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2020 – today
- 2024
[j27]Brian K. Tran
, Melvin Leok:
Geometric Methods for Adjoint Systems. J. Nonlinear Sci. 34(1): 25 (2024)- [j26]Brian K. Tran, Ben S. Southworth, Melvin Leok:
On Properties of Adjoint Systems for Evolutionary PDEs. J. Nonlinear Sci. 34(5): 95 (2024) - [c28]Kehan Long, Khoa Tran, Melvin Leok, Nikolay Atanasov:
Safe Stabilizing Control for Polygonal Robots in Dynamic Elliptical Environments. ACC 2024: 312-317 - [i18]Brian K. Tran, Ben S. Southworth, Melvin Leok:
On Properties of Adjoint Systems for Evolutionary PDEs. CoRR abs/2404.02320 (2024) - [i17]Pol Mestres, Kehan Long, Melvin Leok, Nikolay Atanasov, Jorge Cortés:
Stabilization of Nonlinear Systems through Control Barrier Functions. CoRR abs/2408.08398 (2024) - [i16]Harsh Choudhary, Chandan Gupta, Vyacheslav kungrutsev, Melvin Leok, Georgios Korpas:
Learning Generalized Hamiltonians using fully Symplectic Mappings. CoRR abs/2409.11138 (2024) - 2023
- [j25]Valentin Duruisseaux, Melvin Leok:
Practical perspectives on symplectic accelerated optimization. Optim. Methods Softw. 38(6): 1230-1268 (2023) - [c27]Wu Lin, Valentin Duruisseaux, Melvin Leok, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt:
Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning. ICML 2023: 21026-21050 - [c26]Valentin Duruisseaux, Thai Duong, Melvin Leok, Nikolay Atanasov:
Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems. L4DC 2023: 731-744 - [i15]Wu Lin, Valentin Duruisseaux, Melvin Leok, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt:
Simplifying Momentum-based Riemannian Submanifold Optimization. CoRR abs/2302.09738 (2023) - [i14]Kehan Long, Khoa Tran, Melvin Leok, Nikolay Atanasov:
Safe Stabilizing Control for Polygonal Robots in Dynamic Elliptical Environments. CoRR abs/2310.00273 (2023) - [i13]Khoa Tran, Melvin Leok:
Lie Group Variational Collision Integrators for a Class of Hybrid Systems. CoRR abs/2310.15356 (2023) - [i12]Brian K. Tran, Melvin Leok:
Type II Hamiltonian Lie Group Variational Integrators with Applications to Geometric Adjoint Sensitivity Analysis. CoRR abs/2311.03527 (2023) - 2022
- [j24]Brian K. Tran, Melvin Leok:
Multisymplectic Hamiltonian variational integrators. Int. J. Comput. Math. 99(1): 113-157 (2022) - [j23]Valentin Duruisseaux, Melvin Leok:
Accelerated Optimization on Riemannian Manifolds via Discrete Constrained Variational Integrators. J. Nonlinear Sci. 32(4): 42 (2022) - [j22]Kehan Long, Vikas Dhiman, Melvin Leok, Jorge Cortés, Nikolay Atanasov:
Safe Control Synthesis With Uncertain Dynamics and Constraints. IEEE Robotics Autom. Lett. 7(3): 7295-7302 (2022) - [j21]Valentin Duruisseaux, Melvin Leok:
A Variational Formulation of Accelerated Optimization on Riemannian Manifolds. SIAM J. Math. Data Sci. 4(2): 649-674 (2022) - [i11]Xuefeng Shen, Khoa Tran, Melvin Leok:
High-order symplectic Lie group methods on SO(n) using the polar decomposition. CoRR abs/2201.10768 (2022) - [i10]Álvaro Rodríguez Abella, Melvin Leok:
Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups. CoRR abs/2202.00803 (2022) - [i9]Kehan Long, Vikas Dhiman, Melvin Leok, Jorge Cortés, Nikolay Atanasov:
Safe Control Synthesis with Uncertain Dynamics and Constraints. CoRR abs/2202.09557 (2022) - [i8]Brian K. Tran, Melvin Leok:
Geometric Methods for Adjoint Systems. CoRR abs/2205.02901 (2022) - [i7]Valentin Duruisseaux, Thai Duong, Melvin Leok, Nikolay Atanasov:
Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems. CoRR abs/2211.16006 (2022) - 2021
- [j20]Valentin Duruisseaux, Jeremy Schmitt, Melvin Leok:
Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization. SIAM J. Sci. Comput. 43(4): A2949-A2980 (2021) - [c25]Taeyoung Lee, Molei Tao, Melvin Leok:
