Abstract

As we begin to analyze and construct extremely complex systems, a theory for understanding and designing the underlying architecture becomes very important. To move in the direction of a precise theory of architecture, this thesis will provide some concrete tools to analyze and design complex systems with a given network structure. The first main result of this thesis analyzes the vulnerability of a system and shows that a system's vulnerability depends on its network structure. We will consider destabilization attacks acting on a single link in a system's logical interconnection structure. The concept of a vulnerable link is characterized and necessary and sufficient conditions for identifying these links are provided. The vulnerability of various system architectures are then characterized by the vulnerability of their weakest link, and it is shown that every transfer function has a completely secure architecture with no vulnerable links. The second part of this thesis focuses on synthesizing controllers with a specified network structure. It presents a new approach to distributed controller design that exploits the dynamical structure function representation of linear time invariant systems to characterize the structure of a system. The design technique sequentially constructs each link in an arbitrary controller signal structure, and the main theorem proves that either the resulting controller is stabilizing or that no controller with the desired structure can stabilize the system.

Degree

College and Department

Physical and Mathematical Sciences; Computer Science

Rights

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