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This paper considers a collection of networked nonlinear dynamical systems,and addresses the synthesis of feedback controllers that seek optimal operatingpoints corresponding to the solution of network-wide constrained optimizationproblems. Particular emphasis is placed on the solution of semidefiniteprograms (SDPs). The design of the feedback controller is grounded on a dualepsilon-subgradient approach, with the dual iterates utilized to dynamicallyupdate the dynamical-system reference signals. Global convergence is guaranteedfor diminishing stepsize rules, even when the reference inputs are updated at afaster rate than the dynamical-system settling time. The application of theproposed framework to the control of power-electronic inverters in ACdistribution systems is discussed. The objective is to bridge the time-scaleseparation between real-time inverter control and network-wide optimization.Optimization objectives assume the form of SDP relaxations of prototypical ACoptimal power flow problems.

Regulation of Dynamical Systems to Optimal Solutions of Semidefinite Programs: Algorithms and Applications to AC Optimal Power Flow