Non-Singular Predefined-Time Stable Manifolds

In this paper it is introduced a class of non-singular manifolds with predefinedtime stability. That is, for a given dynamical system with its trajectories constrained to this manifold it can be shown predefined-time stability to the origin. In addition, the function that defines the manifold and its derivative along the system trajectories are continuous, therefore no singularities are presented for the system evolution once the constrained motion starts. The problem of reaching the proposed manifold is solved by means of a continuous predefined-time stable controller. The proposal is applied to the predefined-time exact tracking of fully actuated and unperturbed mechanical systems. It is assumed the availability of the state and the desired trajectory as well as its two first derivatives. As an example, the proposed solution is applied over a two-link planar manipulator and numerical simulations are conducted to show its performance.

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