Advanced Topics in Control

Abstract

Advanced Topics in Control (ATIC) covers advanced research topics in control theory. It is offered each Spring semester with the topic rotating from year to year. Repetition for credit is possible, with consent of the instructor. During the spring of 2026, the course will cover a range of topics in logic-constrained control systems.

Objective

In this course, we study control problems involving dynamical systems whose behavior is constrained by logical system specifications. By the end of the course, you will have developed a solid and versatile toolkit for translating formal specifications into verified controllers. We will build methodological foundations in three main areas: • Formal modeling of specifications: Boolean and temporal logics, as well as stability and invariance properties. • System verification: sum-of-squares programming, first-order logic solvers, and barrier or Lyapunov functions. • Logic-based control: mixed-integer programming and automata-theoretic methods. Depending on the interests of the participants, we may also explore emerging connections between control, machine learning, and AI — for instance, links between large language models and logic or verification and control of learning-enabled systems. Building on these foundations, we will discuss a range of applications in autonomous systems and robotics.

Content

Logic-constrained control systems arise in a wide range of applications, including multi-robot disaster response, autonomous transportation, and manufacturing. Such systems are typically safety-critical, requiring formal safety certificates, while also being expected to satisfy complex logical specifications that go beyond the stability and invariance properties addressed in standard control courses. The challenges of designing and analyzing these systems stem from their complex dynamics coupled with nonconvex and nonsmooth requirements. This course lies at the intersection of logic, verification, and control, bridging ideas from formal methods (traditionally studied in computer science) and control theory. Students will learn key concepts from both communities and how to integrate them into a unified framework for verified control design. Throughout the course, we will critically assess limitations of the various design methods we encounter.

Resources