Model simplification and robust control in deterministic and stochastic systems using singular perturbation methods

"The class of uncertainties that may be present in dynamical systems includes, but is not limited to, unknown disturbance inputs, unpredictable abrupt structural changes, unknown parameters, and unmodeled fast dynamics. A number of different stochastic and deterministic models that incorporate these uncertainties have been proposed in the literature, and these have led to different robust control and filtering problem formulations, methodologies, and resulting robust designs. This thesis presents novel formulations of three different classes of problems featuring the types of uncertainties described above, studies them from the points of view of model reduction and robust controller design, and develops new theory and methodology for their solutions. The common thread that runs through these three classes of problems (which involve both deterministic and stochastic systems) is the use of ""singular perturbations,"" either as a modeling tool or as a computational tool. The reason for adopting the singular perturbations framework is threefold. First, we must study robustness with respect to fast unmodeled dynamics of different control or filtering designs. The second reason is to incorporate appropriate knowledge on fast dynamics into the design, without using the full-order system, so as to improve performance and to alleviate the numerical ill-conditioning associated with the computation of the full-order solution. Third, we must obtain ""reliable"" reduced-order models for large-scale systems that exhibit two or multi time-scale behavior, such that the solution to the reduced-order model can achieve a desired performance for the full-order system."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Pan, Zigang

Contributors dc:contributor

• Basar, Tamer

• Engineering, Aerospace
• Engineering, Electronics and Electrical
• Engineering, Mechanical

Statement dc:rights

• Copyright 1996 Pan, Zigang

Language dc:language

eng

Identifier

AAI9625176
(UMI)AAI9625176

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/20859