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

TL;DR

This paper investigates the inverse problem in infinite-horizon linear-quadratic differential games with descriptor dynamics, characterizing the solution set and providing algorithms for realization.

Contribution

It introduces a characterization of the solution set for inverse LQ differential games with descriptor dynamics and analyzes how these dynamics affect identifiability.

Findings

Solution set is rectangular and convex.

Descriptor dynamics alter the geometry of the solution set.

Numerical examples illustrate the theoretical results.

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.