Minimization of the estimation error by control in systems with multiplicative noise

Abstract

In this paper, we consider a problem of the estimation for the stochastic system with multiplicative noise. For the current state the system with additive noise, the estimation problem is solved by Kalman-Bucy filter. For stochastic systems, this filter is widely used in the control theory for the construction of optimal regulators under the incomplete information. Many results of this theory, a separation theorem, e.g., rely on the following important property of the systems with additive noise. The fact is that in linear systems with additive noise, a choice of the control strategy does not influence on the uncertainty of the system state. It allows us to distinguish a control and observation. However, systems with multiplicative noises do not exhibit such independence. Estimation errors in these systems depend on the control, so one can regulate the accuracy of the estimation choosing this control. In this paper, we construct a regulator which provides the highest accuracy for the estimator. © Dynamic Publishers, Inc.