M. Leok

发表

Optimal Attitude Control of a Rigid Body Using Geometrically Exact Computations on SO(3)

N. McClamroch, Taeyoung Lee, M. Leok, 2006, math/0601424.

Discrete exterior calculus

Anil N. Hirani, J. Marsden, Mathieu Desbrun, 2005, math/0508341.

Stable Manifolds of Saddle Points for Pendulum Dynamics on S^2 and SO(3)

N. McClamroch, Taeyoung Lee, M. Leok, 2011, 1103.2822.

Variational Integrators

M. Leok, 2012 .

Lie group variational integrators for rigid body problems using quaternions

M. Leok, Xu-Hui Shen, 2017, 1705.04404.

A lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendulum

N. McClamroch, Taeyoung Lee, M. Leok, 2005, Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005..

Lie group variational integrators for the full body problem

N. McClamroch, Taeyoung Lee, M. Leok, 2005, math/0508365.

CONTROLLED LAGRANGIANS AND STABILIZATION OF DISCRETE MECHANICAL SYSTEMS

J. Marsden, A. Bloch, M. Leok, 2009 .

Computing the Fréchet Derivative of the Polar Decomposition

Evan S. Gawlik, M. Leok, 2016, 1608.04491.

Lie group variational integrators for the full body problem in orbital mechanics

N. McClamroch, Taeyoung Lee, M. Leok, 2007 .

General techniques for constructing variational integrators

M. Leok, Tatiana Shingel, 2011, 1102.2685.

Construction and comparison of multidimensional spectral variational integrators and spectral collocation methods

M. Leok, Boying Wu, Yiqun Li, 2018, Applied Numerical Mathematics.

M. Leok, 1996 .

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

Taeyoung, P. Krishnaprasad, J. Grizzle, 2017 .

The Connection between Information Geometry and Geometric Mechanics

M. Leok, Jun Zhang, 2017 .

DISCRETE ROUTH REDUCTION AND DISCRETE EXTERIOR CALCULUS

M. Leok, 2002 .

Generalized Galerkin Variational Integrators

Melvin Leok, M. Leok, 2005 .

Foundations of computational geometric mechanics

Jerrold E. Marsden, Melvin Leok, J. Marsden, 2004 .

An Empirical Chaos Expansion Method for Uncertainty Quantification

M. Leok, Gautam Wilkins, 2017, 1709.08668.

The Discrete Hamel ’ s Formalism and Energy-Momentum Integrators for the n-dimensional Spherical Pendulum

A. Bloch, M. Leok, D. Zenkov, 2013 .

Geometric structure-preserving optimal control of a rigid body

Anthony M. Bloch, Amit K. Sanyal, Melvin Leok, 2007, 0712.4400.

ON MATRIX MANIFOLDS USING PROJECTED POLYNOMIALS ∗

Evan S. Gawlik, M. Leok, 2018 .

Books and Reviews Discrete Control Systems Glossary Definition of the Subject Introduction Discrete Lagrangian and Hamiltonian Mechanics Optimal Control of Discrete Lagrangian and Hamiltonian Systems Controlled Lagrangian Method for Discrete Lagrangian Systems Future Directions Acknowledgments Bibli

M. Leok, H. McClamroch, H. Mcclamroch, 2022 .

Deformable Multi-Body Systems

N. McClamroch, Taeyoung Lee, M. Leok, 2018 .

Generating functionals and Lagrangian partial differential equations

M. Leok, J. Vankerschaver, Cuicui Liao, 2013 .

Generating Functionals and Lagrangian PDEs

M. Leok, J. Vankerschaver, Cuicui Liao, 2011, 1111.0280.

Lagrangian and Hamiltonian Taylor variational integrators

M. Leok, Tatiana Shingel, J. Schmitt, 2017, 1703.06599.

Analysis and Numerical Treatment of Elliptic Equations with Stochastic Data

M. Leok, D. Tartakovsky, Wei Wang, 2015 .

Spectral-collocation variational integrators

Boying Wu, Yiqun Li, Melvin Leok, 2017, J. Comput. Phys..

Extended Research Statement

M. Leok, 2011 .

TIME-ADAPTIVE LAGRANGIAN VARIATIONAL INTEGRATORS

M. Leok, Valentin Duruisseaux, 2022 .

Global Attitude Estimation using Uncertainty Ellipsoids

N. McClamroch, Taeyoung Lee, M. Leok, 2005, math/0512163.

ec 2 00 5 Global Attitude Estimation using Uncertainty Ellipsoids

N. McClamroch, Taeyoung Lee, M. Leok, 2005 .

Geometric Methods for Adjoint Systems

M. Leok, Brian Tran, 2022, ArXiv.

Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups

M. Leok, Álvaro Rodríguez Abella, 2022, ArXiv.

Discrete Routh reduction

Sameer M. Jalnapurkar, J. Marsden, Matthew West, 2005, math/0508330.

