Course Websites

• Mechanical Science and Engineering

This course introduces methods for modeling, analysis, and control of uncertain continuous time systems with emphasis on distributional robustness. It begins with stochastic processes and stochastic differential equations, including probability theory, Brownian motion and Itˆo calculus, and pathwise and distributional representations. Stability of uncertain stochastic systems is studied using Lyapunov methods and generalized robustness concepts defined through metrics on probability measures. The course then covers adaptive control design, starting with deterministic systems and finite-time robustness guarantees, and extending to robust adaptive control in the space of probability measures. Topics include controller design for stochastic systems, comparison with deterministic results, and separation between implementation and certificates. The final part focuses on application examples drawn from the intersection of machine learning and robotics, including distributionally robust optimization for model predictive control (MPC), safety-critical control of systems such as quadrotors and unicycles, and frameworks for certifiable integration of high-dimensional sensing and deep vision models in control.

4 hours

• Linear Systems Theory

• Probability and Random Processes

• Introductory Control Theory (feedback design, Lyapunov methods)

• Familiarity with convex optimization and basic machine learning helpful but not required.

Undergraduate degree.