Hamilton–Jacobi characterization of the state constrained value

A proximal Hamilton–Jacobi characterization of the value function of a state constrained optimal control problem is obtained by exploiting trajectory tracking properties relative to inner approximations of the constraint set. The result is shown to be easily rephrasable in terms of Soner's cons...

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Bibliographic Details
Published in:Nonlinear analysis 2005-05, Vol.61 (5), p.725-734
Main Authors: Clarke, F.H., Stern, R.J.
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
Hamilton–Jacobi equation
Mathematical analysis
Mathematics
Nonsmooth analysis
Sciences and techniques of general use
State constrained value function
Viscosity solution
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Summary:A proximal Hamilton–Jacobi characterization of the value function of a state constrained optimal control problem is obtained by exploiting trajectory tracking properties relative to inner approximations of the constraint set. The result is shown to be easily rephrasable in terms of Soner's constrained viscosity solution concept.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2003.06.005