Lie group variational integrators for the full body problem in orbital mechanics

N. McClamroch, Taeyoung Lee, M. Leok, 2005, math/0508365.

A ug 2 00 5 Discrete Routh Reduction

Sameer M. Jalnapurkar, J. Marsden, Matthew West, 2008 .

A ] 5 Ja n 20 06 Discrete Routh Reduction

Sameer M. Jalnapurkar, J. Marsden, Matthew West, 2008 .

Practical Perspectives on Symplectic Accelerated Optimization

M. Leok, Valentin Duruisseaux, 2022, 2207.11460.

M. Leok, 1996 .

Global Attitude Estimation using Uncertainty Ellipsoids

N. McClamroch, Taeyoung Lee, M. Leok, 2005, math/0512163.

Global Attitude Estimation using Single Direction Measurements

N. McClamroch, Taeyoung Lee, M. Leok, 2006, 2007 American Control Conference.

A combinatorial optimal control problem for spacecraft formation reconfiguration

N. McClamroch, Taeyoung Lee, M. Leok, 2007, 2007 46th IEEE Conference on Decision and Control.

Optimal Attitude Control of a Rigid Body Using Geometrically Exact Computations on SO(3)

N. McClamroch, Taeyoung Lee, M. Leok, 2006, math/0601424.

Properties of Hamiltonian Variational Integrators

M. Leok, J. Schmitt, 2016, 1609.02309.

Variational Structures in Cochain Projection Based Variational Discretizations of Lagrangian PDEs

M. Leok, Brian Tran, 2021, ArXiv.

A Discrete Variational Integrator for Optimal Control Problems on SO(3)

A. Bloch, M. Leok, A. Sanyal, 2005, Proceedings of the 45th IEEE Conference on Decision and Control.

Time-adaptive Lagrangian Variational Integrators for Accelerated Optimization on Manifolds

M. Leok, Valentin Duruisseaux, 2022, 2201.03774.

TIME-ADAPTIVE VARIATIONAL INTEGRATORS FOR ACCELERATED OPTIMIZATION ON MANIFOLDS

M. Leok, Valentin Duruisseaux, 2022 .

Polyhedral Potential and Variational Integrator Computation of the Full Two Body Problem

N. McClamroch, Taeyoung Lee, M. Leok, 2006, math/0608695.

Interpolation on Symmetric Spaces Via the Generalized Polar Decomposition

Evan S. Gawlik, M. Leok, 2017, Foundations of Computational Mathematics.

Variational Integrators for Interconnected Lagrange–Dirac Systems

M. Leok, Helen Parks, 2017, Journal of Nonlinear Science.

Computational geometric optimal control of connected rigid bodies in a perfect fluid

N. McClamroch, Taeyoung Lee, M. Leok, 2009, Proceedings of the 2010 American Control Conference.

Generalized Galerkin Variational Integrators

M. Leok, 2005, math/0508360.

Spectral variational integrators

M. Leok, James Hall, 2014, Numerische Mathematik.

Accelerated Optimization on Riemannian Manifolds via Projected Variational Integrators

Melvin Leok, Valentin Duruisseaux, M. Leok, 2022, 2201.02904.

Accelerated Optimization on Riemannian Manifolds via Discrete Constrained Variational Integrators

M. Leok, Valentin Duruisseaux, 2021, Journal of Nonlinear Science.

A Variational Formulation of Accelerated Optimization on Riemannian Manifolds

Melvin Leok, Valentin Duruisseaux, M. Leok, 2021, SIAM J. Math. Data Sci..

Variational Symplectic Accelerated Optimization on Lie Groups

Melvin Leok, Molei Tao, Taeyoung Lee, 2021, 2021 60th IEEE Conference on Decision and Control (CDC).

Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization

M. Leok, J. Schmitt, Valentin Duruisseaux, 2021, SIAM J. Sci. Comput..

Adaptive Hamiltonian Variational Integrators and Symplectic Accelerated Optimization.

Melvin Leok, Jeremy Schmitt, Valentin Duruisseaux, 2017, 1709.01975.

High-fidelity numerical simulation of complex dynamics of tethered spacecraft

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2014 .

Computational Geometric Optimal Control of Rigid Bodies

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2008, Commun. Inf. Syst..

Time optimal attitude control for a rigid body

Taeyoung Lee, N.H. McClamroch, M. Leok, 2007, 2008 American Control Conference.

