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Verification Theorems for Hamilton-Jacobi-Bellman equations

Mauro Garavello
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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 $\mathcal H^n$-rectifiable set, then it is lower or equal to the value function. These results can be used for optimal synthesis approach.

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Mauro Garavello. 2002-10-17. Verification Theorems for Hamilton-Jacobi-Bellman equations. https://arxiv.org/abs/math/0109034

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