Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics

Yang Liu, Hong Yue, Wei Wang

Research output: Contribution to conferencePaper

Abstract

This paper studies the fixed-time stabilization control for a class of second-order systems with unknown nonlinear dynamics and external disturbance. To achieve the fixed-time stability, two polynomial feedbacks, one with fractional exponent and the other with exponent greater than 1, are exploited in the sliding surface design. Then, considering the unknown nonlinear dynamics and the external disturbance, the unit-vector technique, coupled with the upper bounds related to the Lipschitz condition of nonlinear dynamics and the uncertain disturbance, is utilized to the fixed-time stability controller based on the designed sliding surface function. Finally, a forced pendulum system is used as case study example to examine the effectiveness of the developed design framework.

Conference

ConferenceControl 2018: The 12th International UKACC Conference on Control
CountryUnited Kingdom
CitySheffield
Period5/09/187/09/18
Internet address

Fingerprint

Stabilization
Pendulums
Polynomials
Feedback
Controllers

Keywords

  • fixed-time stability
  • sliding surface
  • nonlinear dynamics
  • external disturbance

Cite this

Liu, Y., Yue, H., & Wang, W. (2018). Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics. 324-329. Paper presented at Control 2018: The 12th International UKACC Conference on Control, Sheffield, United Kingdom.
Liu, Yang ; Yue, Hong ; Wang, Wei. / Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics. Paper presented at Control 2018: The 12th International UKACC Conference on Control, Sheffield, United Kingdom.6 p.
@conference{0744f8e989b740dda704af3d9f5565c9,
title = "Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics",
abstract = "This paper studies the fixed-time stabilization control for a class of second-order systems with unknown nonlinear dynamics and external disturbance. To achieve the fixed-time stability, two polynomial feedbacks, one with fractional exponent and the other with exponent greater than 1, are exploited in the sliding surface design. Then, considering the unknown nonlinear dynamics and the external disturbance, the unit-vector technique, coupled with the upper bounds related to the Lipschitz condition of nonlinear dynamics and the uncertain disturbance, is utilized to the fixed-time stability controller based on the designed sliding surface function. Finally, a forced pendulum system is used as case study example to examine the effectiveness of the developed design framework.",
keywords = "fixed-time stability, sliding surface, nonlinear dynamics, external disturbance",
author = "Yang Liu and Hong Yue and Wei Wang",
year = "2018",
month = "9",
day = "5",
language = "English",
pages = "324--329",
note = "Control 2018: The 12th International UKACC Conference on Control ; Conference date: 05-09-2018 Through 07-09-2018",
url = "https://control2018.group.shef.ac.uk/",

}

Liu, Y, Yue, H & Wang, W 2018, 'Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics' Paper presented at Control 2018: The 12th International UKACC Conference on Control, Sheffield, United Kingdom, 5/09/18 - 7/09/18, pp. 324-329.

Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics. / Liu, Yang; Yue, Hong; Wang, Wei.

2018. 324-329 Paper presented at Control 2018: The 12th International UKACC Conference on Control, Sheffield, United Kingdom.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics

AU - Liu, Yang

AU - Yue, Hong

AU - Wang, Wei

PY - 2018/9/5

Y1 - 2018/9/5

N2 - This paper studies the fixed-time stabilization control for a class of second-order systems with unknown nonlinear dynamics and external disturbance. To achieve the fixed-time stability, two polynomial feedbacks, one with fractional exponent and the other with exponent greater than 1, are exploited in the sliding surface design. Then, considering the unknown nonlinear dynamics and the external disturbance, the unit-vector technique, coupled with the upper bounds related to the Lipschitz condition of nonlinear dynamics and the uncertain disturbance, is utilized to the fixed-time stability controller based on the designed sliding surface function. Finally, a forced pendulum system is used as case study example to examine the effectiveness of the developed design framework.

AB - This paper studies the fixed-time stabilization control for a class of second-order systems with unknown nonlinear dynamics and external disturbance. To achieve the fixed-time stability, two polynomial feedbacks, one with fractional exponent and the other with exponent greater than 1, are exploited in the sliding surface design. Then, considering the unknown nonlinear dynamics and the external disturbance, the unit-vector technique, coupled with the upper bounds related to the Lipschitz condition of nonlinear dynamics and the uncertain disturbance, is utilized to the fixed-time stability controller based on the designed sliding surface function. Finally, a forced pendulum system is used as case study example to examine the effectiveness of the developed design framework.

KW - fixed-time stability

KW - sliding surface

KW - nonlinear dynamics

KW - external disturbance

M3 - Paper

SP - 324

EP - 329

ER -

Liu Y, Yue H, Wang W. Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics. 2018. Paper presented at Control 2018: The 12th International UKACC Conference on Control, Sheffield, United Kingdom.