-
Previous Article
An efficient algorithm for convex quadratic semi-definite optimization
- NACO Home
- This Issue
-
Next Article
Solvability of a class of thermal dynamical contact problems with subdifferential conditions
A bilevel optimization approach to obtain optimal cost functions for human arm movements
1. | Chair for Mathematical Optimization, Department of Mathematics, Technische Universität München (TUM), Boltzmannstr. 3, 85747 Garching b. München, Germany |
2. | Institute of Automatic Control Engineering, Technische Universität München (TUM), Arcisstr. 21, 80290 München, Germany |
3. | Chair for Mathematical Optimization, Department of Mathematics, Technische Universität München (TUM), Boltzmannstr. 3, 85747 Garching b. München, Germany |
References:
[1] |
P. Abbeel and A. Y. Ng, Apprenticeship learning via inverse reinforcement learning, in "Proc. Int. Conf. on Machine Learning," (2004), 1-8. |
[2] |
W. Abend, E. Bizzi and P. Morasso, Human arm trajectory formation, Brain, 105 (1982), 331-348.
doi: 10.1093/brain/105.2.331. |
[3] |
S. Albrecht, C. Weber, M. Sobotka, A. Peer, M. Buss and M. Ulbrich, Optimization criteria for human trajectory formation in dynamic virtual environments, in "Haptics: Generating and Perceiving Tangible Sensations," Lecture Notes in Computer Science, 6192 (2010), 257-262.
doi: 10.1007/978-3-642-14075-4_37. |
[4] |
C. G. Atkeson and J. M. Hollerbach, Kinematic features of unrestrained vertical arm movements, J. Neurosci., 5 (1985), 2318-2330. |
[5] |
J. F. Bard, An algorithm for solving the general bilevel programming problem, Math. Oper. Res., 8 (1983), 260-272.
doi: 10.1287/moor.8.2.260. |
[6] |
J. F. Bard, Convex two-level optimization, Math. Program., 40 (1988), 15-27.
doi: 10.1007/BF01580720. |
[7] |
J. F. Bard, "Practical Bilevel Optimization: Algorithms and Applications," Kluwer Academic Publishers, Dordrecht, 1998. |
[8] |
A. Billard and M. J. Mataric, Learning human arm movements by imitation: evaluation of a biologically inspired connectionist architecture, Robot. Auton. Syst., 37 (2001), 145-160.
doi: 10.1016/S0921-8890(01)00155-5. |
[9] |
J. Bracken and J.T. McGill, Mathematical programs with optimization problems in the constraints, Oper. Res., 21 (1973), 37-44.
doi: 10.1287/opre.21.1.37. |
[10] |
W. Candler and R. Norton, Multilevel Programming, World Bank Development Research Center, Departml Working Paper, 20 (1977). |
[11] |
R. F. Chandler, C. E. Claser, J. T. McConville, H. M. Reynolds and J. W. Young, Investigation of inertial properties of the human body, AMLR Technical Report, Wright-Patterson Air Force Base, OH, (1975). |
[12] |
B. Colson, P. Marcotte and G. Savard, An overview of bilevel optimization, Ann. Oper. Res., 153 (2007), 235-256.
doi: 10.1007/s10479-007-0176-2. |
[13] |
B. Corteville, E. Aertbelien, H. Bruyninckx, J. De Schutter and H. Van Brussel, Human-inspired robot assistant for fast point-to-point movements, in "Proc. IEEE ICRA," (2007), 3639-3644. |
[14] |
S. Dempe, A necessary and a sufficient optimality condition for bilevel programming problems, Optimization, 25 (1992), 341-354.
doi: 10.1080/02331939208843831. |
[15] |
S. Dempe, "Foundations of Bilevel Programming," Kluwer Academic Publishers, Dordrecht, 2002. |
[16] |
S. Dempe, Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints, Optimization, 52 (2003), 333-359.
doi: 10.1080/0233193031000149894. |
[17] |
P. Deuflhard and F. Bornemann, "Scientific Computing with Ordinary Differential Equations," Springer, Berlin, 2002. |
[18] |
M. Diehl, and D.B. Leineweber and A.A.S. Schäfer, "MUSCOD-II User's Manual," IWR-Preprint, University of Heidelberg, Germany, 2001. |
[19] |
T. A. Edmunds and J. F. Bard, Algorithms for nonlinear bilevel mathematical programs, IEEE Trans. Syst. Man Cyb., 21 (1991), 83-89.
