# Optimal control problems with upper semicontinuous Hamiltonians

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

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

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topArkadiusz 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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