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Abstract In the study (Wang et al. 2014), an adaptive reaching law is developed for sliding mode control (SMC). However, a potential issue arises when the sliding mode surface slides at the neighborhood of the origin, causing the adaptive gain in the mentioned scheme to chatter repeatedly. This results in input command chattering and has a negative impact on the stability of the system. In order to address this problem caused by the adaptive gain and switching function in SMC, and to further improve convergence performance, a new adaptive reaching law is proposed. This proposed reaching law improves upon the previous adaptive gain and ensures stable operation as the new adaptive gain converges to a small neighborhood of the origin. This improvement prevents chattering and guarantees that the tracking error of the system converges within a finite time. Finally, comparative simulation experiments are conducted to demonstrate the effectiveness and superiority of the proposed reaching law.
Liu et al. (Sun,) studied this question.