$H_{\infty}$ High-Order Repetitive Control for Functional Electrical Stimulation in Intention Tremor Suppression

Intention tremor is a rhythmic and involuntary limb swing movement that causes significant inconvenience to the daily life of patients. Repetitive control is suitable for functional-electrical-stimulation-based intention tremor suppression because it can significantly attenuate the periodic signals. However, the performance of the repetitive controller may be weakened in tremor suppression due to uncertainties in the dynamics of the musculoskeletal model and the tremor frequency. In this paper, we propose an advanced methodology for tremor suppression by combining $H_{\infty}$ control with high-order repetitive control. The proposed controller can not only guarantee the robust stability of the system subjected to model uncertainty, but also effectively suppress tremors with varying frequency. Comparative experiments on the unimpaired subjects and intention tremor patients were carried out to verify the effectiveness of the proposed method. The experimental statistical analysis results show that the proposed $H_{\infty}$ high-order repetitive controller can suppress tremors by up to $84.97\%$ , which is about $11\%$ and $31\%$ higher than the single memory loop repetitive controller and the traditional filter-based controller, respectively. Note to Practitioners —Patients afflicted with wrist intention tremors encounter significant challenges while executing routine activities such as eating, writing, and dressing. Functional electrical stimulation for tremor suppression operates by generating electrical pulses that oppose the tremor motion, thereby inducing muscle contractions and diminishing tremor magnitude. Given the periodic nature of tremor signals acting as system disturbances, repetitive control emerges as an effective method for tremor suppression. However, the conventional repetitive controller cannot significantly improve the tremor suppression performance in practice due to the uncertain property of the musculoskeletal dynamics and the variation of tremor frequency. In this paper, a robust controller combining $H_{\infty}$ control with high-order repetitive control is proposed to address above issues. The high-order repetitive controller can effectively suppress the periodic tremor signals with varying frequency, and the $H_{\infty}$ controller can provide robust stability and the desired tracking performance by properly choosing of the weighting functions. The comparative experimental results, conducted on our self-built wrist tremor suppression experimental platform, involving unimpaired subjects and patients with intention tremors, validate that the proposed control approach enhances tremor suppression efficacy by 11% and 31%, compared to the traditional repetitive controller and the filter-based controller, respectively. The feasibility and effectiveness of the proposed approach is only initially verified by small scale test, and more clinical verifications will be carried out in tremor patients in the future.