arXiv AI

GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics

arXiv:2607. 01203v1 Announce Type: cross Abstract: This paper studies real-time robust optimal control for uncertain nonlinear systems, where linear time-varying (LTV) approximations make planning tractable but require sound linearization error bounds (LEBs) to guarantee robust constraint satisfaction.

arXiv Machine Learning
Jun 4

Certified Neural Approximations of Nonlinear Dynamics

arXiv:2505. 15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.

By Frederik Baymler Mathiesen, Nikolaus Vertovec, Francesco Fabiano, Luca Laurenti, Alessandro Abate
Hugging Face Trending Papers
Aug 11

Forward Trajectory Steering for Hamilton-Jacobi Reachability Analysis

Hamilton-Jacobi (HJ) reachability provides a mathematically rigorous framework for safe control of dynamical systems, but its practical application is bottlenecked by the computational complexity of solving Hamilton-Jacobi-Isaacs variational inequality PDEs in high dimensions. Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to classical mesh-based solvers, yet their performance is highly sensitive to the choice of collocation sampling.

arXiv AI
22h ago

Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration

arXiv:2507. 15455v3 Announce Type: replace-cross Abstract: We propose a mesh-free policy iteration framework that combines classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic differential games and robust control.

By Hee Jun Yang, Minjung Gim, Yeoneung Kim