Data-driven Resilience Characterization of Control Dynamical Systems

In this paper, we define and quantify resilience of a power network and propose data-driven algorithms for computing the same for the power grid. To do this, we use the Koopman operator framework to lift the controlled dynamical system to an abstract (possibly higher) dimensional space, where the evolution is linear. The linear system representation allows us to relate controllability and observability of a general nonlinear control system to the controllability and observability of the lifted linear system, respectively. Finally, we define the resilience of the underlying power grid in terms of the controllability and observability Gramians of the lifted linear system. We illustrate the proposed approach to compute the resilience metrics on time-series data obtained from a microgrid.