3DIOC: Direct Data-Driven Inverse Optimal Control for LTI Systems

TL;DR

This paper introduces a direct data-driven inverse optimal control method for LTI systems that learns the objective function from input-output data without system identification, improving efficiency and requiring less data.

Contribution

The paper presents a novel model-free inverse optimal control algorithm for LTI systems using the Fundamental Lemma, eliminating the need for system identification.

Findings

Efficient algorithm with reduced computation and data requirements

Successful simulation results demonstrating effectiveness

Established identifiability conditions and perturbation analysis

Abstract

This paper develops a direct data-driven inverse optimal control (3DIOC) algorithm for the linear time-invariant (LTI) system who conducts a linear quadratic (LQ) control, where the underlying objective function is learned directly from measured input-output trajectories without system identification. By introducing the Fundamental Lemma, we establish the input-output representation of the LTI system. We accordingly propose a model-free optimality necessary condition for the forward LQ problem to build a connection between the objective function and collected data, with which the inverse optimal control problem is solved. We further improve the algorithm so that it requires a less computation and data. Identifiability condition and perturbation analysis are provided. Simulations demonstrate the efficiency and performance of our algorithms.