mlsanityData to 7 Oct 2026

Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design

arXiv 1503.03144 ↗First posted 11 Mar 2015eess.SY cs.SY math.OCcited by 38

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Abstract (arXiv)

We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control system. The conditions have a simple geometrical interpretation, can be written as a convex feasibility problem, and are invariant under coordinate changes. We show that these conditions are necessary and sufficient for feedback linearizable systems, and also derive novel convex criteria for exponential stabilization of a nonlinear submanifold of state space. We illustrate the benefits of convexity by constructing a controller for an unstable polynomial system that combines local optimality and global stability, using a metric found via sum-of-squares programming.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Mar 2015.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 13; 2022: 6; 2023: 4; 2024: 4; 2025: 7; 2026: 4.

38 papers.

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  1. 2021Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overviewcited by 42
  2. 2021Adaptive-Control-Oriented Meta-Learning for Nonlinear Systemscited by 38
  3. 2022Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theorycited by 18
  4. 2022SABLAS: Learning Safe Control for Black-box Dynamical Systemscited by 17
  5. 2022Control-oriented meta-learningcited by 17
  6. 2024Neural Contractive Dynamical Systemscited by 14
  7. 2021Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approachcited by 13
  8. 2021Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systemscited by 13
  9. 2022Overcoming Exploration: Deep Reinforcement Learning for Continuous Control in Cluttered Environments from Temporal Logic Specificationscited by 11
  10. 2022Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systemscited by 11
  11. 2024Learning Neural Contracting Dynamics: Extended Linearization and Global Guaranteescited by 11
  12. 2021Youla-REN: Learning Nonlinear Feedback Policies with Robust Stability Guaranteescited by 10
26 more
  1. 2021RNNs of RNNs: Recursive Construction of Stable Assemblies of Recurrent Neural Networkscited by 7
  2. 2021A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stabilitycited by 6
  3. 2022Learning Minimally-Violating Continuous Control for Infeasible Linear Temporal Logic Specificationscited by 5
  4. 2023Learning Control-Oriented Dynamical Structure from Datacited by 5
  5. 2024Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recoverycited by 5
  6. 2025Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systemscited by 5
  7. 2025Tensor-Var: Efficient Four-Dimensional Variational Data Assimilationcited by 3
  8. 2021Discrete-time Contraction-based Control of Nonlinear Systems with Parametric Uncertainties using Neural Networkscited by 2
  9. 2021Online Algorithms and Policies Using Adaptive and Machine Learning Approachescited by 2
  10. 2021Adversarially Robust Stability Certificates can be Sample-Efficientcited by 2
  11. 2025Characterizing control between interacting subsystems with deep Jacobian estimationcited by 2
  12. 2026Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPCcited by 2
  13. 2021Learning-based Adaptive Control using Contraction Theorycited by 1
  14. 2021Learning Provably Robust Motion Planners Using Funnel Librariescited by 1
  15. 2023Stable Modular Control via Contraction Theory for Reinforcement Learningcited by 1
  16. 2024Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regionscited by 1
  17. 2025Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representationscited by 1
  18. 2026Controller Design for Structured State-space Models via Contraction Theorycited by 1
  19. 2021Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimationcited by 0
  20. 2023Enabling Efficient, Reliable Real-World Reinforcement Learning with Approximate Physics-Based Modelscited by 0
  21. 2023CaRT: Certified Safety and Robust Tracking in Learning-based Motion Planning for Multi-Agent Systemscited by 0
  22. 2025Contraction-Aware Reinforcement Learning for Nonlinear Control with Statistical Robustnesscited by 0
  23. 2025A robust and adaptive MPC formulation for Gaussian process modelscited by 0
  24. 2025Verifying Closed-Loop Contractivity of Learning-Based Controllers via Partitioningcited by 0
  25. 2026Verifying Physics-Informed Neural Network Fidelity using Classical Fisher Information from Differentiable Dynamical Systemcited by 0
  26. 2026Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systemscited by 0