The continued growth of air travel and recent advances in new technologies for navigation, surveillance, and communication have led to proposals by the Federal Aviation Administration (FAA) to provide reliable and efficient tools to aid Air Traffic Control (ATC) in performing their tasks. In this dissertation, we address four problems frequently encountered in air traffic surveillance and control; multiple target tracking and identity management, conflict detection, conflict resolution, and safety verification. We develop a set of algorithms and tools to aid ATC; These algorithms have the provable properties of safety, computational efficiency, and convergence. Firstly, we develop a multiple-maneuvering-target tracking and identity management algorithm which can keep track of maneuvering aircraft in noisy environments and of their identities. Secondly, we propose a hybrid probabilistic conflict detection algorithm between multiple aircraft which uses flight mode estimates as well as aircraft current state estimates. Our algorithm is based on hybrid models of aircraft, which incorporate both continuous dynamics and discrete mode switching. Thirdly, we develop an algorithm for multiple (greater than two) aircraft conflict avoidance that is based on a closed-form analytic solution and thus provides guarantees of safety. Finally, we consider the problem of safety verification of control laws for safety critical systems, with application to air traffic control systems. We approach safety verification through reachability analysis, which is a computationally expensive problem. We develop an over-approximate method for reachable set computation using polytopic approximation methods and dynamic optimization. These algorithms may be used either in a fully autonomous way, or as supporting tools to increase controllers' situational awareness and to reduce their work load.
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