Advancing Frontiers of Path Integral Theory for Stochastic Optimal Control

Abstract: Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems due to the curse of dimensionality. This dissertation explores the path integral control framework as a scalable, sampling-based alternative. By reformulating SOC problems as expectations over stochastic trajectories, it enables efficient policy synthesis via Monte Carlo sampling and supports real-time implementation through GPU parallelization. We apply this framework to six classes of SOC problems: Chance-Constrained SOC, Stochastic Differential Games, Deceptive Control, Task Hierarchical Control, Risk Mitigation of Stealthy Attacks, and Discrete-Time LQR. A sample complexity analysis for the discrete-time case is also provided. These contributions establish a foundation for simulator-driven autonomy in complex, uncertain environments.