<![CDATA[Ph.D. Defense Announcement

This dissertation addresses the challenge of performing optimal control for dynamical systems operating in non-convex cost landscapes arising from nonlinear dynamics and cluttered environments. While classical second-order methods like Differential Dynamic Programming (DDP) offer fast local convergence, they easily get trapped in local minima due to their reliance on local information. Although purely sampling-based methods bypass the locality issue, they suffer from high sample complexity and noisy decision-making. To bridge this gap, this work leverages the Maximum Entropy DDP (ME-DDP) framework, in which a structured exploration covariance naturally arises from entropic regularization, balancing second-order local exploitation with robust trajectory perturbation. We extend this mechanism beyond standard Shannon entropy to generalized representations, detailing the development of Tsallis entropy and Stein Variational DDP (SV-DDP) to maintain policy diversity without sacrificing optimization structure. Benchmarked against Model Predictive Path Integral (MPPI) variants within a Model Predictive Control (MPC) framework, the proposed algorithms demonstrate superior overall performance, with their practical robustness validated through hardware experiments on a quadrotor navigation task in cluttered environments.