doi: 10.1109/21.101139. |
[20] |
R. Featherstone, "Robot Dynamics Algorithms," Kluwer Academic Publishers, Dordrecht, 1987. |
[21] |
T. Flash and N. Hogan, The coordination of arm movements: an experimentally confirmed mathematical model, J. Neurosci., 5 (1985), 1688-1703. |
[22] |
M. Gleicher, Retargetting motion to new characters, in "Proc. Int. Conf. on Computer Graphics and Interactive Techniques," (1998), 33-42. |
[23] |
E. Hairer, S. P. N{\o}rsett and G. Wanner, "Solving Ordinary Differential Equations," Springer, New York, 1993. |
[24] |
C. M. Harris and D. M. Wolpert, Signal-dependend noise determines motor planning, Nature, 394 (1998), 780-784.
doi: 10.1038/29528. |
[25] |
H. Hatze, Neuromusculoskeletal control systems modeling - a critical survey of recent developments, IEEE Trans. Autom. Control, 25 (1980), 375-385.
doi: 10.1109/TAC.1980.1102380. |
[26] |
A. V. Hill, The heat of shortening and the dynamic constants of muscle, Proc. Roy. Soc. B, 126 (1938), 136-195.
doi: 10.1098/rspb.1938.0050. |
[27] |
K. W. Lilly, "Efficient Dynamic Simulation of Robotic Mechanisms," Kluwer Academic Publishers, Dordrecht, 1993. |
[28] |
C. K. Liu, A. Hertzmann and Z. Popovi\'c, Learning physics-based motion style with nonlinear inverse optimization, ACM Trans. Graph., 24 (2005), 1071-1081.
doi: 10.1145/1073204.1073314. |
[29] |
Y. Maeda, T. Hara and T. Arai, Human-robot cooperative manipulation with motion estimation, in "Proc. IEEE IROS", 4 (2001), 2240-2245. |
[30] |
P. Marcotte and G. Savard, Bilevel programming: a combinatorial perspective, in "Graph Theory and Combinatorial Optimization" (eds. D. Avis, A. Hertz, and O. Marcotte), Springer, New York (2005), 191-217.
doi: 10.1007/0-387-25592-3_7. |
[31] |
K. Mombaur, A. Truong and J. P. Laumond, From human to humanoid locomotion - an inverse optimal control approach, Auton. Robot., 28 (2010), 369-383.
doi: 10.1007/s10514-009-9170-7. |
[32] |
P. Morasso, Spatial control of arm movements, Exp. Brain Res., 42 (1981), 223-227.
doi: 10.1007/BF00236911. |
[33] |
P. Morasso, Three dimensional arm trajectories, Biol. Cybern., 48 (1983), 187-194.
doi: 10.1007/BF00318086. |
[34] |
E. Nakano, H. Imamizu, R. Osu, Y. Uno, H. Gomi, T. Yoshioka and M. Kawato, Quanitative examinations of internal representations for arm trajectory planning: Minimum commanded torque change model, J. Neurophysiol., 81 (1999), 2140-2155. |
[35] |
W. L. Nelson, Physical principles for economies of skilled movements, Biol. Cybern., 46 (1983), 135-147.
doi: 10.1007/BF00339982. |
[36] |
A. Y. Ng and S. Russell, Algorithms for inverse reinforcement learning, in "Proc. Int. Conf. on Machine Learning," (2000), 663-670. |
[37] |
J. Nocedal and S. J. Wright, "Numerical Optimization," Second Edition, Springer, New York, 2006. |
[38] |
J. V. Outrata, On the numerical solution of a class of Stackelberg problems, Z. Oper. Res., 34 (1990), 255-277. |
[39] |
J. V. Outrata, M. Kocvara and J. Zowe, "Nonsmooth Approach to Optimization Problems with Equilibrium Constraints," Kluwer Academic Publishers, Dordrecht, 1998. |
[40] |
M. J. D. Powell, The BOBYQA algorithm for bound constrained optimization without derivatives, Cambridge DAMTP Report NA2009/06, University of Cambridge, Cambridge, 2009. |
[41] |
D. Ramachandran and E. Amir, Bayesian inverse reinforcement learning, in "Proc. Int. Conf. on Artificial Intelligence," (2007), 2586-2591. |
[42] |
N. D. Ratliff, J. A. Bagnell and M. A. Zinkevich, Maximum margin planning, in "Proc. Int. Conf. on Machine Learning," (2006), 729-736. |
[43] |
S. Russell, Learning agents for uncertain environments (extended abstract), in "Proc. Int. Conf. on Computational Learning Theory," (1998), 101-103. |
