Research
I am largely interested in mathematical questions of a dynamical nature, e.g., in the context of algorithm design, control systems and synthetic biology. In particular, I like to understand the interplay between the underlying problem structure and achievable qualitative behaviour. We typically study these questions by means of appropriate topological invariants.
With special thanks to Raphaël Jungers, Daniel Kuhn, Mengmeng Li, Peyman Mohajerin Esfahani, Emmanuel Moulay, Roland Schwan, Tyler Summers, Tobias Sutter and Man-Chung Yue.
Throughout, kindly supported by the EU, l'EPFL, the TU Delft, the NCCR Automation, the SNSF and l'UCLouvain.
Selected (pre)prints
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Asymptotic stability equals exponential stability—while you twist your eyes Charles Conley himself posed the following ‘‘converse question’’ in the late 1970s: ‘‘To what extent does the homotopy index itself determine the equivalence class of isolated invariant sets which are related by continuation?’’ (Con78, p. 83). This question, as revitalized by Matthew Kvalheim (Kva23), inspired our work. Specifically, the abstract of our work reads as: ‘‘Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this homotopy.’’ Comment added March 20, 2025: Recently, Matthew Kvalheim and Eduardo Sontag posted new work, where they continue, in one way or another, with this program (KS25), (Kva25). |
Books
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Topological Obstructions to Stability and Stabilization: History, Recent Advances and Open Problems |
Journal papers
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Small errors in random zeroth-order optimization are imaginary |
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On continuation and convex Lyapunov functions |
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Efficient Learning of a Linear Dynamical System with Stability Guarantees |
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Topological Linear System Identification via Moderate Deviations Theory |
Peer-reviewed conference proceedings
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A Large Deviations Perspective on Policy Gradient Algorithms |
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On topological properties of compact attractors on Hausdorff spaces |
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On Topological Equivalence in Linear Quadratic Optimal Control |
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Robust Linear Quadratic Regulator: Exact Tractable Reformulation |
Extended abstracts
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On Preorders of Path-complete Lyapunov Functions Through Lifts Comment added March 20, 2025: An extended version is in preparation. |
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On the Conley Index and Controllability Comment added March 20, 2025: An extended version is in preparation. |
Preprints (under review)
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Ordering and refining path-complete Lyapunov functions through composition lifts |
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Imaginary Zeroth-Order Optimization |
Thesis
Stability: a search for structure
Wouter Jongeneel
PhD Thesis, Electrical Engineering, EPFL Jun. 2024, adviser Daniel Kuhn.
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Controlling the Unknown: A Game Theoretic Perspective
Wouter Jongeneel
MSc Thesis, Systems & Control, TU Delft Nov. 2019, adviser Peyman Mohajerin Esfahani.
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Recent talks (feel free to request slides or references)
A coarse view on dynamical systems, control and optimization,
September 2024, UCLouvain, INMA.
A Large Deviations Perspective on Policy Gradient Algorithms,
July 2024, University of Konstanz, Department of Computer and Information Science.
Fika in Paris: on qualitative reasoning in a quantitative age,
May 2024, KTH Stockholm, Division of Decision and Control Systems (DCS).
Towards Qualitative System Identification Through Optimization,
June 2023, SIAM Conference on Optimization, Seattle.
On continuation and convex Lyapunov functions,
March 2023, KU Leuven, 17th International Young Researchers Workshop on Geometry, Mechanics, and Control.
Control theory with Heinz Hopf,
February 2023, ETH Zürich, Institut für Automatik (IfA).
Imaginary Zeroth-Order Optimization,
July 2022, International Conference on Continuous Optimization (ICCOPT), Lehigh.
Topological obstructions to stability and stabilization,
March 2022, University of Warsaw, Department of Mathematical Methods in Physics, Theory of Duality seminar.
Small Errors in Zeroth Order Convex Optimization Are Imaginary,
July 2021, SIAM Conference on Optimization, online.
On Topological Equivalence in Linear Quadratic Optimal Control,
November 2020, Universiteit Utrecht, 15th International Young Researchers Workshop on Geometry, Mechanics, and Control. |video|
From Correlated Data to Guarantees in Stable Identification,
October 2020, ETH Zürich, Institut für Automatik (IfA).
Other notes
Stability via reverse I-projections, a symplectic perspective on the computation
Wouter Jongeneel
technical note, 2022
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