Non-Convex Feedback Optimization with Input and Output Constraints

In this letter, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer 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 schemes or inexact penalty methods, our control approach combines several desirable properties: it asymptotically enforces constraints on the plant steady-state outputs, and temporary constraint violations can be easily quantified. Our scheme requires only reduced model information in the form of steady-state input-output sensitivities of the plant. Further, global convergence is guaranteed even for non-convex problems. Finally, our controller is straightforward to tune, since the step-size is the only tuning parameter. © 2017 IEEE.ISSN:2475-145