Necessary Conditions for Optimal Control Problems defined on Stratified Domains

• Grant number: 14/05558-2
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: August 01, 2014
• End date: July 29, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Geraldo Nunes Silva
• Grantee: Daniella Porto
• Supervisor: Peter R. Wolenski
• Host 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
• Institution abroad: 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.