Inverse optimal control problem in the non autonomous linear-quadratic case

TL;DR

This paper investigates the inverse optimal control problem for non-autonomous linear-quadratic systems, focusing on injectivity and reconstruction, with theoretical insights and numerical validation.

Contribution

It extends the analysis of inverse linear quadratic problems to non-autonomous cases, showing injectivity properties and providing a reconstruction algorithm.

Findings

Injectivity characterization is the same as in autonomous case.

Injectivity is generic within the considered class.

Numerical test confirms the reconstruction algorithm's effectiveness.

Abstract

Inverse optimal control problem emerges in different practical applications, where the goal is to design a cost function in order to approximate given optimal strategies of an expert. Typical application is in robotics for generation of human motions. In this paper we analyze a general class of non autonomous inverse linear quadratic problems. This class of problems is of particular interest because it arises as a linearization of a nonlinear problem around an optimal trajectory. The addressed questions are the injectivity of the inverse problem and the reconstruction. We show that the nonlinear problem admits the same characterization of the injectivity as the autonomous one. In the autonomous case we show moreover that the injectivity property is generic in the considered class. We also provide a numerical test of the reconstruction algorithm in the autonomous setting.