  In this paper we study how high-gain anti-windup schemes can be used to
implement projected dynamical systems in control loops that are subject to
saturation on a (possibly unknown) set of admissible inputs. This insight is
especially useful for the design of autonomous optimization schemes that
realize a closed-loop behavior which approximates a particular optimization
algorithm (e.g., projected gradient or Newton descent) while requiring only
limited model information. In our analysis we show that a saturated integral
controller, augmented with an anti-windup scheme, gives rise to a perturbed
projected dynamical system. This insight allows us to show uniform convergence
and robust practical stability as the anti-windup gain goes to infinity.
Moreover, for a special case encountered in autonomous optimization we show
robust convergence, i.e., convergence to an optimal steady-state for finite
gains. Apart from being particularly suited for online optimization of
large-scale systems, such as power grids, these results are potentially useful
for other control and optimization applications as they shed a new light on
both anti-windup control and projected gradient systems.
