Stanford AA203 Optimal and Learning-Based Control | Spring 2026 | Lecture 1: Course Overview

This course provides a unified framework for controlling dynamic systems by integrating classical control theory with modern optimization and data-driven learning techniques, moving from model-based analysis to scenarios where systems must be learned from data.

• Course objectives — The curriculum prioritizes broad understanding of optimal and learning-based control tools over deep technical mastery of a single method, helping students determine which approach best fits a given problem [05:20].
• Assessment structure — Grades are determined by 80% from four assignments featuring both theory and Python coding tasks, and 20% from a final exam [00:46].
• Modeling systems — Dynamical systems are defined using ordinary differential equations (ODEs), which act as a predictive tool to calculate future states based on current control inputs [28:20].
• Performance calculation — Optimal control problems utilize a cost functional that combines a terminal cost (the final result) with a stage-wise cost (cumulative effort, such as energy usage, incurred during operation) [41:50].
• Control methodologies — The class divides control strategies into two distinct approaches:
  • Model-based control — Assumes knowledge of the system mechanics; includes open-loop, closed-loop, and model predictive control (MPC) [21:05].
  • Data-driven control — Utilizes imitation and reinforcement learning to infer system models when the underlying physics are unknown or too complex to model manually [21:15].
• Loop distinction — While open-loop control is computationally efficient, it lacks robustness because it does not adjust to disturbances; closed-loop control is more complex but manages errors by constantly measuring the system response [17:10].
• Constraint handling — Optimization requires defining boundaries, such as avoiding forbidden regions in state space or staying within actuator power limits, to ensure the control policy remains safe and functional [38:25].

How does the difference between open-loop and closed-loop control affect computational efficiency and system robustness?

What are the three primary components required to mathematically define an optimal control problem?