Quadrotor navigation in cluttered 3-D environments requires global guidance while local motion remains subject to collision and motion limits. Harmonic potentials provide dense guidance from a global boundary value problem, but coupling a volumetric harmonic field to constrained physical quadrotor motion remains an ope...
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...
Amartya Mukherjee, Maxwell Fitzsimmons, D. C. Del Rey Fernández et al.· 0 citations
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.
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.
Amartya Mukherjee, Maxwell Fitzsimmons, D. C. Del Rey Fernández et al.· arXiv.org· 1 citation
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