On feasible set-membership state estimators in constrained command governor control
This paper considers the use of command governor (CG) control for a general discrete time--invariant system with incomplete state information. It is in this latter aspect that it extends prior work on receding horizon control using CG control. A deterministic set-membership state estimator of the state uncertainty set (SUS) is used. The CG controller is a non-linear device added to the compensated control system which has itself (independent of the CG) been a priori designed to track satisfactorily in the absence of constraints. In the presence of constraints the CG selects at each time instant a command \(w(t)\) from the set of constants which if applied do not violate the constraints. This is done by minimizing the distance of \(w(t)\) to the reference signal, then \(w(t)\) is used in place of the reference. When full state information is present this scheme is shown to be effective with the system satisfying the constraint for all possible disturbances. In contrast when simple fixed shape outer approximations of the SUS are used this scheme can lead to infeasibility. It does have the advantage of bounding the complexity of the control scheme requiring a constant number of parameters to describe these sets. To recover the stability and tracking properties of the CG controller, bounds must be placed on the errors involved in these outer approximations of the SUS. These upper bounds estimate the worst over estimation of the SUS over all possible system evolutions. If these are sufficiently small then similar theorems as the complete state information case are proven.
scientific article; zbMATH DE number 1553212