GEOMETRIC OPTIMAL CONTROL OF RIGID BODIES

N. McClamroch, Taeyoung Lee, M. Leok, 2007 .

The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theoriesa)

M. Leok, J. Vankerschaver, Hiroaki Yoshimura, 2012, 1207.2814.

Discrete Hamilton-Jacobi Theory pdf

Tomoki Ohsawa, Anthony M. Bloch, Melvin Leok, 2009, SIAM J. Control. Optim..

Discrete Hamilton-Jacobi theory and discrete optimal control

Tomoki Ohsawa, Anthony M. Bloch, Melvin Leok, 2010, 49th IEEE Conference on Decision and Control (CDC).

Geometric tracking control of a quadrotor UAV on SE(3)

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2010, 49th IEEE Conference on Decision and Control (CDC).

Variational Discretizations of Gauge Field Theories Using Group-Equivariant Interpolation

Melvin Leok, M. Leok, 2019, Found. Comput. Math..

Nonlinear robust tracking control of a quadrotor UAV on SE(3)

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2011, 2012 American Control Conference (ACC).

Prolongation-Collocation Variational Integrators

Melvin Leok, Tatiana Shingel, M. Leok, 2011, 1101.1995.

Control of Complex Maneuvers for a Quadrotor UAV using Geometric Methods on SE(3) pdf

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2010, ArXiv.

Dynamics of connected rigid bodies in a perfect fluid

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2008, 2009 American Control Conference.

A Novel Formulation of Point Vortex Dynamics on the Sphere: Geometrical and Numerical Aspects

Melvin Leok, Joris Vankerschaver, M. Leok, 2012, J. Nonlinear Sci..

A Novel Formulation of Point Vortex Dynamics on the Sphere: Geometrical and Numerical Aspects

M. Leok, J. Vankerschaver, 2013, Journal of Nonlinear Science.

Lie Group Spectral Variational Integrators

James Hall, Melvin Leok, M. Leok, 2014, Foundations of Computational Mathematics.

Variational and Geometric Structures of Discrete Dirac Mechanics

Tomoki Ohsawa, Melvin Leok, M. Leok, 2008, Found. Comput. Math..

Discrete Control Systems

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2007, Encyclopedia of Complexity and Systems Science.

Discrete Dirac Structures and Variational Discrete Dirac Mechanics

M. Leok, T. Ohsawa, 2008 .

A Discrete Theory of Connections on Principal Bundles

Jerrold E. Marsden, Melvin Leok, J. Marsden, 2005, math/0508338.

Discrete Poincaré lemma

Jerrold E. Marsden, Mathieu Desbrun, Melvin Leok, 2005 .

Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures

Jerrold E. Marsden, Melvin Leok, Hiroaki Yoshimura, 2010, 49th IEEE Conference on Decision and Control (CDC).

Multisymplectic Hamiltonian variational integrators pdf

Melvin Leok, Brian Tran, M. Leok, 2021, Int. J. Comput. Math..

Space-Time Finite-Element Exterior Calculus and Variational Discretizations of Gauge Field Theories

John B. Moody, M. Leok, Joe Salamon, 2014 .

Dirac Structures and Hamilton-Jacobi Theory for Lagrangian Mechanics on Lie Algebroids

M. Leok, D. Sosa, 2012, 1211.4561.

Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints

Tomoki Ohsawa, Melvin Leok, M. Leok, 2011, 1109.6056.

Optimal Control of a Rigid Body using Geometrically Exact Computations on SE(3)

Taeyoung Lee, N.H. McClamroch, M. Leok, 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

Symplectic semiclassical wave packet dynamics

M. Leok, T. Ohsawa, 2013, 1302.1139.

Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems

M. Leok, Nikolay A. Atanasov, T. Duong, 2022, L4DC.

Iterative Computation of the Fréchet Derivative of the Polar Decomposition

Melvin Leok, Evan S. Gawlik, M. Leok, 2017, SIAM J. Matrix Anal. Appl..

Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.2603 Lagrangian mechanics and variational integrators on two-spheres

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2022 .

Nearly Periodic Maps and Geometric Integration of Noncanonical Hamiltonian Systems

M. Leok, J. W. Burby, E. Hirvijoki, 2021, Journal of Nonlinear Science.

Spectral Variational Integrators

James Hall, Melvin Leok, M. Leok, 2012, 1211.4534.

Practical perspectives on symplectic accelerated optimization

M. Leok, Valentin Duruisseaux, 2022, Optim. Methods Softw..

Time-adaptive Lagrangian variational integrators for accelerated optimization

M. Leok, Valentin Duruisseaux, 2022, Journal of Geometric Mechanics.

Adaptive Hamiltonian Variational Integrators and Symplectic Accelerated Optimization.

