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.
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