We study an optimal control problem in Bolza form, and we consider the value function associated to this problem. We prove two verification theorems which ensure that, if a function W satisfies some suitable weak continuity assumptions and a Hamilton-Jacobi-Bellman inequality outside a countably H-n-rectifiable set, then it is lower than or equal to the value function. These results can be used for optimal synthesis approach.

Garavello, M. (2003). Verification theorems for Hamilton-Jacobi-Bellman equations. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 42(5), 1623-1642 [10.1137/S0363012902392688].

Verification theorems for Hamilton-Jacobi-Bellman equations

GARAVELLO, MAURO
2003

Abstract

We study an optimal control problem in Bolza form, and we consider the value function associated to this problem. We prove two verification theorems which ensure that, if a function W satisfies some suitable weak continuity assumptions and a Hamilton-Jacobi-Bellman inequality outside a countably H-n-rectifiable set, then it is lower than or equal to the value function. These results can be used for optimal synthesis approach.
Articolo in rivista - Articolo scientifico
verification theorem; optimal control; HJB equation; value function; viscosity solution
English
2003
42
5
1623
1642
none
Garavello, M. (2003). Verification theorems for Hamilton-Jacobi-Bellman equations. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 42(5), 1623-1642 [10.1137/S0363012902392688].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/37098
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