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This paper examines the problem of real-time optimization of networkedsystems and develops online algorithms that steer the system towards theoptimal trajectory without explicit knowledge of the system model. The problemis modeled as a dynamic optimization problem with time-varying performanceobjectives and engineering constraints. The design of the algorithms leveragesthe online zero-order primal-dual projected-gradient method. In particular, theprimal step that involves the gradient of the objective function (and hencerequires networked systems model) is replaced by its zero-order approximationwith two function evaluations using a deterministic perturbation signal. Theevaluations are performed using the measurements of the system output, hencegiving rise to a feedback interconnection, with the optimization algorithmserving as a feedback controller. The paper provides some insights on thestability and tracking properties of this interconnection. Finally, the paperapplies this methodology to a real-time optimal power flow problem in powersystems, and shows its efficacy on the IEEE 37-node distribution test feederfor reference power tracking and voltage regulation.

Model-Free Primal-Dual Methods for Network Optimization with Application to Real-Time Optimal Power Flow