Solution Sets for Inverse Infinite-Horizon Linear-Quadratic Descriptor Differential Games

Abstract

In this letter, we study a model-based inverse problem for infinite-horizon linear-quadratic differential games with descriptor dynamics. Given an observed feedback strategy profile, we seek to identify all cost functions that rationalize it as a feedback Nash equilibrium; this collection is referred to as the solution set. We characterize the solution set, show that it is rectangular and convex, and provide an algorithm for computing an admissible realization whenever it is nonempty. We also show that, compared with the corresponding inverse problem for standard state-space dynamics, descriptor dynamics modify the geometry of the solution set and may reduce identifiability. Finally, we illustrate the results with numerical examples.