Predefined-time tracking of a class of mechanical systems

Abstract

Abstract-In this paper the problem of predefined-time exact tracking of fully actuated and unperturbed mechanical systems is solved by means of a continuous controller. It is assumed the availability of the state and the desired trajectory as well as its two first derivatives. This is accomplished introducing the idea of second-order predefined-time stable systems, which is based on the nested application of the first-order predefinedtime stabilizing function. As an example, the proposed solution is applied over a two-link planar manipulator and numerical simulations are conducted to show its performance.

Time‐varying feedback for stabilization in prescribed finite time

“…1,25 In this work, we present a time-varying feedback alternative to achieving finite-time control, which is referred to as "prescribed-time control" 30 or predefined-time control. [31][32][33] We show that such prescribed-time control exhibits several superior features. (i) The time-varying gain-based prescribed-time control is built upon regular state feedback, not on fractional-power state feedback, thus resulting in smooth (C n ) control action everywhere during the entire operation of the system.…”

Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

“…The results [24,25,27] present first-order predefinedtime stable dynamical systems. Furthermore, the works [9,26] attempt to extend these results to secondorder systems as a nested application of first-order predefined-time stabilizing functions. However, since the predefined-time stabilizing function is non-smooth, these approaches yield singular controllers, which may produce theoretically infinite signals.…”

“…Therefore, this paper presents a controller that stabilizes second-order vector systems in predefined-time. The proposed controller is a variable structure controller that first drives the system trajectories to a linear manifold in a predefined-time, and then drives the system trajectories to a non-smooth manifold with a predefined-time stability property (introduced in [9]), also in predefined time. This mechanism allows the controller to avoid the differentiability/singularity problem mentioned above.…”

Predefined-time stabilization of high order systems

“…To overcome the above, a class of first-order dynamical systems with the minimum upper bound of the fixed stabilization time equal to their only tuning gain has been studied [15], [16], similarly a class of second-order systems with similar features is presented in [17]. It is said that these systems exhibit the property of predefined-time stability.…”

“…Similarly to [17], the proposed scheme allows to define high-order predefined-time stable systems as a nested application of first-order predefined-time stabilizing functions.…”