M. Leok, J. Schmitt, Valentin Duruisseaux, 2020 .

Adaptive Variational Integrators

M. Leok, J. Schmitt, 2017 .

Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization

M. Leok, J. Schmitt, Valentin Duruisseaux, 2017, SIAM J. Sci. Comput..

Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/asjc.567 NONLINEAR ROBUST TRACKING CONTROL OF A QUADROTOR UAV ON SE(3)

N. McClamroch, Taeyoung Lee, M. Leok, 2022 .

Safe Control Synthesis With Uncertain Dynamics and Constraints

M. Leok, J. Cortés, Nikolay A. Atanasov, 2022, IEEE Robotics and Automation Letters.

Hamel's formalism and variational integrators on a sphere

Anthony M. Bloch, Melvin Leok, Dmitry V. Zenkov, 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

Discrete Hamiltonian Variational Integrators

Melvin Leok, M. Leok, Jingjing Zhang, 2010, 1001.1408.

Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning

Mark W. Schmidt, M. E. Khan, M. Leok, 2023, International Conference on Machine Learning.

Optimal Attitude Control for a Rigid Body with Symmetry

N. McClamroch, Taeyoung Lee, M. Leok, 2006, American Control Conference.

Global optimal attitude estimation using uncertainty ellipsoids

Taeyoung Lee, Amit K. Sanyal, N. Harris McClamroch, 2006, Syst. Control. Lett..

Interpolation on Symmetric Spaces Via the Generalized Polar Decomposition

Melvin Leok, Evan S. Gawlik, M. Leok, 2016, Found. Comput. Math..

Discrete Dirac Structures and Implicit Discrete Lagrangian and Hamiltonian Systems

M. Leok, T. Ohsawa, 2010 .

Global symplectic uncertainty propagation on SO(3)

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2008, 2008 47th IEEE Conference on Decision and Control.

Geometric Representations of Whitney Forms and their Generalization to Minkowski Spacetime

Melvin Leok, John B. Moody, M. Leok, 2014, 1402.7109.

Discrete Exterior Calculus

M. Leok, Mathieu Desbrun, A. N. Hirani, 2005, math/0508341.

Computational dynamics of a 3D elastic string pendulum attached to a rigid body and an inertially fixed reel mechanism

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2009, 0909.2083.

Geometric exponential integrators

Melvin Leok, Xuefeng Shen, M. Leok, 2017, J. Comput. Phys..

Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups

M. Leok, Álvaro Rodríguez Abella, 2022, Journal of Geometric Mechanics.

Variational Integrators for Interconnected Lagrange–Dirac Systems

Melvin Leok, Helen Parks, M. Leok, 2016, J. Nonlinear Sci..

Geometric formulations of Furuta pendulum control problems

Taeyoung Lee, M. Leok, H. Mcclamroch, 2016 .

Global formulations of Lagrangian and Hamiltonian mechanics on two-spheres

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

Spectral variational integrators

M. Leok, James Hall, 2012, Numerische Mathematik.

Dynamics and control of a chain pendulum on a cart

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

Stable manifolds of saddle equilibria for pendulum dynamics on S2 and SO(3)

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2011, IEEE Conference on Decision and Control and European Control Conference.

Lagrangian and Hamiltonian Dynamics on $$\mathsf{SO(3)}$$

N. McClamroch, Taeyoung Lee, M. Leok, 2018 .

Global Formulations of Lagrangian and Hamiltonian Dynamics on Embedded Manifolds

N. McClamroch, Taeyoung Lee, M. Leok, 2015 .

Dynamics of a 3D elastic string pendulum

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

N A ] 3 M ar 2 00 9 Dynamics of a 3 D Elastic String Pendulum

N. McClamroch, Taeyoung Lee, M. Leok, 2009 .

Lagrangian and Hamiltonian Dynamics on Manifolds

N. McClamroch, Taeyoung Lee, M. Leok, 2018 .

Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning

Mark W. Schmidt, M. E. Khan, M. Leok, 2023, ICML.

Controlled Lagrangians and Stabilization of Discrete Mechanical Systems I

J. Marsden, A. Bloch, M. Leok, 2007, 0704.3875.

Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems

Anthony M. Bloch, Melvin Leok, Dmitry V. Zenkov, 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

Controlled Lagrangians and Stabilization of the Discrete Cart-Pendulum System

M. Leok, J. Marsden, A. Bloch, 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

Connecting Information Geometry and Geometric Mechanics

Melvin Leok, Jun Zhang, M. Leok, 2017, Entropy.

Geometric numerical integration for complex dynamics of tethered spacecraft

Taeyoung Lee, N. Harris McClamroch, Melvin Leok, 2010, Proceedings of the 2011 American Control Conference.