013)

ESAIM: Control, Optimisation and Calculus of Variations

The paper studies discrete/finite-difference approximations of optimal control problems governed by continuous-time dynamical systems with endpoint constraints. Finite-difference systems, considered as parametric control problems with the decreasing step of discretization, occupy an intermediate position between continuous-time and discrete-time (with fixed steps) control processes and play a significant role in both qualitative and numerical aspects of optimal control. In this paper we derive an...

Arrow-type sufficient conditions for optimality of age-structured control problems

Vladimir Krastev (2013)

Open Mathematics

We consider a class of age-structured control problems with nonlocal dynamics and boundary conditions. For these problems we suggest Arrow-type sufficient conditions for optimality of problems defined on finite as well as infinite time intervals. We examine some models as illustrations (optimal education and optimal offence control problems).

Asymptotics of accessibility sets along an abnormal trajectory

Emmanuel Trélat (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We describe precisely, under generic conditions, the contact of the accessibility set at time T with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-riemannian system of rank 2. As a consequence we obtain in sub-riemannian geometry a new splitting-up of the sphere near an abnormal minimizer γ into two sectors, bordered by the first Pontryagin’s cone along γ , called the L ∞ -sector and the L 2 -sector. Moreover we...

Asymptotics of accessibility sets along an abnormal trajectory

Emmanuel Trélat (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We describe precisely, under generic conditions, the contact of the accessibility set at time T with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer γ into two sectors, bordered by the first Pontryagin's cone along γ, called the L∞-sector and the L2-sector. Moreover...

Currently displaying 81 – 100 of 927