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Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


Continuous Stabilizing Control for a Class Of Non-holonomic systems: Brockett System Example

Journal of Vcibration Testing and System Dynamics 2(2) (2018) 167--172 | DOI:10.5890/JVTSD.2018.06.005

Fazal Ur Rehman$^{1}$, A Baseer Satti$^{1}$,$^{2}$, A. Ahmed Saleem$^{1}$

$^{1}$ Department of Electronic Engineering, Capital University of Science and technology, Pakistan

$^{2}$ Holmes Institute Melbourne, Australia

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A continuous adaptive controller is designed for a famous example of Brockett system which is an example of a class of non-holonomic systems. The controllability Lie Algebra of the Brockett’s system contains Lie brackets of depth one. It is shown that the closed loop system is globally uniformly asymptotically stable. The advantage of this method is that it does not require the conversion of the system model into a “chained form,” and thus does not rely on any special transformation techniques. The practical effectiveness of the controller is illustrated by numerical simulations.


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