A time-varying control method based on Taylor series approximation

In this paper, a time-varying control method based on Taylor series approximation is proposed. By approximation, a time-varying system can be explicated as a polynomial function of the independent variable, and a time-varying control law can be derived. For a time-varying system, this control law guarantees the actual control result as similar as the promising one of a linear time-invariant control method, such as the proportional feedback scheduling or the gain scheduling. A benchmark control problem of stabilizing an inverted pendulum with an oscillating center of mass is used to illustrate the effectiveness of the new method. Stability analysis is also conducted using the state-of-art singular perturbation margin (SPM) approach.