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Dissertation
General input balancing and model reduction
Doctor of Philosophy (Ph.D.), Drexel University
2000
DOI:
https://doi.org/10.17918/00008462
Abstract
In linear system theory, the controllability and observability Gramians arise naturally in many problems pertaining to realization theory, optimal control and reduced order modeling. In 1993, Scherpen generalized the notion of Gramians to the nonlinear setting via the controllability and observability energy functions and demonstrated their usefulness in model reduction problems for smooth systems that were strongly accessible and zero-state observable. However, the property of zero-state observability is not shared by a large class of systems which are otherwise observable when driven by almost any input function. The research described in this thesis offers a new approach to the nonlinear model reduction problem. Specifically, the condition of zero-state observability is relaxed and a more general type of observability energy function is defined. This approach is also considered to be more natural to model reduction problems where there is significant uncertainty in the applied input signal due to controller inaccuracies (e.g., finite word-length effects, sampling), actuator inaccuracies or random disturbances. The new theory and algorithms for the general nonlinear model reduction problem were then applied to linear and bilinear systems.
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Details
- Title
- General input balancing and model reduction
- Creators
- Joseph Paul Mesko
- Contributors
- W. Steven Gray (Advisor) - Drexel University, Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- x, 216 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Engineering (1970-2026); Drexel University
- Other Identifier
- 991021888990804721