Bi-Level Dynamic Optimization with Feedback

This paper considers a bi-level real-time algorithmic framework for networked systems, consisting of several local controllers and a central controller. The central controller issues setpoints to the local controllers to optimize their operational objectives while satisfying system-wide constraints. In this context, the paper develops an online algorithm for tracking the optimal solution of the underlying dynamic optimization problem. The design of the algorithm is based on a projected-gradient method, suitably modified to accommodate appropriate measurements (i.e., feedback). Optimality claims are established in terms of the dynamic regret of the algorithm; the latter is a natural performance criterion in nonstationary environments associated with real-time control problems. Finally, the application of the algorithm to real-time control of power setpoints in an electrical grid is illustrated.