Discrete mechanics and optimal control: An analysis
ESAIM: COCV, 17 2 (2011) 322-352
Published online: 2010-03-31
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Muscle path predictions using a discrete geodesic Euler–Lagrange model in constrained optimisation: comparison with OpenSim and experimental data
Maxence Lavaill, Xiyu Chen, Simon Heinrich, Peter Pivonka and Sigrid LeyendeckerMultibody System Dynamics (2025)
https://doi.org/10.1007/s11044-025-10055-3
Monolithic and Staggered Solution Strategies for Constrained Mechanical Systems in Optimal Control Problems
Ashutosh Bijalwan, Simeon Schneider, Peter Betsch and José J MuñozInternational Journal for Numerical Methods in Engineering 126 (6) (2025)
https://doi.org/10.1002/nme.70026
Extension of Hamiltonian Mechanics to Non-Conservative Systems Via Higher-Order Dynamics
John W. Sanders, Eric T. Becker and Adam C. DeVoriaJournal of Vibration and Acoustics 146 (6) (2024)
https://doi.org/10.1115/1.4067376
Optimal control of constrained mechanical systems in redundant coordinates: Formulation and structure-preserving discretization
Simeon Schneider and Peter BetschComputer Methods in Applied Mechanics and Engineering 432 117443 (2024)
https://doi.org/10.1016/j.cma.2024.117443
Optimization-based trajectory planning for transport collaboration of heterogeneous systems
Jingshan Chen, Wei Luo, Henrik Ebel and Peter Eberhardat - Automatisierungstechnik 72 (2) 80 (2024)
https://doi.org/10.1515/auto-2023-0078
A new Lagrangian approach to control affine systems with a quadratic Lagrange term
Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T. Sato Martín de Almagro and Flóra Orsolya SzemenyeiJournal of Computational Dynamics (2024)
https://doi.org/10.3934/jcd.2024017
Relative-kinematic formulation of geometrically exact beam dynamics based on Lie group variational integrators
Maximilian Herrmann and Paul KotyczkaComputer Methods in Applied Mechanics and Engineering 432 117367 (2024)
https://doi.org/10.1016/j.cma.2024.117367
Discrete maximum principle in Hamel’s formalism for nonholonomic optimal control
Bin Huang, Zhonggui Yi and Donghua ShiMeccanica 59 (7) 1001 (2024)
https://doi.org/10.1007/s11012-024-01790-6
Discrete adjoint method for variational integration of constrained ODEs and its application to optimal control of geometrically exact beam dynamics
Matthias Schubert, Rodrigo T. Sato Martín de Almagro, Karin Nachbagauer, Sina Ober-Blöbaum and Sigrid LeyendeckerMultibody System Dynamics 60 (3) 447 (2024)
https://doi.org/10.1007/s11044-023-09934-4
Time-Optimal Handover Trajectory Planning for Aerial Manipulators Based on Discrete Mechanics and Complementarity Constraints
Wei Luo, Jingshan Chen, Henrik Ebel and Peter EberhardIEEE Transactions on Robotics 39 (6) 4332 (2023)
https://doi.org/10.1109/TRO.2023.3301298
Predicting Sit-to-Stand Body Adaptation Using a Simple Model
Sarra Gismelseed, Amur Al-Yahmedi, Riadh Zaier, Hassen Ouakad and Issam BahadurAxioms 12 (6) 559 (2023)
https://doi.org/10.3390/axioms12060559
A biped model to predict a wide range of gait and posture results
Sarra Gismelseed, Amur Al-Yahmedi and Riadh ZaierFranklin Open 3 100020 (2023)
https://doi.org/10.1016/j.fraope.2023.100020
Stochastic Variational Principles for Dissipative Equations with Advected Quantities
Xin Chen, Ana Bela Cruzeiro and Tudor S. RatiuJournal of Nonlinear Science 33 (1) (2023)
