projects

Optimal Control of Sweeping Processes

Discrete approximations, optimality conditions, and applications of Moreau's sweeping process and its controlled variants.

Catching-Up Algorithm for Differential Inclusions

Convergence, stability, and quantitative error bounds for discretizations of differential inclusions driven by maximal monotone operators.

Crowd Motion & Marine Vehicle Control

Optimal control of nonconvex sweeping processes applied to pedestrian dynamics, evacuation, and autonomous marine surface vehicles.

UG: Python Toolbox for Optimal Control

Build a small, well-documented Python toolbox that solves classic optimal-control problems (brachistochrone, LQR, simple sweeping process) and visualizes trajectories.

UG: Reinforcement Learning for Crowd Evacuation

Train an RL agent that learns to evacuate a simulated crowd from a room with obstacles in minimum time — a friendly entry point into RL and nonsmooth dynamics.

UG: Trajectory Planning for a Simulated Boat

Implement and visualize a free-time optimal navigation problem for an autonomous surface vehicle avoiding circular obstacles.

UG: Policy Gradient for Mean-Variance Portfolio Optimization

Reproduce a regime-switching financial market and train a policy-gradient agent to balance expected return and variance — a bridge between optimization, finance, and RL.

UG: Catching-Up Algorithm — Numerical Experiments

Implement Moreau's catching-up algorithm in Python and experimentally verify the error bounds for several test problems.

UG: Bouncing Ball in a Moving Polygon

Implement a ball constrained to live inside a deforming polygon using only linear algebra — and discover, along the way, that you've coded a sweeping process.

UG: From Lagrange Multipliers to Discrete Pontryagin

Climb the ladder from constrained calculus to optimal control's necessary conditions using only multivariable calculus and a willingness to write down chain rules carefully.

UG: From Gridworld MDP to Crowd Evacuation

Start with the Bellman equation as a linear system on a 5×5 grid and end with a continuous-space multi-agent crowd evacuation simulator — touching every concept that bridges classical dynamic programming to modern reinforcement learning.

UG: Flow Matching — Learning to Turn Noise into Data with ODEs

Build a modern generative model from scratch using nothing but vector fields, ODEs, and a willingness to follow a particle along a straight line. A gentle on-ramp from multivariable calculus to the math behind today's image and robotics generative models.

research