Continuous-Time Inverse Quadratic Optimal Control Problem

TL;DR

This paper addresses the inverse optimal control problem for linear-quadratic systems, providing necessary and sufficient conditions for solution existence, explicit solution characterizations, and methods for approximate solutions in infeasible cases.

Contribution

It offers the first complete characterization of solution conditions for finite horizon inverse LQ control, including analytic solutions and approximation methods for infeasible cases.

Findings

Derived necessary and sufficient conditions for solution existence.

Provided explicit solution space expressions for feasible cases.

Developed a convex optimization approach for approximate solutions in infeasible cases.

Abstract

In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose the first complete result of the necessary and sufficient condition for the existence of corresponding LQ cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices in LQ problems is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual. And the optimality condition is solved under a static quadratic programming framework to facilitate the computation. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.