About the Workshop
- Category theory provides a powerful mathematical framework for understanding composition and modularity in complex systems. This workshop brings together researchers from control theory, robotics, optimization, and computational science to explore how categorical methods can transform decision-making processes.
- Distinguished experts will present Organizercutting-edge research and practical applications, demonstrating how categorical thinking enables more principled, modular approaches to system design and control. The workshop emphasizes both theoretical foundations and real-world implementations, making it accessible to participants across experience levels.
- Join us to discover how applied category theory is reshaping our understanding of complex decision-making systems and fostering new interdisciplinary collaborations.
Organizers
Gioele Zardini
MIT
Compositional System Design
James Fairbanks
University of Florida
Scientific Computing & Categories
Matthew Hale
Georgia Tech
Categories in Optimization & Control
Aaron D. Ames
Caltech
Categories in Control & Hybrid Systems
Workshop Schedule
Workshop Opening & Motivation
Introduction to the workshop and motivation.
Primer on Applied Category Theory
Foundational concepts with examples from various disciplines.
Abstract
This talk will build up the infrastructure of categories with applications.
Coffee Break & Networking
Networking opportunity and informal discussions.
Introduction to Categorical Lyapunov Theory
Categorical foundations for stability analysis.
Abstract
In this talk we give an introduction to the category needed to state and prove Lyapunov's stability theorem. As a consquence, we get an analog of the result for many different sorts of systems.
Compositional Modeling of Sequential Decision Systems
Category theory for decision-making processes.
Abstract
Multi-stage decision problems often require the computation of optimal decisions, such as in Markov processes, various classes of games, and many types of control systems. In their most general form, the computation of optimal decisions can require the solution of non-convex optimization problems. The solution to one such problem is a decision that, when applied to a system, affects its future states in ways that constrain future decisions. To formally model these dependencies, this talk will present a novel category – called AlgBifun – in which we can model the composition of non-convex optimization problems. We focus on the case of model-predictive control (MPC), and our main result shows that an MPC problem is a composition of morphisms in this category. We will also see how constraints on initial states, terminal states, and periodicity are readily formulated in this setting. This talk will also discuss future work on connecting these categorical formalisms to other work in category theory on dynamical systems.
Scientific Computing with Categories
Categorical approaches to computational methods.
Abstract
This talk will cover the specification of complex models from simpler components. We will use universal properties such as (co)limits to build systems by gluing together components and stratifying along multiple dimensions. Automated approaches to system identification will be used as a motivating example.
Compositional Design of Complex Systems
System-level design using compositional principles.
Abstract
Abstract coming soon...
Closing Remarks & Future Directions
Wrap-up and discussion of future research directions.
Recommended Reading
Applied Category Theory for Engineering
2024
Comprehensive guide to applying categorical methods in engineering systems.
Read BookSeven Sketches in Compositionality
2018
An invitation to applied category theory with practical examples and exercises.
Read BookModeling Model Predictive Control
2024
A category theoretic framework for multistage control problems.
Read PaperA Compositional Framework for First-Order Optimization
2024
Categorical approaches to optimization algorithms.
Read PaperCategorical Lyapunov Theory II: Stability of Systems
2025
Advanced stability analysis through categorical methods.
Read PaperCo-Design of Complex Systems: From Autonomy to Future Mobility Systems
2024
Co-design methodologies for complex autonomous systems.
Read Thesis