Description
This thesis presents ways to tackle this "curse of dimensionality" from multiple fronts, bringing tractable verification of complex, practical systems such as unmanned aerial systems, autonomous cars and robots, and biological systems closer to reality. The theoretical contributions pertain to Hamilton-Jacobi (HJ) reachability analysis, with applications to unmanned aerial system. In addition, this thesis also explores two frontiers of HJ reachability by combining the formal guarantees of reachability with the computational advantages of optimization and machine learning, and with fast motion planning algorithms commonly used in robotics. The potential and benefits of the theoretical advances are demonstrated in numerous practical applications.