Minimax control of systems with uncertain state measurements

Abstract

A system is controlled with the aid of uncertain state measurements, the errors of which are known to lie within a given, compact set. Control of the system incurs a cost of which it is desired that the largest value consistent with the measurements obtained be minimized. Two different measurement régimes are considered. In the first, measurements are obtained throughout the history of the process and, in the second, only an initial state measurement is obtained. Under certain circumstances, it is shown that the optimization problems for the two régimes are equivalent. The general solution of the problem for the second régime is given for the case when the dynamics are linear, and the cost function quadratic.