Brockett's theorem states the three necessary conditions for the existence of a continuously differentiable closed loop control that asymptotically stabilizes the nonlinear control system to an equilibrium point. Kinematic systems are shown to fail to meet Brockett's third necessary condition. A normal form is introduced so that nonholonomic control systems are defined directly over a reduced constraint distribution. In normal form, nonholonomic control systems can then easily be shown to fail to be stabilizable to a point via a C1 control. The conditions for the smooth stabilization of the nonholonomic systems to an equilibrium submanifold are then presented. For a particular case of the reduced form of mechanical control systems (Chaplygin systems), stabilization to a point can be achieved by applying the concept of geometric phase and using piecewise differentiable state controls.
|Commitee:||Simic, Slobodan, Stanley, Maurice|
|School:||San Jose State University|
|School Location:||United States -- California|
|Source:||MAI 49/06M, Masters Abstracts International|
|Keywords:||Brockett's theorem, Geometric phase, Nonholonomic control system, Normal form equations, Smooth stabilization, Strongly accessible|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be