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ArticleOriginal scientific text

Title

Optimal control problems with upper semicontinuous Hamiltonians

Authors 1

Affiliations

  1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

In this paper we give examples of value functions in Bolza problem that are not bilateral or viscosity solutions and an example of a smooth value function that is even not a classic solution (in particular, it can be neither the viscosity nor the bilateral solution) of Hamilton-Jacobi-Bellman equation with upper semicontinuous Hamiltonian. Good properties of value functions motivate us to introduce approximate solutions of equations with such type Hamiltonians. We show that the value function is the unique approximate solution.

Keywords

ENG
Hamilton-Jacobi-Bellman equation, Bolza problem, viscosity solution, bilateral solution, monotonic approximation, semicontinuous Hamiltonian

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2010/30/1
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Pages:
71-99
Main language of publication
English
Received
2009-02-19
Accepted
2009-10-01
Published
2010

DOI: 10.7151/dmdico.1113

Exact and natural sciences