https://doi.org/10.1007/s00332-022-09846-1
On the Discrete-Time Minimum Principle in Multiple-Mode Systems
José Daniel López-Barrientos, Manuel Jiménez-Lizárraga and Beatris Adriana Escobedo-TrujilloCybernetics and Systems 1 (2023)
https://doi.org/10.1080/01969722.2023.2175492
Informatics in Control, Automation and Robotics
Wei Luo and Peter EberhardLecture Notes in Electrical Engineering, Informatics in Control, Automation and Robotics 1006 39 (2023)
https://doi.org/10.1007/978-3-031-26474-0_3
Symplectic Integration Schemes for Systems With Nonlinear Dissipation
David J. N. Limebeer, Farhang Haddad Farshi and Sina Ober-BlöbaumIEEE Transactions on Automatic Control 68 (4) 2338 (2023)
https://doi.org/10.1109/TAC.2023.3235908
A control Hamiltonian-preserving discretisation for optimal control
Ashutosh Bijalwan and José J. MuñozMultibody System Dynamics 59 (1) 19 (2023)
https://doi.org/10.1007/s11044-023-09902-y
Optimal Control of Dielectric Elastomer Actuated Multibody Dynamical Systems
Dengpeng Huang and Sigrid LeyendeckerSoft Robotics 10 (5) 897 (2023)
https://doi.org/10.1089/soro.2022.0162
4587 (2023)
https://doi.org/10.23919/ACC55779.2023.10156020
3262 (2023)
https://doi.org/10.1109/CDC49753.2023.10383697
A general numerical scheme for the optimal control of fractional Birkhoffian systems
Lin He, Chunqiu Wei, Jiang Sha, Delong Mao and Kangshuo WangNonlinear Dynamics 110 (2) 1543 (2022)
https://doi.org/10.1007/s11071-022-07720-z
A dual-oscillator approach to complex-stiffness damping based on fourth-order dynamics
John W. SandersNonlinear Dynamics 109 (2) 285 (2022)
https://doi.org/10.1007/s11071-022-07597-y
CONTROLO 2022
María Barbero Liñán and David Martín de DiegoLecture Notes in Electrical Engineering, CONTROLO 2022 930 735 (2022)
https://doi.org/10.1007/978-3-031-10047-5_65
Discrete LQR and ILQR methods based on high order Runge-Kutta discretizations
Zuodi Xie and Tieqiang GangApplied Numerical Mathematics 182 196 (2022)
https://doi.org/10.1016/j.apnum.2022.07.015
Optimized flapping flight in Venus surface atmospheric conditions
Zdravko Terze, Marko Kasalo, Viktor Pandža and Dario ZlatarActa Astronautica 194 83 (2022)
https://doi.org/10.1016/j.actaastro.2022.01.031
729 (2022)
https://doi.org/10.23919/ECC55457.2022.9838240
Forced Variational Integrators for the Formation Control of Multiagent Systems
Leonardo Jesus Colombo and Hector Garcia de MarinaIEEE Transactions on Control of Network Systems 8 (3) 1336 (2021)
https://doi.org/10.1109/TCNS.2021.3065635
Explicit multiobjective model predictive control for nonlinear systems with symmetries
Sina Ober‐Blöbaum and Sebastian PeitzInternational Journal of Robust and Nonlinear Control 31 (2) 380 (2021)
https://doi.org/10.1002/rnc.5281
Numerical simulation of tethered–wing power systems based on variational integration
M. Kakavand and A. NikoobinJournal of Computational Science 51 101351 (2021)
https://doi.org/10.1016/j.jocs.2021.101351
Optimized flapping wing dynamics via DMOC approach
Zdravko Terze, Viktor Pandža, Marko Kasalo and Dario ZlatarNonlinear Dynamics 103 (1) 399 (2021)
https://doi.org/10.1007/s11071-020-06119-y
Encyclopedia of Systems and Control
David Martin De DiegoEncyclopedia of Systems and Control 584 (2021)
https://doi.org/10.1007/978-3-030-44184-5_47
2438 (2021)
https://doi.org/10.23919/ECC54610.2021.9655193
