The paper introduces a two‑stage training framework for neural network observers that guarantees Lyapunov stability for uncertain dynamical systems. First, a point‑guided Lyapunov pre‑training phase quickly achieves high estimation accuracy and local stability over sampled states. Second, an LMI fine‑tuning phase efficiently enforces a strict global Lyapunov stability certificate, yielding provably stable observers that train faster than direct LMI methods and generalize robustly across diverse systems.
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.
arXiv:2609.22576v1 Announce Type: cross Abstract: Semidefinite programming (SDP) certificates for feedback systems containing deep neural networks (NNs) typically scale with the total number of neuro...
arXiv:2606. 14536v1 Announce Type: new Abstract: Safe reinforcement learning (RL) aims to learn policies that optimize rewards while satisfying constraints.
arXiv:2606. 30935v1 Announce Type: cross Abstract: While neural network control policies are powerful, their deployment on safety critical systems depends on ensuring that they obey strict constraints.
arXiv:2606. 05247v1 Announce Type: new Abstract: Enforcing nonlinear inequality constraints in neural networks remains challenging, especially when the output is subject to many coupled constraints.
Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-conservative safety guarantees due to significant...
arXiv:2607. 01794v1 Announce Type: cross Abstract: With the rapid development of autonomous aerial systems, Unmanned Aerial Vehicles (UAVs) are increasingly deployed in applications such as inspection, environmental monitoring, and rescue, creating growing demand for reliable autonomous navigation.
arXiv:2608.24743v1 Announce Type: new Abstract: Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-...
The paper presents a robust multi‑agent reinforcement learning framework for small unmanned aircraft systems (sUAS) to maintain separation assurance when GPS data is degraded or spoofed. By modeling state observation corruption as a zero‑sum game, the authors derive a closed‑form adversarial perturbation that eliminates iterative inner optimization and can be evaluated in linear time. Integrating this perturbation into a policy‑gradient MARL algorithm yields a counter‑policy that achieves near‑zero collision rates in high‑density simulations even with up to 35% observation corruption, outperforming non‑adversarial baselines.
CALOS is a runtime safety layer for quadrotor control that enforces attitude constraints without altering the underlying deep reinforcement learning algorithm. It formulates tilt-angle inequalities and a Lyapunov descent condition into a single quadratic program, solved exactly via active-set enumeration over a three-dimensional torque space. In NVIDIA Isaac Lab trajectory-tracking tasks, CALOS reduces lateral tracking error by 55‑60% compared to an unconstrained Proximal Policy Optimization baseline and eliminates attitude-constraint violations during training.
arXiv:2604. 26836v3 Announce Type: replace Abstract: Predictive safety filters (PSFs) leverage model predictive control to enforce constraint satisfaction during deep reinforcement learning (RL) exploration, yet their reliance on first-principles models or Gaussian processes limits scalability and broader applicability.
The paper introduces Linearized Subspace Refinement (LSR), a post‑training framework that uses the local linearized model of a trained neural network to compute a low‑dimensional correction via a reduced least‑squares problem. LSR is architecture‑agnostic and improves accuracy across tasks such as function approximation, operator learning, physics‑informed fine‑tuning, and noisy inverse problems, often achieving order‑of‑magnitude error reductions. The method reveals that standard training can leave significant accuracy plateaus due to numerical ill‑conditioning, and it offers a subspace rank that balances correction strength, stability, and noise sensitivity.