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The results show that globally constructed harmonic guidance can directly support local constrained motion generation on a physical quadrotor, and is the first physical quadrotor demonstration of volumetric harmonic field navigation.
Constructing Lyapunov functions for nonlinear dynamical systems is a central problem in stability analysis, yet remains challenging. Lyapunov functions are commonly characterized as solutions to first-order partial differential equations (PDEs), but these solutions are typically obtained for single systems, limiting th...
It is proved that SGD with clipping and additive Gaussian noise (SGD-CN) converges almost surely (a.s.) under smoothness and uniformly bounded stochastic-gradient noise assumptions, provided the step sizes satisfy some standard decaying conditions.
Outliers are important for stress-testing algorithms and understanding system behaviour under rare conditions. Despite being commonly described as low-likelihood events, existing generative approaches rarely control likelihood explicitly. In this work, we introduce a measure-theoretic notion of outliers based on the di...
It is proved that when neural approximations lie in a compact subset of the solution space, vanishing residual error guarantees convergence to the true solution.
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