Computationally Tractable Methods for Constrained Optimal Control and Reachability Analysis of Nonlinear Stochastic Dynamical Systems

Autonomous systems operating in uncertain environments require methods that can rigorously quantify safety, predict future behavior, and compute optimal decisions tractably. The unifying challenge is reasoning about uncertainty propagation in constrained dynamical systems. Motivated by autonomous spacecraft inspection, this dissertation develops model-based and data-driven methods for stochastic optimal control and stochastic reachability. First, it studies optimal on-orbit inspection of an uncertain tumbling spacecraft in both single-agent and multi-agent settings, and derives computationally efficient reformulations for exploring trade-offs among sensing, trajectory deviation, and fuel use. Second, it develops a probabilistically safe penalty-based reinforcement learning method that preserves gradient information during training while steering policies toward safety. Finally, it formulates data-driven stochastic reachability in a probability-measure framework and constructs a neural network approximation of backward reachable sets using forward simulations, with applications to spacecraft autonomy and other safety-critical dynamical systems.