This manuscript proposes an integral formulation of the newly defined quadratic embedding method for identifying nonlinear systems (QENDy). In the original algorithm, trajectory data points along with their time derivatives are used.
arXiv:2606. 11629v1 Announce Type: cross Abstract: This manuscript proposes an integral formulation of the newly defined quadratic embedding method for identifying nonlinear systems (QENDy).
The paper proposes a new interpretable machine learning approach for discovering unknown nonlinear ordinary differential equations from a single state trajectory. It differs from existing methods by deriving its formulation from Functional Analysis and Operator Theory and by defining a cost function as an integral distance between functions rather than a discrete error sum. An incremental learning algorithm enables online updates, allowing simultaneous identification of both system dynamics and external time‑varying forces, with numerical examples illustrating its benefits.
arXiv:2607. 15077v1 Announce Type: new Abstract: Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known.
The paper proposes a new receding‑horizon algorithm for the Linear Quadratic Regulator (LQR) with unknown dynamics, inspired by REINFORCE. It removes the need for two‑point gradient estimates and does not require a stable initial policy, while maintaining the same order of sample complexity. A refined analysis of error propagation via the Riccati operator’s contraction under Riemannian distance yields improved sample complexity and convergence guarantees.
arXiv:2606. 23827v1 Announce Type: cross Abstract: A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics.
arXiv:2606. 15690v1 Announce Type: new Abstract: Data from simulations and experiments are rarely noise-free and often exhibit heterogeneous levels of fidelity.
arXiv:2606. 24769v1 Announce Type: cross Abstract: Even when Dirac-Frenkel dynamics determine a well-defined evolution in function space, the corresponding parameter dynamics can be non-unique or ill-conditioned for redundant nonlinear parametrizations such as neural networks or mixture models.
arXiv:2410.23667v2 Announce Type: replace Abstract: Neural differential equations offer a powerful approach for learning dynamical systems from data. However, they do not inherently respect known con...
arXiv:2606. 00298v1 Announce Type: cross Abstract: Data-driven reduced-order modeling is an essential component in the computer-aided design of control systems.
arXiv:2609.38877v1 Announce Type: new Abstract: Physical parameter estimation from video aims to recover the parameters of a known family of governing dynamical equations from pixel observations. Exi...
arXiv:2605. 01835v2 Announce Type: replace Abstract: Nonlinear coupled systems are ubiquitous in science and engineering.
The paper introduces a robust and adaptive model predictive control framework for uncertain nonlinear systems with bounded disturbances and unmodeled nonlinearities, leveraging Gaussian Processes to learn dynamics from noisy measurements. It derives robust predictions for GP models using contraction metrics, integrating them into the MPC formulation to ensure recursive feasibility, robust constraint satisfaction, and convergence to a reference state with high probability. A numerical example involving a planar quadrotor experiencing challenging ground effects demonstrates significant performance gains from the robust prediction method and online learning.