Algebraic Dynamics, Optimization, and Control

Three agents' trajectories, marked in green, orange and blue, converging on a triangular formation that is itself sliding to the right
Three agents holding a formation while it moves, from the AlgebraicOptimization.jl documentation.

AlgebraicControl.jl

Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon. We present a novel Julia library that leverages our theoretical results to automate the implementation of correct-by-construction MPC problems in software.

Project team

Project articles

  1. Hanks, T., Fairbanks, J., & Klawonn, M. (2025). Generalized Gradient Descent is a Hypergraph Functor. In Electronic Proceedings in Theoretical Computer Science (pp. 217-233). https://doi.org/10.4204/EPTCS.429.12
  2. Hanks, T., She, B., Hale, M., Patterson, E., Klawonn, M., & Fairbanks, J. (2024). Modeling Model Predictive Control: A Category Theoretic Framework for Multistage Control Problems. In 2024 American Control Conference (ACC) (pp. 4850-4857). IEEE. https://doi.org/10.23919/ACC60939.2024.10644848
  3. Hanks, T., Klawonn, M., Patterson, E., Hale, M., & Fairbanks, J. (2024). A Compositional Framework for First-Order Optimization. arXiv. https://doi.org/10.48550/arXiv.2403.05711
  4. She, B., Hanks, T., Fairbanks, J., & Hale, M. (2023). Characterizing Compositionality of LQR from the Categorical Perspective. In 2023 62nd IEEE Conference on Decision and Control (CDC) (pp. 1680-1685). https://doi.org/10.1109/CDC49753.2023.10383467

Sponsors

National Science Foundation Office of Naval Research Air Force Research Laboratory

AlgebraicOptimization and Control has been supported by the following programs:

  • NSF: Graduate Research Fellowship Program
  • ONR: Domain Transfer for Continuity of Performance
  • AFRL: Griffis Summer Internship Program