Data Measurement Smoothing in the Guaranteed Estimation Algorithm for Dynamical Systems Control

The present article delves into the problems of linear dynamical system state estimation and optimal control under uncertainty. Two approaches to filtering, Kalman filtering and the guaranteed estimation are compared. It has been shown that comparison requires correspondence between stochastic and deterministic mathematical models describing uncertain quantities. The optimal control solution is found. It ensures the result with the worst possible value of the cost function over all uncertain factors. A numerical example is given for the linear second order system. For the case of a time-varying dynamical system it has been demonstrated that the point estimate obtained by the guaranteed approach can have dynamics that is quite different from the dynamical behavior of the observed system. The smoothing algorithm for the point estimate dynamics is proposed.