Data-driven Characterization of Recovery Energy in Controlled Dynamical Systems using Koopman Operator

A key aspect of a resilient dynamical system is its ability to recover from large disruptions. In this paper, we define and characterize recovery energy as a quantitative measure of the minimum effort required by a control dynamical system to return to a safe operating region after large disruptions. The problem of steering the system state to a pre-specified safe region with minimum recovery energy is posed as an optimization problem which turns out to be a nonconvex due to the nonlinear nature of the system dynamics. To this end, we use the Koopman operator theoretic framework to obtain a convex reformulation in a lifted observable space. Finally, we demonstrate the approach on an IEEE 123-bus test feeder and quantify its ability to recover from disruptions.