Human Behavior Learning for a Class of Nonlinear Human-in-the-Loop Systems via Takagi-Sugeno Fuzzy Model

In this article, the issue of human behavior learning (HBL) is addressed for a class of nonlinear human-in-the-loop (HiTL) systems where the human operator is viewed as a nonlinear optimal controller. Owing to its outstanding interpretability and strong nonlinear representation capability, the Takagi–Sugeno (T–S) fuzzy model is employed to represent the nonlinear HiTL control system and approximate the unknown human control law based on the parallel distributed compensation (PDC) scheme. A quadratic-like cost function with fuzzy weighting matrices is built to depict the human behavior, which conforms to human thinking and is unknown to the machine. The aim of the HBL is to retrieve the fuzzy weighting matrices such that the human control law will be optimal in the sense of minimizing the retrieved cost function. In the proposed HBL scheme, the state-dependent Riccati equation-based nonlinear optimal control technique plays an important role, which has a similar structure to the linear quadratic regulator theory and thus is of low computational complexity. With the help of the PDC-based fuzzy approximator for the unknown human control law, a two-step procedure is proposed for the HBL. First, a filter-based adaptive law is developed to learn the gain matrices of the fuzzy approximator using the system state data only. The convergence analysis of the adaptive estimator is also given. Then, a semidefinite programming problem with the quadratic objective function can be set up for determining the fuzzy weighting matrices of the cost function. The simulation study on a steering control system of the intelligent vehicle is given to show the effectiveness and applicability of the developed approach.