Determining the likelihood of un-controllability in large scale systems

Large-scale dynamical systems are of interest due to their broad applications in various areas, such as physiological systems, gene networks, large-scale energy systems, robot motions, multiple space air, and buildings. In such systems there are a large number of interconnected systems whose behavior can be observed by some output variables. The mathematical structure of these large-scale systems can be described by a dynamic consensus graph consisting of nodes and dynamic edges (links). For a given graph, the node variables represent the observable variables, and the edges represent the dynamic interconnections. In the literature, the controllability of these systems has been addressed under the leaderfollower framework, where some nodes are designated to be followers and the trajectories of the followers are controlled by the leader's trajectory. Graphic tools, in particular, the equitable partitions technique have been used to investigate the controllability for such systems. In these studies authors have utilized static gains to describe the interconnection behavior. However, we focus on a more general class of systems involving interconnections of rational transfer functions. In this dissertation, we explore the controllability of the proposed systems using the leader-follower framework. We extend the equitable partitions method and apply it for such systems with rational interconnection functions. We develop a new notion of mode controllability for these systems based on canceling the natural system modes due to non-zero initial conditions. Finally, when the rational links are unknown, we propose a new method of uncertain controllability based on estimating these rational weights and investigate the controllability using probability sets with a certain condence level in the frequency domain. A real experiential application of the thermal behavior of a building will be discussed to demonstrate the concept of this dissertation.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Electrical Engineering and Computer Science

Grantor dc:publisher

Colorado School of Mines. Arthur Lakes Library

Year dc:date.issued

2015

Author dc:creator

• Abohtyra, Rammah M.

Advisor dc:contributor.advisor

• Vincent, Tyrone

Committee members dc:contributor.committeemember

• Moore, Kevin L., 1960-
• Steele, John P. H.
• Braun, Robert J.
• Johnson, Kathryn E.

• uncertain controllability
• probability set and confidence region
• mode and node controllability
• dynamic networks
• determining the likelihood|controllability

Statement dc:rights

• Copyright of the original work is retained by the author.

Language dc:language.iso

eng, English

Identifier

T 7762

OAI identifier oai:identifier

oai:repository.mines.edu:11124/17120