THE MINIMIZATION OF THE MEAN SQUARE OF THE DEVIATION OF A RANDOM SIGNAL FROM A GIVEN TARGET
Vasile F. Drǎgan, Ivan Ganchev Ivanov · Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application · 2021
In this paper we consider the problem of minimization of the mean square value of the deviation of a random signal z(tf ) from a given target ζ. The random signal z(tf ) represents the value at instant time tf of an output of a controlled dynamical system described by an Itˆo differential equation. Both the case when the set of admissible controls consist of general nonanticipative stochastic processes and the case when only piecewise constant controls are available are analyzed. We show that in both cases the optimal controls are in affine state feedback forms. Explicit formulae of the gain matrices of the optimal controls are provided.