Paper Info
Title
Global uniform asymptotic Lyapunov stabilization of a vectorial chained-form system with a smooth time-varying control law
Abstract
This work presents two continuous time-varying control laws that globally uniformly asymptotically stabilize the origin of a vectorial generalization of the basic chained- form system. A strict Lyapunov function for the controlled system is developed, and the results verified through numerical simulation. I. INTRODUCTION Chained-form systems are classical nonholonomic sys- tems, and several control laws have been made for them. For the general chained-form system, an algorithmic ap- proach using sinusoids was developed in (1) that gave global uniform asymptotic stability of the origin. In (2), a globally uniformly asymptotically stabilizing time-varying control law was developed, in addition to dis- continuous time-varying control laws. This, however, was for a subsystem and not the most general chained-form system. Discontinuous control laws have been developed in (3), (4), (5) and (6), among others. While not explicitly stating so, (7) developed a contin- uous time-varying control law that globally asymptotically stabilized the lowest-order chained form system. In this paper we present two continuous time-varying con- trol laws that globally uniformly asymptotically stabilize the origin of a vectorial generalization of the basic chained-form system. To the authors' best knowledge, no previous control laws have been presented for this specific generalization of the chained form system. The paper is organized as follows: In Section II, the model is presented. In Sections III and IV, the control laws are presented. Section V presents simulation results. Conclusions are given in Section VI. The Appendix provides some further details into the proof in Section III. II. THE MODEL We look at a system on the form
Year
DOI
Venue
2008
10.1109/CDC.2008.4739321
Cancun
Keywords
Field
DocType
asymptotic stability,time-varying systems,vectors,continuous time-varying control laws,global uniform asymptotic Lyapunov stabilization,numerical simulation,vectorial chained-form system,vectorial generalization
Lyapunov function,Mathematical optimization,Lyapunov equation,Computer simulation,Control-Lyapunov function,Control theory,Exponential stability,Lyapunov redesign,Control system,Law,Lyapunov exponent,Mathematics
Conference
ISSN
ISBN
Citations 
0191-2216 E-ISBN : 978-1-4244-3124-3
978-1-4244-3124-3
0
PageRank 
References 
Authors
0.34
6
2
Name
Order
Citations
PageRank
Christian Holden143.90
Kristin Ytterstad Pettersen240242.59