Abstract

The talk focuses on the synthesis and analysis of online algorithmic solutions to control systems or networked systems based on performance objectives and engineering constraints that may evolve over time. Particular emphasis is given to applications in power systems operations and control. The time-varying optimization formalism is leveraged to model optimal operational trajectories of the systems, as well as explicit local and network-level constraints. The design of the algorithms then capitalizes on an online implementation of primal-dual projected-gradient methods; the gradient steps are, however, suitably modified to accommodate actionable feedback in the form of measurements from the network—hence, the term feedback-based online optimization. By virtue of this approach, the resultant running algorithms can cope with model mismatches in the algebraic representation of the system states and outputs, they avoid pervasive measurements of exogenous inputs, and they naturally lend themselves to a distributed implementation. Under suitable assumptions, Q-linear convergence to optimal solutions of a time-varying convex problem is shown. On the other hand, under a generalization of the Mangasarian-Fromovitz constraint qualification, sufficient conditions are derived for the running algorithm to track a Karush-Kuhn-Tucker point of a time-varying nonconvex problem. Examples of applications in power systems will be provided.

Joint work with: A. Simonetto, Y. Tang, A. Bernstein, and S. Low.