Understandings of the incremental backstepping control through theoretical analysis under the model uncertainties

In this paper, theoretical analysis on the incremental backstepping control is suggested especially under the existence of model uncertainties. This algorithm is proposed in the previous studies by modifying the backstepping method to reduce model dependency. Because this method is a type of nonlinear control and the model uncertainties are assumed to be considered, it is difficult to have theoretical analysis, which causes lack of understandings about this algorithm. Therefore, this paper suggests closed-loop analysis with simplified dynamics under the model uncertainty. Transfer function is derived and poles, stability condition, steady state error, and settling time are presented. In addition, the effects of model uncertainties and gains are identified through analysis. Proposed analysis is meaningful in terms of establishing critical understandings about the algorithm, even though the simplified dynamics is applied for analysis purpose.