Optimal control problems with upper semicontinuous Hamiltonians

Arkadiusz Misztela

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2010)

  • Volume: 30, Issue: 1, page 71-99
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Arkadiusz Misztela. "Optimal control problems with upper semicontinuous Hamiltonians." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30.1 (2010): 71-99. <http://eudml.org/doc/271194>.

@article{ArkadiuszMisztela2010,
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.},
author = {Arkadiusz Misztela},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Hamilton-Jacobi-Bellman equation; Bolza problem; viscosity solution; bilateral solution; monotonic approximation; semicontinuous Hamiltonian},
language = {eng},
number = {1},
pages = {71-99},
title = {Optimal control problems with upper semicontinuous Hamiltonians},
url = {http://eudml.org/doc/271194},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Arkadiusz Misztela
TI - Optimal control problems with upper semicontinuous Hamiltonians
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2010
VL - 30
IS - 1
SP - 71
EP - 99
AB - 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.
LA - eng
KW - Hamilton-Jacobi-Bellman equation; Bolza problem; viscosity solution; bilateral solution; monotonic approximation; semicontinuous Hamiltonian
UR - http://eudml.org/doc/271194
ER -

References

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