Some topics in deterministic and stochastic control : LP methods, PDMP associated to gene networks, controllability
type: Dataset
description: The aim of this synthesis is to present my research activity covering the period elapsed since the terminal year of my PhD program (i.e. the period October 2008 - February 2013). My subjects of research roughly correspond to three main directions, each one presented in a separate section : ∙ Linear programming (LP) methods in deterministic and stochastic control problems; ∙ Control methods in piecewise deterministic Markov processes and their applications to stochastic gene networks; ∙ Controllability properties for linear stochastic systems and related topics. In the first section, we study several classes of deterministic/stochastic control problems with semicontinuous cost. In the stochastic framework, we consider the Mayer problem and optimal stopping for controlled diffusions (corresponding to the paper [G10]), dynamic programming principles (corresponding to the paper [G6]) and control problems with state constraints (corresponding to the paper [G2]). We also study optimal control problems with discounted payoffs in an infinite horizon setting and long-time averaging (corresponding to [G12]), systems driven by stochastic variational inequalities ([G3]), and Zubov's characterization of asymptotic stability domains ([G3]). We investigate the existence of the limit value function for a class of nonlinear stochastic control problems under nonexpansive assumptions and uniform Tauberian theorems (corresponding to [G19]). In the deterministic setting, we consider the linearization and the dynamic programming principles for L^{∞}-control problems (corresponding to the paper [G9]) and for systems with state constraints (in [G1]). We propose a linearization method for min-max control problems (corresponding to [G18]). The common point between these articles is the method employed relying on linearized formulation and viscosity tools. We also present some viability results for singularly perturbed control systems (corresponding to [G13]). The second section is devoted to…
landing page: https://theses.hal.science/tel-00864555
keyword: controlabilite
keyword: controle-deterministe-et-stochastique
keyword: controllability
keyword: deterministic-and-stochastic-control
keyword: habilitation-a-diriger-des-recherches
keyword: infoeu-reposemanticsother
keyword: inifinite-dimensional-linear-programming-methods
keyword: mathmath-ocmathematics-mathoptimization-and-control-mathoc
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: piecewise-deterministic-markov-processes
keyword: processus-markoviens-deterministes-par-morceaux
keyword: programmation-lineaire-infini-dimensionnelle
keyword: reseaux-de-genes
keyword: stochastic-gene-networks
issued: 2026-05-09T16:01:15.451399
modified: 2026-05-09T16:01:15.451404
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Some topics in deterministic and stochastic control : LP methods, PDMP associated to gene networks, controllability
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format: HTML
access URL: https://theses.hal.science/tel-00864555
issued: 2026-05-09T16:01:15.454454
modified: 2026-05-09T16:01:15.437491