1 code implementation • 20 Feb 2023 • Wu Lin, Valentin Duruisseaux, Melvin Leok, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt
Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations.
1 code implementation • 29 Nov 2022 • Valentin Duruisseaux, Thai Duong, Melvin Leok, Nikolay Atanasov
In this paper, we introduce a new structure-preserving deep learning architecture, the Lie group Forced Variational Integrator Network (LieFVIN), capable of learning controlled Lagrangian or Hamiltonian dynamics on Lie groups, either from position-velocity or position-only data.
no code implementations • 14 Feb 2011 • Melvin Leok, Tatiana Shingel
These two characterizations lead to the Galerkin and shooting-based constructions for discrete Lagrangians, which depend on a choice of a numerical quadrature formula, together with either a finite-dimensional function space or a one-step method.
Numerical Analysis
5 code implementations • 10 Mar 2010 • Taeyoung Lee, Melvin Leok, N. Harris McClamroch
The flight maneuvers are defined by a concatenation of flight modes or primitives, each of which is achieved by a nonlinear controller that solves an output tracking problem.
Optimization and Control Systems and Control