  This paper examines the problem of real-time optimization of networked
systems and develops online algorithms that steer the system towards the
optimal trajectory without explicit knowledge of the system model. The problem
is modeled as a dynamic optimization problem with time-varying performance
objectives and engineering constraints. The design of the algorithms leverages
the online zero-order primal-dual projected-gradient method. In particular, the
primal step that involves the gradient of the objective function (and hence
requires networked systems model) is replaced by its zero-order approximation
with two function evaluations using a deterministic perturbation signal. The
evaluations are performed using the measurements of the system output, hence
giving rise to a feedback interconnection, with the optimization algorithm
serving as a feedback controller. The paper provides some insights on the
stability and tracking properties of this interconnection. Finally, the paper
applies this methodology to a real-time optimal power flow problem in power
systems, and shows its efficacy on the IEEE 37-node distribution test feeder
for reference power tracking and voltage regulation.
