We investigate here a continuous time minimization problem in the

presence of disturbances in the dynamics. The only information available to

the controller is an incomplete observation of the state space at times

given in advance. Also, the initial state is not supposed to be perfectly

known. The corresponding control problem can be understood as a dynamic

game of Min-Max type where the controller wants to minimize the cost - by

choosing a strategy depending on a discrete-time incomplete measurement -

against the worst case of disturbance and initial state. Our main goal is

to pass from imperfect information in the measurement space to perfect

information in the estimation space, hence we introduce a second problem

based on estimation sets on the state. We prove that the value functions of

both problems are equal. Finally, we provide a characterization of the

value function through a system of Hamilton-Jacobi equations and

inequalities in terms of Dini derivatives.