Backward Reachability

Backward reachability analysis aims to determine the set of initial states that can reach a target set within a given system, often under uncertainty or constraints. Current research focuses on developing efficient algorithms, such as those employing semidefinite programming (SDP) or mixed-integer linear programming (MILP), to compute backward reachable sets for various system models, including those incorporating neural networks for control. This work is crucial for verifying safety properties in autonomous systems and other safety-critical applications where guaranteeing collision avoidance or other constraints is paramount. The development of more accurate and computationally tractable methods for complex systems remains a key challenge and area of active investigation.