Variational Symplectic Accelerated Optimization on Lie Groups. CDC 2021: 233-240 - [i6]Brian K. Tran, Melvin Leok:
Multisymplectic Hamiltonian Variational Integrators. CoRR abs/2101.07536 (2021) - [i5]Brian K. Tran, Melvin Leok:
Variational Structures in Cochain Projection Based Variational Discretizations of Lagrangian PDEs. CoRR abs/2103.09338 (2021) - [i4]Valentin Duruisseaux, Melvin Leok:
Accelerated Optimization on Riemannian Manifolds via Discrete Constrained Variational Integrators. CoRR abs/2104.07176 (2021)
2010 – 2019
- 2019
- [j19]Melvin Leok:
Variational Discretizations of Gauge Field Theories Using Group-Equivariant Interpolation. Found. Comput. Math. 19(5): 965-989 (2019) - [j18]Xuefeng Shen, Melvin Leok:
Geometric exponential integrators. J. Comput. Phys. 382: 27-42 (2019) - 2018
- [j17]Evan S. Gawlik, Melvin Leok:
Interpolation on Symmetric Spaces Via the Generalized Polar Decomposition. Found. Comput. Math. 18(3): 757-788 (2018) - [j16]Evan S. Gawlik, Melvin Leok:
High-Order Retractions on Matrix Manifolds Using Projected Polynomials. SIAM J. Matrix Anal. Appl. 39(2): 801-828 (2018) - [j15]Evan S. Gawlik, Melvin Leok:
Embedding-Based Interpolation on the Special Orthogonal Group. SIAM J. Sci. Comput. 40(2) (2018) - 2017
- [j14]Melvin Leok, Jun Zhang:
Connecting Information Geometry and Geometric Mechanics. Entropy 19(10): 518 (2017) - [j13]James Hall, Melvin Leok:
Lie Group Spectral Variational Integrators. Found. Comput. Math. 17(1): 199-257 (2017) - [j12]Yiqun Li, Boying Wu, Melvin Leok:
Spectral variational integrators for semi-discrete Hamiltonian wave equations. J. Comput. Appl. Math. 325: 56-73 (2017) - [j11]Yiqun Li, Boying Wu, Melvin Leok:
Spectral-collocation variational integrators. J. Comput. Phys. 332: 83-98 (2017) - [j10]Helen Parks, Melvin Leok:
Variational Integrators for Interconnected Lagrange-Dirac Systems. J. Nonlinear Sci. 27(5): 1399-1434 (2017) - [j9]Evan S. Gawlik, Melvin Leok:
Iterative Computation of the Fréchet Derivative of the Polar Decomposition. SIAM J. Matrix Anal. Appl. 38(4): 1354-1379 (2017) - 2015
- [j8]Zahra Ebrahimzadeh, Melvin Leok, Mojtaba Mahzoon:
A novel variational formulation for thermoelastic problems. Commun. Nonlinear Sci. Numer. Simul. 22(Issues): 263-268 (2015) - [j7]James Hall, Melvin Leok:
Spectral variational integrators. Numerische Mathematik 130(4): 681-740 (2015) - [c24]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Global formulations of Lagrangian and Hamiltonian mechanics on two-spheres. CDC 2015: 6010-6015 - 2014
- [j6]Joris Vankerschaver, Melvin Leok:
A Novel Formulation of Point Vortex Dynamics on the Sphere: Geometrical and Numerical Aspects. J. Nonlinear Sci. 24(1): 1-37 (2014) - 2012
- [c23]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Nonlinear robust tracking control of a quadrotor UAV on SE(3). ACC 2012: 4649-4654 - [c22]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Dynamics and control of a chain pendulum on a cart. CDC 2012: 2502-2508 - [c21]Dmitry V. Zenkov, Melvin Leok, Anthony M. Bloch:
Hamel's formalism and variational integrators on a sphere. CDC 2012: 7504-7510 - 2011
- [j5]Melvin Leok, Tomoki Ohsawa:
Variational and Geometric Structures of Discrete Dirac Mechanics. Found. Comput. Math. 11(5): 529-562 (2011) - [j4]Nalin A. Chaturvedi, Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Nonlinear Dynamics of the 3D Pendulum. J. Nonlinear Sci. 21(1): 3-32 (2011) - [j3]Tomoki Ohsawa, Anthony M. Bloch, Melvin Leok:
Discrete Hamilton-Jacobi Theory. SIAM J. Control. Optim. 49(4): 1829-1856 (2011) - [c20]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Geometric numerical integration for complex dynamics of tethered spacecraft. ACC 2011: 1885-1891 - [c19]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Stable manifolds of saddle equilibria for pendulum dynamics on S2 and SO(3). CDC/ECC 2011: 3915-3921 - [i3]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3). CoRR abs/1109.4457 (2011) - 2010
