  In this paper, we present a novel control scheme for feedback optimization.
That is, we propose a discrete-time controller that can steer the steady state
of a physical plant to the solution of a constrained optimization problem
without numerically solving the problem. Our controller can be interpreted as a
discretization of a continuous-time projected gradient flow. Compared to other
schemes used for feedback optimization, such as saddle-point flows or inexact
penalty methods, our algorithm combines several desirable properties: It
asymptotically enforces constraints on the plant steady-state outputs, and
temporary constraint violations can be easily quantified. Our algorithm
requires only reduced model information in the form of steady-state
input-output sensitivities of the plant. Further, as we prove in this paper,
global convergence is guaranteed even for non-convex problems. Finally, our
algorithm is straightforward to tune, since the step-size is the only tuning
parameter.
