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<p dir="ltr">Safety and explainability are a top priority across many real-world applications of control in safety-critical systems. Networked dynamic systems are one sub-class of models that encompass many of the safety-critical systems in need of such safety guarantees. In this dissertation, we present our work in the safety-critical control of general non-networked epidemic processes, as well as our work on the modeling and analysis of networked epidemic-spreading processes. We then present a framework for the safety-critical control of networked dynamic systems including individual node vulnerability analysis and a CBF-based collaborative-safety condition. We develop a collaborative-safety framework that leverages high-order barrier functions to encode the effect of neighbors on individual safety requirements and demonstrate how this framework can be used in both epidemic models and in formation control problems. We provide an analysis on the finite-time convergence rate of our collaborative-safety algorithm in the special case of a tree structure network for a formation control application. Finally, we provide some concluding remarks and discussion on important directions for future work in the field of collaborative control for multi-agent autonomous systems.</p>

<div>In this thesis, we explore different methods to enhance the safety and robustness for autonomous systems. We achieve this goal using concepts and tools from reachability analysis and control barrier functions. We first take on a multi-player reach-avoid game that involves two teams of players with competing objectives, namely the attackers and the defenders. We analyze the problem and solve the game from the attackers' perspectives via a moving horizon approach. The resulting solution provides a safety guarantee that allows attackers to reach their goals while avoiding all defenders. </div><div><br></div><div>Next, we approach the problem of target re-association after long-term occlusion using concepts from reachability as well as Bayesian inference. Here, we set out to find the probability identity matrix that associates the identities of targets before and after an occlusion. The solution of this problem can be used in conjunction with existing state-of-the-art trackers to enhance their robustness.</div><div><br></div><div>Finally, we turn our attention to a different method for providing safety guarantees, namely control barrier functions. Since the existence of a control barrier function implies the safety of a control system, we propose a framework to learn such function from a given user-specified safety requirement. The learned CBF can be applied on top of an existing nominal controller to provide safety guarantees for systems.</div>