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Necessary conditions for optimal control problems defined on stratified domains

Grant number: 14/05558-2
Support type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): August 01, 2014
Effective date (End): July 29, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Geraldo Nunes Silva
Grantee:Daniella Porto
Supervisor abroad: Peter R. Wolenski
Home Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
Research place: Louisiana State University (LSU), United States  
Associated to the scholarship:11/14121-9 - Discretization methods for impulsive optimal control problems, BP.DR

Abstract

The main goal of this project is to provide necessary conditions for an optimal control problem with a stratified form of dynamics. The state space of the system takes the form of a stratified domain, a concept recently introduced in the literature that is a structured partitioning into subdomains of the underlying space. Dynamics are given on each subdomain satisfying a standard set of assumptions. The overall dynamics, however, is not standard, and in particular is not even Lipschitz along a trajectory that moves across and through the various subdomains. Recent work has provided sufficient conditions for optimality via Hamilton-Jacobi theory. The goal of the current project is to derive necessary optimality conditions in a suitable form of the Pontryagin Maximum Principle for the Mayer and Min Time problems. (AU)

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