An online inverse optimal control method for learning human behavior in a class of noisy discrete-time linear HiTL systems

The main goal of human behavior learning (HBL) is to enable machines to better understand and imitate human behavior, thereby enhancing their adaptability and intelligence. This paper explores the real-time learning of human behavior in noisy, discrete-time, linear human-in-the-loop (HiTL) systems by combining moving horizon estimation (MHE), recursive least squares (RLS) and linear matrix inequality (LMI)-based optimization. We assume that human behavior can be modeled using a discrete-time optimal control (DTOC) framework, where the quadratic cost function includes an unknown weighting matrix that characterizes the human decision-making process. To mitigate the effects of noise, we first employ MHE to estimate the state trajectory by minimizing an objective function over a moving, fixed-size estimation window. Then, using the estimated states and control inputs, we identify the state feedback gain via RLS, for which we provide a convergence proof. Once the state feedback gain is obtained, we recover the cost matrix via an LMI-based optimization. Finally, simulation results on a steering assistance system for intelligent vehicles validate the proposed approach.