6 Stochastic Control over Finite Time Intervals

Abstract

Here we shall discuss finite time interval problems where the main idea is to control a system, and where estimation, if it is a part of the problem at all, is of secondary importance. We shall discuss problems with and without dynamic compensators. Dynamic compensators are important for the case when full state measurements are not available, so that an observer is useful [1]. They are also important for the case where only a noisy measurement of the observation is available and filtering of the noise is necessary. Such problems have been considered in [2, 3]. We will see that only under very special circumstances do such problems have elegant solutions. Such is the case when full order compensators are used, and the result known as the separation theorem [4], is probably the most elegant result in all of systems theory. We will begin our examination of Stochastic Control problems by examining the output feedback control problem which has been studied by Axsater [5].

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