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

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.