On the achievable accuracy in stochastic control

Abstract

The behaviour of regulators for stochastic systems can be described with the variances of the input and the output. With these variances on the axes a diagram can be drawn. When the regulator parameters are varied an area in the diagram will be obtained. A particular regulator design method will be analysed in this respect. It is based on minimization of the conditional expectation of a wheighted sum of variances. The expectation is then taken conditional on all old measured data. It is shown that the regulator gives a reasonably good behaviour for systems with a positive real transfer function, For some other cases, e.g. non-minimum phase systems the regulator gives unstable closed loop systems.