[44] |
S. Schaal, Is imitation learning the route to humanoid robots?, Trends in Cognitive Sciences, 3 (1999), 233-242.
doi: 10.1016/S1364-6613(99)01327-3. |
[45] |
K. Shimizu and M. Lu, A global optimization method for the Stackelberg problem with convex functions via problem transformation and concave programming, IEEE Trans. Syst. Man Cyb., 25 (1995), 1635-1640.
doi: 10.1109/21.478449. |
[46] |
C. Smith and H. I. Christensen, A minimum jerk predictor for teleoperation with variable time delay, in "Proc. IEEE IROS," (2009), 5621-5627. |
[47] |
S. Stroeve, Impedance characteristics of neuromusculoskeletal model of the human arm, Biol. Cybern., 81 (1999), 475-494.
doi: 10.1007/s004220050577. |
[48] |
W. Suleiman, E. Yoshida, F. Kanehiro, J. P. Laumond and A. Monin, On human motion imitation by humanoid robot, in "Proc. IEEE ICRA," (2008), 2697-2704. |
[49] |
E. Todorov, Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system, Neural. Comput., 17 (2005), 1084-1108.
doi: 10.1162/0899766053491887. |
[50] |
E. Todorov, Optimality principles in sensorimotor control, Nature Neurosci., 7 (2004), 907-915.
doi: 10.1038/nn1309. |
[51] |
Y. Uno, M. Kawato and R. Suzuki, Formation and control of optimal trajectory in human multijoint arm movement, Biol. Cybern., 61 (1989), 89-101.
doi: 10.1007/BF00204593. |
[52] |
Y. Uno, R. Suzuki and M. Kawato, Minimum muscle-tension-change model which reproduces human arm movement, in "Proc. 4th Symp. Biol. Physiol. Eng.," (1989), 299-302. |
[53] |
L. N. Vicente and P. H. Calamai, Bilevel and multilevel programming: a bibliography review, J Global. Optim., 5 (1994), 291-306.
doi: 10.1007/BF01096458. |
[54] |
A. Wächter and L.T. Biegler, Line search filter methods for nonlinear programming: motivation and global convergence, SIAM J. Optim., 16 (2005), 1-31. |
[55] |
A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program., 106 (2006), 25-57. |
[56] |
D. A. Winter, "Biomechanics and Motor Control of Human Movement," Third Edition, Wiley, New York, 2005. |
[57] |
J. M. Winters and L. Stark, Analysis of fundamental human movement patterns through the use of in-depth antagonistic muscle models, IEEE Trans. Biomedical Eng., 10 (1985), 826-839.
doi: 10.1109/TBME.1985.325498. |
[58] |
J. J. Ye and D. L. Zhu, Optimality conditions for bilevel programming problems, Optimization, 33 (1995), 9-27.
doi: 10.1080/02331939508844060. |
[59] |
T. Yoshikawa, "Foundations of Robotics: Analysis and Control," MIT Press, Cambridge, 1990. |
show all references
References:
[1] |
P. Abbeel and A. Y. Ng, Apprenticeship learning via inverse reinforcement learning, in "Proc. Int. Conf. on Machine Learning," (2004), 1-8. |
[2] |
W. Abend, E. Bizzi and P. Morasso, Human arm trajectory formation, Brain, 105 (1982), 331-348.
doi: 10.1093/brain/105.2.331. |
[3] |
S. Albrecht, C. Weber, M. Sobotka, A. Peer, M. Buss and M. Ulbrich, Optimization criteria for human trajectory formation in dynamic virtual environments, in "Haptics: Generating and Perceiving Tangible Sensations," Lecture Notes in Computer Science, 6192 (2010), 257-262.
