Data-based Online Optimization of Networked Systems: High-probability Analysis and Applications to Power Grids

The talk focuses on the synthesis of data-based online algorithms to optimize the behavior of networked systems – with a specific focus on power grids – operating in uncertain, dynamically changing environments, and with human-in-the-loop components. Formalizing the optimization objectives through a time-varying optimization problem, the talk considers the design of online algorithms with the following features: i) concurrent learning modules are utilized to learn the cost function on the fly (using infrequent functional evaluations, and leveraging Gaussian Processes), and ii) algorithms are implemented in closed-loop with the plant to bypass the need for accurate knowledge of the algebraic map of the system. Leveraging contraction arguments, the performance of the online algorithm is analyzed in terms of tracking of an optimal solution trajectory implicitly defined by the time-varying optimization problem; in particular, results in terms of convergence in expectation and in high-probability are presented, with the latter derived by adopting a sub-Weibull assumption on measurement errors and the error in the reconstruction of the cost. Additional results are offered in terms of cumulative fixed-point residual. The online algorithm is applied to solve real-time demand response problems in power grids, where one would like to strike a balance between maximizing the profit for providing grid services and minimizing the (unknown) discomfort function of the end-users. Additional examples include real-time optimal power flow applications.