Discrete-Time Differential Dynamic Programming on Lie Groups: Derivation, Convergence Analysis, and Numerical Results
George I. Boutselis and Evangelos TheodorouIEEE Transactions on Automatic Control 66 (10) 4636 (2021)
https://doi.org/10.1109/TAC.2020.3034206
Superconvergence of Galerkin variational integrators
Sina Ober-Blöbaum and Mats VermeerenIFAC-PapersOnLine 54 (19) 327 (2021)
https://doi.org/10.1016/j.ifacol.2021.11.098
Fractional Damping Through Restricted Calculus of Variations
Fernando Jiménez and Sina Ober-BlöbaumJournal of Nonlinear Science 31 (2) (2021)
https://doi.org/10.1007/s00332-021-09700-w
Variational order for forced Lagrangian systems II. Euler–Poincaré equations with forcing
D Martín de Diego and R T Sato Martín de AlmagroNonlinearity 33 (8) 3709 (2020)
https://doi.org/10.1088/1361-6544/ab8bb1
Multibody Dynamics 2019
Michael Burger, Simon Gottschalk and Michael RollerComputational Methods in Applied Sciences, Multibody Dynamics 2019 53 68 (2020)
https://doi.org/10.1007/978-3-030-23132-3_9
A review of structure-preserving numerical methods for engineering applications
Harsh Sharma, Mayuresh Patil and Craig WoolseyComputer Methods in Applied Mechanics and Engineering 366 113067 (2020)
https://doi.org/10.1016/j.cma.2020.113067
Variational Integrators for Dissipative Systems
David J. N. Limebeer, Sina Ober-Blobaum and Farhang Haddad FarshiIEEE Transactions on Automatic Control 65 (4) 1381 (2020)
https://doi.org/10.1109/TAC.2020.2965059
On optical data-guided optimal control simulations of human motion
Ramona Hoffmann, Bertram Taetz, Markus Miezal, Gabriele Bleser and Sigrid LeyendeckerMultibody System Dynamics 48 (1) 105 (2020)
https://doi.org/10.1007/s11044-019-09701-4
Discrete mechanics and optimal control optimization of flapping wing dynamics for Mars exploration
Zdravko Terze, Viktor Pandža, Marko Kasalo and Dario ZlatarAerospace Science and Technology 106 106131 (2020)
https://doi.org/10.1016/j.ast.2020.106131
Advances in Dynamics, Optimization and Computation
Kathrin Flaßkamp, Sina Ober-Blöbaum and Sebastian PeitzStudies in Systems, Decision and Control, Advances in Dynamics, Optimization and Computation 304 209 (2020)
https://doi.org/10.1007/978-3-030-51264-4_9
Epistemic uncertainty in optimal control simulation
Markus Eisentraudt and Sigrid LeyendeckerMechanical Systems and Signal Processing 121 876 (2019)
https://doi.org/10.1016/j.ymssp.2018.12.001
Variational integrator based optimal feedback control for constrained mechanical systems
Daniel Glaas and Sigrid LeyendeckerZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 99 (1) (2019)
https://doi.org/10.1002/zamm.201700221
Structure‐preserving local optimal control of mechanical systems
Kathrin Flaßkamp and Todd D. MurpheyOptimal Control Applications and Methods 40 (2) 310 (2019)
https://doi.org/10.1002/oca.2479
Image Extrapolation for the Time Discrete Metamorphosis Model: Existence and Applications
Alexander Effland, Martin Rumpf and Florian SchäferSIAM Journal on Imaging Sciences 11 (1) 834 (2018)
https://doi.org/10.1137/17M1129544
A Variational Integrator for the distance-based formation control of multi-agent systems
Leonardo J. Colombo and Hector Garcia de MarinaIFAC-PapersOnLine 51 (23) 76 (2018)
https://doi.org/10.1016/j.ifacol.2018.12.014
Variational order for forced Lagrangian systems
