Dissertation/Thesis Abstract

Brockett's necessary conditions and the stabilization of nonlinear control systems
by Michot, Marc A., M.S., San Jose State University, 2011, 71; 1495083
Abstract (Summary)

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.

Indexing (document details)
Advisor: Maruskin, Jared
Commitee: Simic, Slobodan, Stanley, Maurice
School: San Jose State University
Department: Mathematics
School Location: United States -- California
Source: MAI 49/06M, Masters Abstracts International
Subjects: Applied Mathematics
Keywords: Brockett's theorem, Geometric phase, Nonholonomic control system, Normal form equations, Smooth stabilization, Strongly accessible
Publication Number: 1495083
ISBN: 978-1-124-71397-7
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