Contraction analysis of nonlinear systems

This thesis derives new results in nonlinear system analysis using methods inspired from fluid mechanics and differential geometry. Based on a differential analysis of convergence, these results may be viewed as generalizing the classical Krasovskii the­orem, as well as linear eigenvalue analysis. A central feature is that convergence and limit behavior are in a sense treated separately, leading to significant conceptual simplifications. We establish new combination properties of nonlinear dynamic systems and use them to derive simple controller and observer designs for mechanical systems such as aircraft, underwater vehicles, and robots. The method is also applied to chemical chain reactions and mixture processes. The relative simplicity of these designs stems from their effective exploitation of the systems' structural specificities. Next, we analyze and quantify the global stability properties of physical partial differential equations such as the heat equation, or the Schroedinger equation. Lyapunov exponents are not coordinate-invariant, and thus their exact physical meaning is somewhat questionable. As an alternative, we suggest an extension of linear eigenvalue analysis to nonlinear dynamic systems. Finally, the thesis derives new controller and observer designs for general nonlinear dynamic systems. In particular, an extension of feedback linearization is proposed when the corresponding integrability conditions are violated.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mechanical Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

1999

Author dc:creator

• Lohmiller, Winfried Stefan, 1971-

Advisor dc:contributor.advisor

• Jean-Jacques E. Slotine.

• Mechanical Engineering

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/9793

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/9793