Verification Theorems for Hamilton--Jacobi--Bellman Equations
Mauro Garavello · SIAM Journal on Control and Optimization · 2003
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 than or equal to the value function. These results can be used for optimal synthesis approach.