  Reference and command governors are add-on schemes that augment nominal
closed-loop systems with the capability to enforce state and control
constraints. They do this by monitoring and modifying, when necessary, the
reference command. Existing command governors do this by solving at each
sampling time a quadratic programming problem to find a modified reference
closest to the original command such that the current state and the modified
reference pair are constraint admissible. In this paper, we show that a simple
modification of the basic command governor enables it to operate with inexact
optimization and even without requiring invariance of the constraint admissible
set. Thus this modification significantly extends the applicability of the
reference and command governors to practical problems where finding invariant
sets may be problematic and where exact optimization may not be feasible due to
reliability of the optimizers or limited computing power. Numerical examples
are reported which illustrate the approach.
