Mathematical foundations of the theory of coordinate-operator feedback

We study the control problem for dynamic plants operating under uncertainty, in particular, in the case of unmeasurable external disturbances of coordinate and operator types. The complexity of such a problem essentially increases under the assumption of rapidly varying parametric disturbances. The problem of constructing efficient control algorithms in this case remains unsolved. We present a brief survey of known control methods for dynamic plants subjected to various disturbances. To solve the control problem in the case of rapidly varying parametric disturbances, we suggest an approach based on the binarity principle, which permits one to introduce new types of feedback, in particular, a coordinate-operator feedback; in turn, this feedback permits one to synthesize controllers providing the small sensitivity of the closed-loop plants to coordinate and parametric disturbances varying arbitrarily rapidly.