Optimal control problems with upper semicontinuous Hamiltonians

• Autorzy: Arkadiusz Misztela
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 49L25: Viscosity solutions
• 70H20: Hamilton-Jacobi equations
• 70H14: Stability problems

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2010
• Tom: 30
• Numer: 1
• Strony: 71-99

Daty

wydano

2010

otrzymano

2009-02-19

poprawiono

2009-10-01

Twórcy

autor

Arkadiusz Misztela

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

Bibliografia

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Identyfikatory

DOI

10.7151/dmdico.1113