Input and state constrained inverse optimal control with application to power networks

We study input and state constrained inverse optimal control problems starting from a stabilizing controller with a control Lyapunov function, where the goal is to make the controller an explicit solution of the resulting constrained optimal control problem. For an appropriate cost design and initial states for which a sublevel set of the Lyapunov function is contained in the state constraint set and the initial input lies on an ellipsoid inside the input constraint set, we show that the stabilizing controller solves the constrained optimal control problem. Compared to the state-of-the-art, we avoid solving nonlinear optimization problems evaluated pointwise, i.e., for every state, or in a repetitive fashion, i.e., at each time step. We apply our theoretical results to study the angular droop control studied in (Jouini et al., 2022) of an inverter-based power network. For this, we accommodate the constraints on the angle and power generation and exemplify our approach through a two-inverter case study.