Min-max control of quadratic systems

The controller of a system initially obtains an imperfect measurement of its state variables, and obtains no measurements thereafter. He is therefore constrained to choose an open-loop control function, depending only on the initial measurement. Control of the system incurs a cost which the controller wishes to make as small as possible. However, because the initial state is not known exactly, it is not possible to control the system so that the minimum cost is guaranteed. In this paper, I will consider the problem of controlling the system so that the worst possible cost, consistent with the initial measurement, is minimized. The system considered will have linear dynamics and a quadratic cost function.