Safety Constraints in Control Systems

Abstract

This dissertation highlights the research of myself and my numerous collaborators throughout my time at the University of Washington on topics such as: safety constraints, controlled invariant sets, Markov chains, Markov decision processes, and swarm guidance. As autonomous systems become more prevalent, great care must be taken to ensure that they remain in well-understood operating regimes, despite the unavoidable uncertainty of the real world. Safety constraints are therefore critical to consider for a wide variety of models, especially those which explicitly incorporate uncertainty. If safety cannot be guaranteed in some well-defined sense, then a model cannot confidently be applied to a practical problem---or may even guarantee an undesired outcome. Therefore, the analysis of control systems under safety constraints is integral to bridging the gap between mathematical models and real-world processes.