A high-order Lie groups scheme for solving the recovery of external force in nonlinear system

摘要

In this paper, we develop the high-order Lie group scheme to estimate a real-time external force exerted on nonlinear system. For estimating a real-time data, the equations of motion and the supplemental data are combined into a set of differential algebraic equations (DAEs), which is solved by an implicit Lie group differential algebraic equations method (LGDAE) and a Newton iterative algorithm. However, an explicit LGDAE cannot work, and an implicit scheme cannot avoid a lot of iterative numbers and overcome numerical instability under a long time span and noisy-level effect. Because the original implicit LGDAE cannot satisfy the constraint of the cone structure, Lie group and Lie algebra at each time step, solutions highly dependent on ones cannot easily converge by a large time step. Therefore, we develop a high-order explicit LGDAE to avoid iterative numbers and numerical instability, and at the same time combined with higher order sliding modes to obtain real-time external force. The accuracy and efficiency of the novel scheme is validated by comparing the estimation results with the previous literature.