D Martín de Diego and R Sato Martín de AlmagroNonlinearity 31 (8) 3814 (2018)
https://doi.org/10.1088/1361-6544/aac5a6
Design optimization of dynamic flexible multibody systems using the discrete adjoint variable method
Mehran Ebrahimi, Adrian Butscher, Hyunmin Cheong and Francesco IorioComputers & Structures (2018)
https://doi.org/10.1016/j.compstruc.2018.12.007
A discrete-time Pontryagin maximum principle on matrix Lie groups
Karmvir Singh Phogat, Debasish Chatterjee and Ravi N. BanavarAutomatica 97 376 (2018)
https://doi.org/10.1016/j.automatica.2018.08.026
Variational Integrators for Parameter Identification of Mechanical Systems
Kathrin Flaßkamp, Kai Schäfer and Christof BüskensPAMM 18 (1) (2018)
https://doi.org/10.1002/pamm.201800284
Discrete-Time Optimal Attitude Control of a Spacecraft with Momentum and Control Constraints
Karmvir Singh Phogat, Debasish Chatterjee and Ravi BanavarJournal of Guidance, Control, and Dynamics 41 (1) 199 (2018)
https://doi.org/10.2514/1.G002861
Inverse Dynamics for Discrete Geometric Mechanics of Multibody Systems With Application to Direct Optimal Control
Staffan Björkenstam, Sigrid Leyendecker, Joachim Linn, Johan S. Carlson and Bengt LennartsonJournal of Computational and Nonlinear Dynamics 13 (10) (2018)
https://doi.org/10.1115/1.4040780
Fast Nonlinear Moving Horizon Estimation with Discrete Mechanics and Optimal Control
Ke XuIFAC-PapersOnLine 51 (20) 78 (2018)
https://doi.org/10.1016/j.ifacol.2018.10.178
A Fractional Variational Approach for Modelling Dissipative Mechanical Systems:Continuous and Discrete Settings
Fernando Jiménez and Sina Ober-BlöbaumIFAC-PapersOnLine 51 (3) 50 (2018)
https://doi.org/10.1016/j.ifacol.2018.06.013
Variational Integrators for Structure-Preserving Filtering
Jarvis Schultz, Kathrin Flaßkamp and Todd D. MurpheyJournal of Computational and Nonlinear Dynamics 12 (2) (2017)
https://doi.org/10.1115/1.4034728
1755 (2017)
https://doi.org/10.1109/AIM.2017.8014272
Optimal Control: Novel Directions and Applications
Maria Soledad Aronna, Daniela Tonon, Andrea Boccia, et al.Lecture Notes in Mathematics, Optimal Control: Novel Directions and Applications 2180 1 (2017)
https://doi.org/10.1007/978-3-319-60771-9_1
Conservation of generalized momentum maps in mechanical optimal control problems with symmetry
Peter Betsch and Christian BeckerInternational Journal for Numerical Methods in Engineering 111 (2) 144 (2017)
https://doi.org/10.1002/nme.5459
On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function
Maik Ringkamp, Sina Ober-Blöbaum and Sigrid LeyendeckerMathematical Programming 161 (1-2) 551 (2017)
https://doi.org/10.1007/s10107-016-1023-5
Towards Discrete Mechanics and Optimal Control for Complex Models * *Financial support by the European Commission within the H2020 project Spexor (GA 687662) is gratefully acknowledged
Paul Manns and Katja MombaurIFAC-PapersOnLine 50 (1) 4812 (2017)
https://doi.org/10.1016/j.ifacol.2017.08.966
C1‐continuous space‐time discretization based on Hamilton's law of varying action
Janine C. Mergel, Roger A. Sauer and Sina Ober‐BlöbaumZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 97 (4) 433 (2017)
https://doi.org/10.1002/zamm.201600062
Variational integrators for open‐loop and closed‐loop optimal control of mechanical systems
Kathrin Flaßkamp, Todd D. Murphey and Christof BüskensPAMM 17 (1) 791 (2017)
