Predefined-Time Sliding Mode Control with Prescribed Convergent Region

In recent years, the finite-time and fixed-time control techniques have drawn much attention. This letter will present a new method for designing a predefined-time adaptive sliding mode controller with prescribed convergent region. More specifically, class
$\mathcal{K}^{1}$
function is used to construct the sliding function, and to achieve a real sliding mode, the function is also adopted in designing the adaptive gain without knowing the disturbance's upper bound (DUB). Compared to the existing finite-time and fixed-time controllers, the key superiority of the proposed method is that the system can converge to a prescribed arbitrarily small region in predefined time irrespective of the initial condition. In addition, the control signal is bounded along the settling period, where the settling time instance can be estimated without conservation. The proposed method is applicable to the control of a wide range of uncertain nonlinear systems such as networked control systems with significant network-induced delay.