- [c18]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Computational geometric optimal control of connected rigid bodies in a perfect fluid. ACC 2010: 5985-5990 - [c17]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Geometric tracking control of a quadrotor UAV on SE(3). CDC 2010: 5420-5425 - [c16]Tomoki Ohsawa, Anthony M. Bloch, Melvin Leok:
Discrete Hamilton-Jacobi theory and discrete optimal control. CDC 2010: 5438-5443 - [c15]Joris Vankerschaver, Hiroaki Yoshimura, Melvin Leok, Jerrold E. Marsden:
Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures. CDC 2010: 6265-6270 - [i2]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Control of Complex Maneuvers for a Quadrotor UAV using Geometric Methods on SE(3). CoRR abs/1003.2005 (2010)
2000 – 2009
- 2009
- [c14]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Dynamics of connected rigid bodies in a perfect fluid. ACC 2009: 408-413 - [c13]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Dynamics of a 3D elastic string pendulum. CDC 2009: 3347-3352 - [r1]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Discrete Control Systems. Encyclopedia of Complexity and Systems Science 2009: 2002-2019 - [i1]Tomoki Ohsawa, Anthony M. Bloch, Melvin Leok:
Discrete Hamilton-Jacobi Theory. CoRR abs/0911.2258 (2009) - 2008
- [j2]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Computational Geometric Optimal Control of Rigid Bodies. Commun. Inf. Syst. 8(4): 445-472 (2008) - [j1]Amit K. Sanyal, Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Global optimal attitude estimation using uncertainty ellipsoids. Syst. Control. Lett. 57(3): 236-245 (2008) - [c12]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Time optimal attitude control for a rigid body. ACC 2008: 5210-5215 - [c11]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
Global symplectic uncertainty propagation on SO(3). CDC 2008: 61-66 - 2007
- [c10]Taeyoung Lee, N. Harris McClamroch, Melvin Leok:
Optimal Attitude Control for a Rigid Body with Symmetry. ACC 2007: 1073-1078 - [c9]Taeyoung Lee, Melvin Leok, N. Harris McClamroch, Amit K. Sanyal:
Global Attitude Estimation using Single Direction Measurements. ACC 2007: 3659-3664 - [c8]Taeyoung Lee, Nalin A. Chaturvedi, Amit K. Sanyal, Melvin Leok, N. Harris McClamroch:
Propagation of uncertainty in rigid body attitude flows. CDC 2007: 2689-2694 - [c7]Taeyoung Lee, Melvin Leok, N. Harris McClamroch:
A combinatorial optimal control problem for spacecraft formation reconfiguration. CDC 2007: 5370-5375 - 2006
- [c6]Taeyoung Lee, N. Harris McClamroch, Melvin Leok:
Attitude maneuvers of a rigid spacecraft in a circular orbit. ACC 2006: 1-6 - [c5]Taeyoung Lee, N. Harris McClamroch, Melvin Leok:
Optimal Control of a Rigid Body using Geometrically Exact Computations on SE(3). CDC 2006: 2710-2715 - [c4]Taeyoung Lee, Amit K. Sanyal, Melvin Leok, N. Harris McClamroch:
Deterministic Global Attitude Estimation. CDC 2006: 3174-3179 - [c3]Anthony M. Bloch, Melvin Leok, Jerrold E. Marsden, Dmitry V. Zenkov:
Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems. CDC 2006: 3333-3338 - [c2]Islam I. Hussein, Melvin Leok, Amit K. Sanyal, Anthony M. Bloch:
A Discrete Variational Integrator for Optimal Control Problems on SO(3). CDC 2006: 6636-6641 - 2005
- [c1]Anthony M. Bloch, Melvin Leok, Jerrold E. Marsden, Dmitry V. Zenkov:
Controlled Lagrangians and Stabilization of the Discrete Cart-Pendulum System. CDC/ECC 2005: 6579-6584
Coauthor Index
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