https://doi.org/10.1002/pamm.201710363
Optimal control of a slot car racer
Johann Penner, Tristan Schlögl and Sigrid LeyendeckerPAMM 17 (1) 537 (2017)
https://doi.org/10.1002/pamm.201710238
Galerkin variational integrators and modified symplectic Runge–Kutta methods
Sina Ober-BlöbaumIMA Journal of Numerical Analysis 37 (1) 375 (2017)
https://doi.org/10.1093/imanum/drv062
Swing-up of the moving double pendulum on a cart with simulation based LQR-Trees
Ke Xu, Julia Timmermann and Ansgar TrächtlerIFAC-PapersOnLine 50 (1) 4094 (2017)
https://doi.org/10.1016/j.ifacol.2017.08.794
Efficient Planning of Optimal Trajectory for a Furuta Double Pendulum Using Discrete Mechanics and Optimal Control
Jawad Ismail and Steven LiuIFAC-PapersOnLine 50 (1) 10456 (2017)
https://doi.org/10.1016/j.ifacol.2017.08.1975
Discrete Mechanics and Optimal Control of Walking Gaits
M. W. Koch, M. Ringkamp and S. LeyendeckerJournal of Computational and Nonlinear Dynamics 12 (2) (2017)
https://doi.org/10.1115/1.4035213
Variational integrator for constrained mechanical systems with pulsed disturbances and optimal feedback control
Daniel Glaas and Sigrid LeyendeckerPAMM 17 (1) 149 (2017)
https://doi.org/10.1002/pamm.201710044
Autonomous Suspended Load Operations via Trajectory Optimization and Variational Integrators
Gerardo De La Torre, Evangelos Theodorou and Eric N. JohnsonJournal of Guidance, Control, and Dynamics 40 (2) 278 (2017)
https://doi.org/10.2514/1.G001769
Symplectic Runge--Kutta Schemes for Adjoint Equations, Automatic Differentiation, Optimal Control, and More
J. M. Sanz-SernaSIAM Review 58 (1) 3 (2016)
https://doi.org/10.1137/151002769
Minimizing control variation in discrete-time optimal control problems
Ying Zhang, Changjun Yu, Yingtao Xu and Kok Lay TeoJournal of Computational and Applied Mathematics 292 292 (2016)
https://doi.org/10.1016/j.cam.2015.07.010
Astrodynamics Network AstroNet-II
Natasha Bosanac, Kathleen C. Howell and Ephraim FischbachAstrophysics and Space Science Proceedings, Astrodynamics Network AstroNet-II 44 1 (2016)
https://doi.org/10.1007/978-3-319-23986-6_1
Geometric Integrators for Higher-Order Variational Systems and Their Application to Optimal Control
Leonardo Colombo, Sebastián Ferraro and David Martín de DiegoJournal of Nonlinear Science 26 (6) 1615 (2016)
https://doi.org/10.1007/s00332-016-9314-9
Simultaneous path planning and trajectory optimization for robotic manipulators using discrete mechanics and optimal control
Zeeshan Shareef and Ansgar TrächtlerRobotica 34 (6) 1322 (2016)
https://doi.org/10.1017/S0263574714002318
4463 (2016)
https://doi.org/10.1109/CDC.2016.7798947
Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics
Peter BetschCISM International Centre for Mechanical Sciences, Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics 565 31 (2016)
https://doi.org/10.1007/978-3-319-31879-0_2
A natural autonomous force added in the restricted problem and explored via stability analysis and discrete variational mechanics
Natasha Bosanac, Kathleen C. Howell and Ephraim FischbachAstrophysics and Space Science 361 (2) (2016)
https://doi.org/10.1007/s10509-015-2638-3
7384 (2016)
https://doi.org/10.1109/CDC.2016.7799410
Optimal feedback control for constrained mechanical systems
Daniel Glaas and Sigrid LeyendeckerPAMM 16 (1) 55 (2016)
https://doi.org/10.1002/pamm.201610016
Geometry, Mechanics, and Dynamics
