Koopman-based Data-driven Model Predictive Control of Limb Tremor Dynamics with Online Model Updating: A Theoretical Modeling and Simulation Approach

Patients suffering from tremors have difficulty performing activities of daily living. The development of a model of a limb with tremors can pave the way for non-surgical tremor suppression control techniques. Nevertheless, nonlinearity and actuator saturation make it difficult to develop an accurate model and a tremor suppression control method. Towards addressing this issue, this paper describes a Koopman-based method for system identification and its application to the design of a model predictive control (MPC) scheme to suppress tremors. Since model prediction accuracy is critical to the performance of an MPC, it is essential to update the model online if the predictions are not sufficiently accurate. We propose a recursive least squares (RLS) algorithm to improve control performance with low computational complexity. Finally, for the first time, stability analysis and recursive feasibility of the Koopman-based MPC (KMPC) closed-loop updated system are presented. The proposed modeling and control approach have been validated by experimental data and simulation results.