doi: 10.1007/978-3-642-14075-4_37. |
[4] |
C. G. Atkeson and J. M. Hollerbach, Kinematic features of unrestrained vertical arm movements, J. Neurosci., 5 (1985), 2318-2330. |
[5] |
J. F. Bard, An algorithm for solving the general bilevel programming problem, Math. Oper. Res., 8 (1983), 260-272.
doi: 10.1287/moor.8.2.260. |
[6] |
J. F. Bard, Convex two-level optimization, Math. Program., 40 (1988), 15-27.
doi: 10.1007/BF01580720. |
[7] |
J. F. Bard, "Practical Bilevel Optimization: Algorithms and Applications," Kluwer Academic Publishers, Dordrecht, 1998. |
[8] |
A. Billard and M. J. Mataric, Learning human arm movements by imitation: evaluation of a biologically inspired connectionist architecture, Robot. Auton. Syst., 37 (2001), 145-160.
doi: 10.1016/S0921-8890(01)00155-5. |
[9] |
J. Bracken and J.T. McGill, Mathematical programs with optimization problems in the constraints, Oper. Res., 21 (1973), 37-44.
doi: 10.1287/opre.21.1.37. |
[10] |
W. Candler and R. Norton, Multilevel Programming, World Bank Development Research Center, Departml Working Paper, 20 (1977). |
[11] |
R. F. Chandler, C. E. Claser, J. T. McConville, H. M. Reynolds and J. W. Young, Investigation of inertial properties of the human body, AMLR Technical Report, Wright-Patterson Air Force Base, OH, (1975). |
[12] |
B. Colson, P. Marcotte and G. Savard, An overview of bilevel optimization, Ann. Oper. Res., 153 (2007), 235-256.
doi: 10.1007/s10479-007-0176-2. |
[13] |
B. Corteville, E. Aertbelien, H. Bruyninckx, J. De Schutter and H. Van Brussel, Human-inspired robot assistant for fast point-to-point movements, in "Proc. IEEE ICRA," (2007), 3639-3644. |
[14] |
S. Dempe, A necessary and a sufficient optimality condition for bilevel programming problems, Optimization, 25 (1992), 341-354.
doi: 10.1080/02331939208843831. |
[15] |
S. Dempe, "Foundations of Bilevel Programming," Kluwer Academic Publishers, Dordrecht, 2002. |
[16] |
S. Dempe, Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints, Optimization, 52 (2003), 333-359.
doi: 10.1080/0233193031000149894. |
[17] |
P. Deuflhard and F. Bornemann, "Scientific Computing with Ordinary Differential Equations," Springer, Berlin, 2002. |
[18] |
M. Diehl, and D.B. Leineweber and A.A.S. Schäfer, "MUSCOD-II User's Manual," IWR-Preprint, University of Heidelberg, Germany, 2001. |
[19] |
T. A. Edmunds and J. F. Bard, Algorithms for nonlinear bilevel mathematical programs, IEEE Trans. Syst. Man Cyb., 21 (1991), 83-89.
doi: 10.1109/21.101139. |
[20] |
R. Featherstone, "Robot Dynamics Algorithms," Kluwer Academic Publishers, Dordrecht, 1987. |
[21] |
T. Flash and N. Hogan, The coordination of arm movements: an experimentally confirmed mathematical model, J. Neurosci., 5 (1985), 1688-1703. |
[22] |
M. Gleicher, Retargetting motion to new characters, in "Proc. Int. Conf. on Computer Graphics and Interactive Techniques," (1998), 33-42. |
[23] |
E. Hairer, S. P. N{\o}rsett and G. Wanner, "Solving Ordinary Differential Equations," Springer, New York, 1993. |
[24] |
C. M. Harris and D. M. Wolpert, Signal-dependend noise determines motor planning, Nature, 394 (1998), 780-784.
doi: 10.1038/29528. |
[25] |
H. Hatze, Neuromusculoskeletal control systems modeling - a critical survey of recent developments, IEEE Trans. Autom. Control, 25 (1980), 375-385.
