Research

My research develops controllers for nonlinear systems that are both near-optimal and provably safe. The central problem is that optimizing performance and enforcing safety pull in different directions: an optimal policy will happily drive the state into an unsafe region if the cost rewards it. My dissertation addresses this with a two-stage framework that computes an approximate value function offline (via sum-of-squares and policy iteration on the Hamilton-Jacobi-Bellman equation) and then enforces safety online through a control-barrier-function quadratic program. This decouples performance from constraint enforcement: the safe set can be modified online without recomputing the value function. I have also designed real-time CLF/CBF-QP controllers for spacecraft attitude control under reaction-wheel torque and momentum limits, treating state and input bounds as hard constraints. These methods matter wherever a system must act efficiently while respecting hard safety limits, such as aerospace and autonomous systems.

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