Controllability, Reachability, and Inference for Complex Dynamic Systems

The focus of this dissertation is on developing a data-driven framework to infer interconnections in networks of dynamic agents, development of theoretical foundations for the controllability of bilinear systems, and reachability analysis of linear time invariant systems. Inspired by some existing methodologies on discovering the governing dynamics using time- series data, here we introduce two new data manipulation techniques that can be applied to infer interconnections when the agents are of the second-order dynamics and have hidden states, the states not available for direct measurements. In the next step, the controllability of single-input bilinear systems is investigated. It will be shown that some of the conditions required for the controllability of such systems can be relaxed at the expense of losing control over regions with zero Lebesgue measures in the state space. We then show how these relaxations can open path to achieve conditions on the near controllability of multi-input bilinear systems. Lastly, the reachability problem is studied for discrete-time linear systems where we propose new techniques for verifying the inclusion and exclusion of given sets with applications to the security of cyber-physical systems.