projects | Tan Hoang Cao

Preparing for undergraduate research

Before choosing a project, review the recommended mathematics, computing, optimization, and research-practice pathway for work in optimal control, nonsmooth dynamics, robotics, traffic and crowd models, or safe reinforcement learning.

View the undergraduate research learning path

research

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.

undergraduate

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

A first undergraduate research project on projections, constrained motion, and sweeping processes, starting from linear algebra and Python.

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.