Robust performance control with prescribed time feature for strict-feedback systems under time-varying control gain

We propose a robust prescribed performance control strategy for nonlinear strict-feedback system under time-varying control coefficient in this paper, and the tracking error will converge to the preset error band in prescribed time. Our work addressed three issues. Firstly, we introduce unified performance function, normalized function and barrier function to convert the actual tracking error into analytical form, which can deal with global and semi-global conditions; Meanwhile, we propose the concept of transformed rate function. Together with the unified performance function, we achieve the prescribed-time feature. Finally, we use a special form of Nussbaum function to deal with the problem of time-varying control coefficients. The effectiveness of this strategy is verified by theoretical analysis.