Frequency Response of Self-Similar Dynamic Networks with Applications to Health Monitoring and Control
While humankind's intellectual limit is advancing forward, the implementations of large-scale systems are expanding as well. No matter whether possessing interconnected appearances, those large-scale systems are often mathematically modelled as dynamic networks which involve abundant nodes and intricate rules regarding the interaction among those nodes. Hence, it can be anticipated that plentiful research concerning dynamic networks exist in literature, including studies about graph theories, multi-agent systems and materials' complicated behaviors. However, there exist few applications of frequency-domain methods to a general class of dynamic networks, mostly due to the complexity of computing their frequency response. That gap is filled by this dissertation, which shows that problem is tractable once self-similarities are leveraged and that the resultant outcomes can be further employed in dynamic networks' simulation, monitoring and control through available tools in the frequency domain.
The proposed method in this work could efficiently simulate some quantities spreading over complex systems that are typically described by partial differential equations. In addition to being efficient, that method offers another degree of freedom by handling the situation where the physical properties of those complex systems are nonuniformly distributed, in which case partial differential equations are almost impossible to be solved analytically. For health monitoring, this dissertation suggests a new feature for candidate damage cases through their frequency response which can identify the existence, location and extent of the damage state. For controlling dynamic networks, this study takes advantage of the fact that the frequency response of a dynamic network is likely to form a set of neighboring plants when it is undergoing some variations in order to design a unified controller for those different situations by using robust control methods.
Another merit of this work is that it provides specific examples, i.e., infinite dynamic networks, where fractional and irrational transfer functions naturally come to light. That offers the possibilities for understanding the physical meaning of fractional-order derivatives and implicit operators in the future.
The main motivation of this dissertation is to advocate studying dynamic networks through their frequency response. The author hopes that this work would build a bridge between monitoring and controlling complex systems and numerous frequency-domain tools.
History
Date Modified
2021-03-13Defense Date
2021-02-23CIP Code
- 14.1901
Research Director(s)
J. William GoodwineCommittee Members
Panos Antsaklis James Schmiedeler Patrick WensingDegree
- Doctor of Philosophy
Degree Level
- Doctoral Dissertation
Alternate Identifier
1241254526Library Record
5990113OCLC Number
1241254526Program Name
- Aerospace and Mechanical Engineering