arXiv:2607. 18251v1 Announce Type: new Abstract: In this paper, we propose angular stabilization of drone motion using distributed feedback control in the form of an integral operator.
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The paper introduces a conflict‑predictive variable horizon for distributed model predictive control in multi‑drone collision avoidance. Each drone locally estimates future conflicts using observed positions and confidence funnels, then selects the minimal horizon that covers the farthest predicted conflict, shrinking in clear air and expanding only when necessary. The authors prove that this adaptive horizon preserves recursive feasibility and asymptotic stability for linear models, and demonstrate in simulation that it reduces per‑step solver cost and total computation while maintaining separation on dense benchmarks.
The paper investigates how parameter Jacobians influence the stability of network outputs within the framework of network dynamics, learning models, and neural tangent kernels (NTK). It demonstrates that linearized dynamics can be expressed as a semigroup of linear operators on Hilbert spaces, and provides explicit a priori perturbation bounds for fixed‑kernel linearizations in the NTK setting. The authors also offer refinements for task‑specific spaces, ergodic comparison estimates, spectral‑distribution conditions, and extensions to nonautonomous NTK evolutions, supported by worked examples.
The paper investigates the Lyapunov solution operator, which maps a vector field to its corresponding Lyapunov function via a dissipation-based PDE. It proves that this operator is well-defined, unique, and continuous on compact subsets of the domain of attraction under exponential stability, enabling uniform approximation across families of nonlinear systems. Using Fourier Neural Operators, the authors demonstrate that a single trained operator can accurately approximate Lyapunov functions for parameterized dynamics, showcasing the potential of neural operators in stability analysis.
The paper investigates observability in neural state‑space models, particularly the Mamba architecture, using tools from ordinary differential equations and control theory. It introduces several strategies—based on eigenvalues, roots of unity, permutations, Fourier transforms, and Vandermonde matrices—to enforce observability in high‑dimensional, learnable hidden states while maintaining computational efficiency. The authors also present a shared‑parameter construction for Mamba and a training algorithm that satisfies a Robbins‑Monro condition, contrasting it with classical procedures that fail to meet contraction requirements.
arXiv:2610.08764v1 Announce Type: cross Abstract: We develop the first feedback design for rapid stabilization of the Kuramoto--Sivashinsky equation with a spatially varying anti-diffusion coefficien...
arXiv:2608. 16084v1 Announce Type: new Abstract: Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions.