Koopman-Based Fractional Predefined-Time Control for Wearable Exoskeleton System

Abstract

In this paper, an innovative fractional predefined-time control scheme based on the Koopman operator is proposed for the wearable exoskeleton system (WES). Leveraging the nonlinear mapping of the Koopman operator and the prior information of the exoskeleton system, a prior Koopman model (PIKOM) is devised. As a data-driven model, the PIKOM can be constructed through measuring input/output (I/O) data, avoiding complex dynamic modeling. Besides, the integer-order PIKOM is broadened into a fractional-order form, and the tanh function is adopted to handle the problem of saturation constraint. The fractional predefined-time controller is meticulously designed to enhance the tracking performance of the WES. The tracking error converges to a narrow range near the origin within a predefined time. The experimental results verify the effectiveness and superiority of the proposed approach. Compared with state-of-the-art (SOTA) methods (Schemes 1-4), the proposed method achieves improvements of 12.2%, 18.2%, 8.8%, and 20.7%, respectively. Note to Practitioners—In recent years, the trajectory tracking of the WES has garnered significant and escalating research interests. Owing to the complicated structure of the WES, dynamic model-based control methods generally fail to realize satisfactory control performance. A PIKOM that only embraces I/O data is constructed to avoid this problem. Meanwhile, the PIKOM is converted into a fractional form because of the outstanding advantages of fractional-order control (FOC). With the rapid development of automatic control technology, there is a growing demand for the convergence rate of the WES. The asymptotic FOC method is no longer applicable. In this paper, a PIKOM-based fractional predefined-time control is presented to achieve trajectory tracking. In addition to inheriting the merits of fixed-time control strategies, this method exhibits a characteristic that the upper bound of convergence time is solely determined by a single parameter. The control performance of the proposed scheme is demonstrated by experimental results.