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Determining the likelihood of un-controllability in large scale systems
Abohtyra, Rammah M.
Abohtyra, Rammah M.
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2015
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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.
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