Conformal Koopman for Embedded Nonlinear Control with Statistical Robustness: Theory and Real-World Validation

• URL: http://arxiv.org/abs/2603.21580v1
• Date: Mon, 23 Mar 2026 05:04:32 GMT
• Title: Conformal Koopman for Embedded Nonlinear Control with Statistical Robustness: Theory and Real-World Validation
• Abstract summary: We propose a data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems.<n>We provide a bound on the state-dependent modeling uncertainty throughout the trajectory, ensuring safety and robustness.<n>We validate our method both in numerical simulations with the Dubins car and in real-world experiments with a highly nonlinear flapping-wing drone.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers distribution-free probabilistic bounds on the state tracking error under Koopman modeling uncertainty. Conformal prediction is employed here to rigorously derive a bound on the state-dependent modeling uncertainty throughout the trajectory, ensuring safety and robustness without assuming a specific error prediction structure or distribution. Unlike prior approaches that merely combine conformal prediction with Koopman-based control in an open-loop setting, our method establishes a closed-loop control architecture with formal guarantees that explicitly account for both forward and inverse modeling errors. Also, by expressing the tracking error bound in terms of the control parameters and the modeling errors, our framework offers a quantitative means to formally enhance the performance of arbitrary Koopman-based control. We validate our method both in numerical simulations with the Dubins car and in real-world experiments with a highly nonlinear flapping-wing drone. The results demonstrate that our method indeed provides formal safety guarantees while maintaining accurate tracking performance under Koopman modeling uncertainty.

Related papers

• Koopman-Based Robust Model Predictive Control for Nonlinear Systems with Stochastic Intermittent Measurements [11.153670606528545]
  Intermittent state measurements pose fundamental challenges to model predictive control of constrained nonlinear systems.<n>This paper develops a Koopman-based MPC framework with probabilistically truncated soft constraints.
  arXiv  Detail & Related papers  (2026-09-02T04:08:49Z)
• Noise Titration: Exact Distributional Benchmarking for Probabilistic Time Series Forecasting [1.5939955861266883]
  We propose a paradigm shift toward interventionist, exact-statistical benchmarking.<n>We transform forecasting from a black-box sequence matching game into an exact distributional inference task.<n>We find that state-of-the-art zero-shot models behave consistently with the context-parroting mechanism.
  arXiv  Detail & Related papers  (2026-03-23T17:14:11Z)
• Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems [0.0]
  Our framework employs conformal inference to generate confidence sets for the closed-loop dynamics around arbitrary reference trajectories.<n>Via appropriate constraint tightening, chance constraints can be reformulated into tractable, statistically valid deterministic constraints on the reference trajectories.<n>This enables a formal pathway to leverage and validate learning-based motion planners and controllers, such as those with neural contraction metrics, in safety-critical real-world applications.
  arXiv  Detail & Related papers  (2026-03-07T08:01:20Z)
• Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guarantees [8.09931279904483]
  We use Koopman theory with a neural network (NN) lifting function to learn an approximate linear representation of the dynamics.<n>We map closed-loop reachable sets back to the original state space via NN verification tools.<n>Results on high-dimensional MuJoCo tasks show improved reachable set coverage rate, computational efficiency, and conservativeness over existing methods.
  arXiv  Detail & Related papers  (2026-01-03T05:31:08Z)
• Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees [0.9374652839580183]
  We consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman model to predict future outputs, we design a subspace predictive controller in the Koopman space.
  arXiv  Detail & Related papers  (2024-05-02T13:54:21Z)
• Certified Human Trajectory Prediction [66.1736456453465]
  We propose a certification approach tailored for trajectory prediction that provides guaranteed robustness.<n>To mitigate the inherent performance drop through certification, we propose a diffusion-based trajectory denoiser and integrate it into our method.<n>We demonstrate the accuracy and robustness of the certified predictors and highlight their advantages over the non-certified ones.
  arXiv  Detail & Related papers  (2024-03-20T17:41:35Z)
• Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study [56.283944756315066]
  We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman modeling and state estimation. A case study demonstrates that our approach provides accurate control models and enables real-time capable nonlinear model predictive control of a high-purity cryogenic distillation column.
  arXiv  Detail & Related papers  (2024-01-09T11:54:54Z)
• Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior [51.60683890503293]
  We propose a theoretical framework for studying behavior cloning of complex expert demonstrations using generative modeling. We show that pure supervised cloning can generate trajectories matching the per-time step distribution of arbitrary expert trajectories.
  arXiv  Detail & Related papers  (2023-07-27T04:27:26Z)
• Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems [1.0323063834827415]
  We propose a sampling-based planner that uses the mean dynamics model and simultaneously bounds the closed-loop tracking error via a learned disturbance bound. We validate that our guarantees translate to empirical safety in simulation on a 10D quadrotor, and in the real world on a physical CrazyFlie quadrotor and Clearpath Jackal robot.
  arXiv  Detail & Related papers  (2022-12-13T19:38:39Z)
• Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty [68.00748155945047]
  Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. Our contribution is a novel abstraction-based controller method for continuous-state models with noise, uncertain parameters, and external disturbances.
  arXiv  Detail & Related papers  (2022-10-12T07:57:03Z)
• Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations [50.37808220291108]
  This paper addresses learning safe output feedback control laws from partial observations of expert demonstrations. We first propose robust output control barrier functions (ROCBFs) as a means to guarantee safety. We then formulate an optimization problem to learn ROCBFs from expert demonstrations that exhibit safe system behavior.
  arXiv  Detail & Related papers  (2021-11-18T23:21:00Z)
• Trust but Verify: Assigning Prediction Credibility by Counterfactual Constrained Learning [123.3472310767721]
  Prediction credibility measures are fundamental in statistics and machine learning. These measures should account for the wide variety of models used in practice. The framework developed in this work expresses the credibility as a risk-fit trade-off.
  arXiv  Detail & Related papers  (2020-11-24T19:52:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.