Contraction Theory

Latest papers

8 papers2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Manifold-Stable Flow Matching
Sep 28, 2026Amirhossein Nazerian, Ali Pezeshki, Jianguo ZhaoConstrained Generative Modeling Flow Matching
Department of Mechanical Engineering Colorado State University Fort Collins, CO 80523, USA · Department of Electrical and Computer Engineering Colorado State University Fort Collins, CO 80523, USA
Impact-Time Guidance via Normal Contraction to a Time-to-Go Isochron
Sep 22, 2026Shivam Bajpai, Abhinav SinhaContraction Theory
Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, OH, 45221, USA
Feedback Motion Planning for Stochastic Nonlinear Systems with Signal Temporal Logic Specifications
May 4, 2026Liqian Ma, Zishun Liu, Glen Chou +1Constrained Motion Planning Trajectory Optimization
Georgia Institute of Technology, Atlanta, GA 30332
A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning
Apr 16, 2026Anand Gokhale, Anton V. Proskurnikov, Yu Kawano +1Dynamical Systems Contraction Theory
Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, Santa Barbara, CA 93106 USA · Department of Electronics and Telecommunications, Politecnico di Torino, Italy, 10129 · Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan
Controller Design for Structured State-space Models via Contraction Theory
Apr 8, 2026Muhammad Zakwan, Vaibhav Gupta, Alireza Karimi +2Contraction Theory Feedback Control
Control & Automation Group, Inspire AG, 8005 Zürich, Switzerland · Automatic Control Laboratory (IfA), ETH Zürich, 8092 Zürich, Switzerland. · Laboratoire d’Automatique, EPFL, 1015 Lausanne, Switzerland.
Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems
Mar 7, 2026Rihan Aaron D'Silva, Hiroyasu TsukamotoContraction Theory Trajectory Optimization
Department of Aerospace Engineering, The Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801
Riemannian Optimization in Modular Systems
Mar 4, 2026Christian Pehle, Jean-Jacques SlotineContraction Theory Riemannian Optimization
Cold Spring Harbor Laboratory Cold Spring Harbor, NY 11724 · Massachusetts Institute of Technology Cambridge, MA 02139
Environment-Aware Learning of Smooth GNSS Covariance Dynamics for Autonomous Racing
Feb 24, 2026Y. Deemo Chen, Arion Zimmermann, Thomas A. Berrueta +1Contraction Theory Covariance Estimation
Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA.

Sep 28, 2026J/K move · Enter open · S save

Manifold-Stable Flow Matching

Amirhossein Nazerian, Ali Pezeshki, Jianguo Zhao

Department of Mechanical Engineering Colorado State University Fort Collins, CO 80523, USA · Department of Electrical and Computer Engineering Colorado State University Fort Collins, CO 80523, USA

Constrained Generative Modeling Flow Matching Contraction Theory Flow-Based Generative Modeling

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Flow matching (FM) learns generative dynamics through velocity regression. Geometric FM variants commonly assume a prior supported on the data manifold, requiring geometric knowledge that is often unavailable. Without such knowledge, low regression error alone does not guarantee manifold adherence. Adherence keeps generated samples within valid configurations and is empirically associated with better task performance. We introduce manifold-stable flow matching (MSFM), which can start from an arbitrary ambient prior, not necessarily supported on the manifold. Using tools from nonlinear dynamics, namely contraction theory, MSFM combines learned tangential transport with prescribed normal contraction. The construction uses analytical projectors for known manifolds and local affine proxies estimated by principal component analysis for unknown data geometry. By implementing contraction theory in both cases of known and unknown manifolds, we guarantee manifold invariance and transverse convergence to the manifold within a desired time window (e.g., one second). We derive a family of compatible probability paths and decompose the training loss into a learnable tangential term and a normal residual. An ellipse experiment attains a mean terminal off-manifold error of order

10^{-6}

. In Push-T robotic experiments, MSFM raises success from

74\%

82\%

. In the Robomimic Square task, success increases from

60\%

72\%

, while rotation-manifold deviation decreases from order

10^{-2}

10^{-7}

. The MSFM terminal geometric errors are controlled by the chosen numerical tolerance. These results demonstrate stronger geometric adherence and higher observed task performance, supporting prescribed normal contraction as a complement to learned generative transport.