Practical Prescribed Time Tracking Control With Bounded Time-Varying Gain Under Non-Vanishing Uncertainties

This paper investigates the prescribed-time control (PTC) problem for a class of strict-feedback systems subject to non-vanishing uncertainties. The coexistence of mismatched uncertainties and non-vanishing disturbances makes PTC synthesis nontrivial. In this work, a control method that does not involve infinite time-varying gain is proposed, leading to a practical and global prescribed time tracking control solution for the strict-feedback systems, in spite of both the mismatched and non-vanishing uncertainties. Different from methods based on control switching to avoid the issue of infinite control gain that involves control discontinuity at the switching point, in our method a softening unit is exclusively included to ensure the continuity of the control action. Furthermore, in contrast to most existing prescribed-time control works where the control scheme is only valid on a finite time interval, in this work, the proposed control scheme is valid on the entire time interval. In addition, the prior information on the upper or lower bound of $g_{i}$ is not in need, enlarging the applicability of the proposed method. Both the theoretical analysis and numerical simulation confirm the effectiveness of the proposed control algorithm.