A Finite-Horizon Inverse Linear Quadratic Optimal Control Method for Human-in-the-Loop Behavior Learning

The key to enhancing machine intelligence is to make the machine learn how human beings perform tasks. In this article, the issue of finite-horizon inverse linear quadratic (LQ) optimal control is investigated for human behavior learning in a class of human-in-the-loop (HiTL) systems. A novel finite-horizon inverse optimal control (FHIOC) approach is developed by integrating time-varying parameter identification and linear matrix inequality (LMI) optimization techniques. The proposed approach covers three steps: by only using the system state measurement, 1) an offline identification method is developed to provide a batch least-squares estimation for the human time-varying feedback gain matrix; 2) a recursive least-squares adaptive law is proposed to online learn the human time-varying feedback gain in real time; and 3) the weighting matrices of the human cost function are recovered via the time-convexity and LMI optimization techniques with the learned time-varying feedback gain. Finally, the validity of the proposed methods is supported by a supplementary steering system of an intelligent vehicle.