Juan C. Marrero, David Martín de Diego and Eduardo MartínezFields Institute Communications, Geometry, Mechanics, and Dynamics 73 285 (2015)
https://doi.org/10.1007/978-1-4939-2441-7_13
2594 (2015)
https://doi.org/10.1109/CDC.2015.7402607
Variational integrators for mechanical control systems with symmetries
Leonardo Colombo, Fernando Jiménez and David Martín de DiegoJournal of Computational Dynamics 2 (2) 193 (2015)
https://doi.org/10.3934/jcd.2015003
High order variational integrators in the optimal control of mechanical systems
Cédric M. Campos, Sina Ober-Blöbaum and Emmanuel TrélatDiscrete & Continuous Dynamical Systems - A 35 (9) 4193 (2015)
https://doi.org/10.3934/dcds.2015.35.4193
Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control
Elliot Johnson, Jarvis Schultz and Todd MurpheyIEEE Transactions on Automation Science and Engineering 12 (1) 140 (2015)
https://doi.org/10.1109/TASE.2014.2333239
Construction and analysis of higher order Galerkin variational integrators
Sina Ober-Blöbaum and Nils SaakeAdvances in Computational Mathematics 41 (6) 955 (2015)
https://doi.org/10.1007/s10444-014-9394-8
Symmetry exploiting control of hybrid mechanical systems
Kathrin Flasskamp, Sebastian Hage-Packhäuser and Sina Ober-BlöbaumJournal of Computational Dynamics 2 (1) 25 (2015)
https://doi.org/10.3934/jcd.2015.2.25
Discrete variational Lie group formulation of geometrically exact beam dynamics
F. Demoures, F. Gay-Balmaz, S. Leyendecker, et al.Numerische Mathematik 130 (1) 73 (2015)
https://doi.org/10.1007/s00211-014-0659-4
Time Discrete Geodesic Paths in the Space of Images
B. Berkels, A. Effland and M. RumpfSIAM Journal on Imaging Sciences 8 (3) 1457 (2015)
https://doi.org/10.1137/140970719
Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response
Francesco dell'Isola, David Steigmann and Alessandro Della CorteApplied Mechanics Reviews 67 (6) (2015)
https://doi.org/10.1115/1.4032206
5140 (2015)
https://doi.org/10.1109/ACC.2015.7172141
3232 (2015)
https://doi.org/10.1109/ECC.2015.7331032
2422 (2014)
https://doi.org/10.1109/ChiCC.2014.6897013
Discrete mechanics and mixed integer optimal control of dynamical systems
Maik Ringkamp, Sina Ober‐Blöbaum and Sigrid LeyendeckerPAMM 14 (1) 919 (2014)
https://doi.org/10.1002/pamm.201410440
An Improved DMOC Method with Gradient Penalty Term
Lei Gao and Jie Yu DingAdvanced Materials Research 945-949 2784 (2014)
https://doi.org/10.4028/www.scientific.net/AMR.945-949.2784
Higher Order Variational Integrators for Multibody System Dynamics with Constraints
Jieyu Ding and Zhenkuan PanAdvances in Mechanical Engineering 6 383680 (2014)
https://doi.org/10.1155/2014/383680
Multibody Dynamics
Thomas Leitz, Sina Ober-Blöbaum and Sigrid LeyendeckerComputational Methods in Applied Sciences, Multibody Dynamics 35 175 (2014)
https://doi.org/10.1007/978-3-319-07260-9_8
Advances in Differential Equations and Applications
Cédric M. CamposSEMA SIMAI Springer Series, Advances in Differential Equations and Applications 4 249 (2014)
https://doi.org/10.1007/978-3-319-06953-1_24
8984 (2014)
https://doi.org/10.1109/ChiCC.2014.6896513
Dependability of Self-Optimizing Mechatronic Systems
Rafal Dorociak and Juergen GausemeierLecture Notes in Mechanical Engineering, Dependability of Self-Optimizing Mechatronic Systems 37 (2014)
https://doi.org/10.1007/978-3-642-53742-4_3