Real-world control problems are complex and safety‑critical, so PID control often needs more advanced methods. This module covers modern techniques, starting with optimal control, which uses optimization to boost performance and reduce costs. We introduce MPC for fast, constrained control, and explore multiagent systems to manage large‑scale interactions efficiently.

Beyond complexity, uncertainty is a key challenge. Models may be inaccurate, sensor data noisy, or actuator responses delayed. To address these issues, this module introduces essential tools such as system identification, state estimation, and robust control—methods that help maintain reliable performance despite real‑world imperfections.

This module introduces systems theory and automatic control. It outlines the historical and modern role of control theory and highlights its hidden importance in today’s technologies. Key topics include the basic control loop, the role of feedback, and using differential equations to model physical systems.

A major recent shift in control has been the rise of data‑driven and reinforcement learning methods. With data now central across industries, we show how to use it to design controllers that optimize performance and ensure safety. This module introduces key reinforcement learning techniques and the emerging theory of data‑enabled predictive control.

Dynamical systems are mathematical models used to describe reality, from robots to diseases to human decisions. This module covers key concepts such as solutions, equilibria, stability, controllability, and observability—core properties that form the basis for designing controllers that automatically regulate system behavior.

In this module we move from analysis to control. A controller uses sensor data to generate corrective actions through actuators, ensuring the system behaves as desired. We introduce open‑loop vs. closed‑loop control and explain the core ideas behind the Proportional, Integral, and Derivative actions of a PID controller.