Regular Papers

International Journal of Control, Automation and Systems 2023; 21(2): 359-366

Published online January 30, 2023

https://doi.org/10.1007/s12555-021-0899-x

© The International Journal of Control, Automation, and Systems

Prescribed-time Stabilization for a Class of Nonlinear Systems with Control Singularities

Lulu Fu, Ruicheng Ma*, and Jun Fu

Liaoning University.

Abstract

This paper studies the prescribed-time stabilization of a class of nonlinear systems with control singularities. The settling time is independent of not only the design parameters but also the initial conditions, and can be set according to per our will. By using backstepping, we simultaneously construct a control Lyapunov function (CLF) with singularity and a control law to prescribed-time stabilize the equilibrium point of the studied system in settling time, and avoid all trajectories from crossing the control singularity set. Further, the feasibility region is consistent with the attraction region, and the attraction region is also maximized. That is, the positive invariance condition is achieved. Finally, two examples are presented to illustrate the effectiveness of our proposed method.

Keywords Backstepping, control singularities, feasibility regions, nonlinear systems, prescribed-time stabilization.

Article

Regular Papers

International Journal of Control, Automation and Systems 2023; 21(2): 359-366

Published online February 1, 2023 https://doi.org/10.1007/s12555-021-0899-x

Copyright © The International Journal of Control, Automation, and Systems.

Prescribed-time Stabilization for a Class of Nonlinear Systems with Control Singularities

Lulu Fu, Ruicheng Ma*, and Jun Fu

Liaoning University.

Abstract

This paper studies the prescribed-time stabilization of a class of nonlinear systems with control singularities. The settling time is independent of not only the design parameters but also the initial conditions, and can be set according to per our will. By using backstepping, we simultaneously construct a control Lyapunov function (CLF) with singularity and a control law to prescribed-time stabilize the equilibrium point of the studied system in settling time, and avoid all trajectories from crossing the control singularity set. Further, the feasibility region is consistent with the attraction region, and the attraction region is also maximized. That is, the positive invariance condition is achieved. Finally, two examples are presented to illustrate the effectiveness of our proposed method.

Keywords: Backstepping, control singularities, feasibility regions, nonlinear systems, prescribed-time stabilization.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

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