  This paper considers a collection of networked nonlinear dynamical systems,
and addresses the synthesis of feedback controllers that seek optimal operating
points corresponding to the solution of network-wide constrained optimization
problems. Particular emphasis is placed on the solution of semidefinite
programs (SDPs). The design of the feedback controller is grounded on a dual
epsilon-subgradient approach, with the dual iterates utilized to dynamically
update the dynamical-system reference signals. Global convergence is guaranteed
for diminishing stepsize rules, even when the reference inputs are updated at a
faster rate than the dynamical-system settling time. The application of the
proposed framework to the control of power-electronic inverters in AC
distribution systems is discussed. The objective is to bridge the time-scale
separation between real-time inverter control and network-wide optimization.
Optimization objectives assume the form of SDP relaxations of prototypical AC
optimal power flow problems.
