  This paper investigates the problem of regulating in real time a linear
dynamical system to the solution trajectory of a time-varying constrained
convex optimization problem. The proposed feedback controller is based on an
adaptation of the saddle-flow dynamics, modified to take into account
projections on constraint sets and output-feedback from the plant. We derive
sufficient conditions on the tunable parameters of the controller (inherently
related to the time-scale separation between plant and controller dynamics) to
guarantee exponential and input-to-state stability of the closed-loop system.
The analysis is tailored to the case of time-varying strongly convex cost
functions and polytopic output constraints. The theoretical results are further
validated in a ramp metering control problem in a network of traffic highways.
