Approximation to Impulsive Optimal Control Problem and Minimum Time Problem on Stratified Domains

Author(s)

Daniella Porto

• Document type: Doctoral Thesis
• Press: São José do Rio Preto. 2016-03-24.
• Institution: Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto
• Defense date: 2016-03-15
• Advisor: Geraldo Nunes Silva

Abstract

We consider two types of optimal control problems: a) Impulsive control problems and b) optimal control problems in stratified domains. So we organize this work in two distinct parts. The first part is dedicated to the study of an impulsive optimal control problem where the usual reparametrization technique of the impulsive problem is used to obtain a regular problem. Then we provide consistent approximation results via Euler discretization in which a sequence of related approximated problems is obtained with the property that if there is a subsequence of processes which are optimal for the corresponding discrete problems which converge to some limit process, then the latter is optimal to the original reparametrized problem. From the reparametrized optimal solution we are able to provide the solution to the original impulsive problem. The second part is regarding the minimal time problem defined on stratified domains. We sate the problem and establish Hamilton-Jacobi inequalities. Then we give some motivation via Snell's law and the Elvis problem and finally we provide necessary and sufficient conditions of optimality. (AU)

• FAPESP's process: 11/14121-9 - Discretization methods for impulsive optimal control problems
• Grantee: Daniella Porto
• Support Opportunities: Scholarships in Brazil - Doctorate