Optimal control of control-affine systems under the presence of uncertainty

Resumo

This thesis presents a collection of results concerning the optimal control of control-affine systems subject to uncertainty. We investigate the existence of optimal controls in scenarios where uncertainties affect both the system dynamics and the initial conditions. For the case of uncertainty in the initial condition, we establish first-order necessary conditions for optimality and provide characterization for singular control in the case of scalar control and for the case when the vector fields of the system commutes. We further analyze the value function for problems with terminal cost, providing its main structural properties and characterizing the associated viscosity solution when the initial condition is fixed. Additionally, we address a minimal escape-time problem with uncertain initial conditions taking values in a Hilbert space. Finally, we develop numerical methods designed to compute optimal controls and to support the qualitative analysis of the system under uncertainty.

Ficha do documento

Tipo

Tese

Ano

2026

Instituição

Fundação Getulio Vargas

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Acesso aberto

Identificador

oai:repositorio.fgv.br:10438/38653

Palavras-chave

Optimal control theoryControl-affine systemsUncertainty quantificationSingular arcsReinforcement learningMatemáticaAnálise matemáticaEquações diferenciaisSistemas dinâmicos diferenciaisAnálise numérica