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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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Abstract

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.

References

1. [1]	Astolfi, A. (1998), Discontinuous control of the Brockett integrator, European Journal of Control, 4(1), 49-63.

2. [2]	Behal, A., Dawson, D., Dixon, W., and Fang. Y. (2002), Tracking and regulation control of an underactuated surface vessel with nonintegrable dynamics, IEEE Transactions on Automatic Control, 47(3), 495-500.

3. [3]	Branicky, M.S. (1998), Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control 43(4), 475-482.

4. [4]	Brockett, R.W. (1983), Asymptotic stability and feedback stabilization, Differential Geometric Control Theory (Birkhauser, Boston, USA) (R. W. Brockett, R. S. Millman, and H. J. Sussman, eds.), 181-191.

5. [5]	Campion, G., Bastin, G., and d'Andrea-Novel, B. (1996), Structural properties and classification of kinematics and dynamic models of wheeled mobile robots, IEEE Trans. on Robotics and Automation, 12(1), 47-62.

6. [6]	Coron, J.M. (1991), Global asymptotic stabilization for controllable systems without drift, Mathematics of Control, Signals, and Systems, 5(3), 295-312.

7. [7]	Duleba, I. and Sasiaek, J. (2001), Calibration of controls in steering nonholonomic systems, Control Engineering Practice, 9, 217-225.

8. [8]	Guldner, J. and Utkin, V.I. (1994), Stabilization of nonholonomic mobile robots using Lyapunov functions for navigation and sliding mode control (Orlando, Florida, USA), 2967-2972.

9. [9]	Kolmanovsky, I. and McClamroch, N.H. (1995), Developments in nonholonomic control problems, IEEE Control Systems Magazine, 15, 20-36.