Adaptive Fuzzy Prescribed-Time Tracking Control for Nonlinear Systems with Uncertain Leader

This paper studies the prescribed-time tracking problem for nonlinear systems with an uncertain parameter leader. Due to the important role of leaders in the tracking controller design, a leader dynamic observer with the prescribed-time performance is firstly designed to estimate the uncertain leader system while ensuring that the estimation error can approach the origin in the pre-given finite time. In addition, due to the presence of the uncertain parameter leader dynamics in the virtual controller, the derivative of the virtual controller is unknown, which makes the backstepping technique unusable. Thus, a novel filter is constructed by combining with the prescribed-time function to avoid using the virtual controller derivative in the tracking controller design.Further, based on the estimated leader dynamics, an adaptive fuzzy prescribed-time tracking control strategy is proposed by using the backstepping approach, which enables the system output signal can track the uncertain leader without errors in the pre-given finite time. Finally, the vitality of the developed controller is checked by an actual example with comparisons.