Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

A controller that stabilizes second‐order vector systems in predefined‐time is introduced in this paper. That is, for second‐order systems a controller is designed such that the trajectories reach the origin in a time defined in advance. The proposed controller is a variable structure controller tha...

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Bibliographic Details
Published in:Asian journal of control 2019-05, Vol.21 (3), p.1179-1188
Main Authors: Jiménez‐Rodríguez, Esteban, Sánchez‐Torres, Juan Diego, Gómez‐Gutiérrez, David, Loukinanov, Alexander G.
Format: Article
Language:English
Subjects:
Computer simulation
Control systems design
Controllers
Manifolds
Mechanical systems
Predefined‐time stability
second order systems
Trajectories
Variable structure control
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Summary:A controller that stabilizes second‐order vector systems in predefined‐time is introduced in this paper. That is, for second‐order systems a controller is designed such that the trajectories reach the origin in a time defined in advance. The proposed controller is a variable structure controller that first drive the system trajectories to a linear manifold in predefined time and then drives the system trajectories to a non‐smooth manifold with the predefined‐time stability property, in predefined time also; this is done in order to avoid the differentiability problem that inherently appears when stabilizing high‐order systems in finite time under the block control principle technique. The proposal is applied to the predefined‐time exact tracking of fully actuated mechanical systems. As an example, the proposed solution is applied to a two‐link planar manipulator, and numerical simulations are conducted to show its performance.
ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.1785