doi: 10.1109/TAC.1980.1102380. |
[26] |
A. V. Hill, The heat of shortening and the dynamic constants of muscle, Proc. Roy. Soc. B, 126 (1938), 136-195.
doi: 10.1098/rspb.1938.0050. |
[27] |
K. W. Lilly, "Efficient Dynamic Simulation of Robotic Mechanisms," Kluwer Academic Publishers, Dordrecht, 1993. |
[28] |
C. K. Liu, A. Hertzmann and Z. Popovi\'c, Learning physics-based motion style with nonlinear inverse optimization, ACM Trans. Graph., 24 (2005), 1071-1081.
doi: 10.1145/1073204.1073314. |
[29] |
Y. Maeda, T. Hara and T. Arai, Human-robot cooperative manipulation with motion estimation, in "Proc. IEEE IROS", 4 (2001), 2240-2245. |
[30] |
P. Marcotte and G. Savard, Bilevel programming: a combinatorial perspective, in "Graph Theory and Combinatorial Optimization" (eds. D. Avis, A. Hertz, and O. Marcotte), Springer, New York (2005), 191-217.
doi: 10.1007/0-387-25592-3_7. |
[31] |
K. Mombaur, A. Truong and J. P. Laumond, From human to humanoid locomotion - an inverse optimal control approach, Auton. Robot., 28 (2010), 369-383.
doi: 10.1007/s10514-009-9170-7. |
[32] |
P. Morasso, Spatial control of arm movements, Exp. Brain Res., 42 (1981), 223-227.
doi: 10.1007/BF00236911. |
[33] |
P. Morasso, Three dimensional arm trajectories, Biol. Cybern., 48 (1983), 187-194.
doi: 10.1007/BF00318086. |
[34] |
E. Nakano, H. Imamizu, R. Osu, Y. Uno, H. Gomi, T. Yoshioka and M. Kawato, Quanitative examinations of internal representations for arm trajectory planning: Minimum commanded torque change model, J. Neurophysiol., 81 (1999), 2140-2155. |
[35] |
W. L. Nelson, Physical principles for economies of skilled movements, Biol. Cybern., 46 (1983), 135-147.
doi: 10.1007/BF00339982. |
[36] |
A. Y. Ng and S. Russell, Algorithms for inverse reinforcement learning, in "Proc. Int. Conf. on Machine Learning," (2000), 663-670. |
[37] |
J. Nocedal and S. J. Wright, "Numerical Optimization," Second Edition, Springer, New York, 2006. |
[38] |
J. V. Outrata, On the numerical solution of a class of Stackelberg problems, Z. Oper. Res., 34 (1990), 255-277. |
[39] |
J. V. Outrata, M. Kocvara and J. Zowe, "Nonsmooth Approach to Optimization Problems with Equilibrium Constraints," Kluwer Academic Publishers, Dordrecht, 1998. |
[40] |
M. J. D. Powell, The BOBYQA algorithm for bound constrained optimization without derivatives, Cambridge DAMTP Report NA2009/06, University of Cambridge, Cambridge, 2009. |
[41] |
D. Ramachandran and E. Amir, Bayesian inverse reinforcement learning, in "Proc. Int. Conf. on Artificial Intelligence," (2007), 2586-2591. |
[42] |
N. D. Ratliff, J. A. Bagnell and M. A. Zinkevich, Maximum margin planning, in "Proc. Int. Conf. on Machine Learning," (2006), 729-736. |
[43] |
S. Russell, Learning agents for uncertain environments (extended abstract), in "Proc. Int. Conf. on Computational Learning Theory," (1998), 101-103. |
[44] |
S. Schaal, Is imitation learning the route to humanoid robots?, Trends in Cognitive Sciences, 3 (1999), 233-242.
doi: 10.1016/S1364-6613(99)01327-3. |
[45] |
K. Shimizu and M. Lu, A global optimization method for the Stackelberg problem with convex functions via problem transformation and concave programming, IEEE Trans. Syst. Man Cyb., 25 (1995), 1635-1640.
doi: 10.1109/21.478449. |
[46] |
C. Smith and H. I. Christensen, A minimum jerk predictor for teleoperation with variable time delay, in "Proc. IEEE IROS," (2009), 5621-5627. |
[47] |
S. Stroeve, Impedance characteristics of neuromusculoskeletal model of the human arm, Biol. Cybern., 81 (1999), 475-494.
doi: 10.1007/s004220050577. |
[48] |
W. Suleiman, E. Yoshida, F. Kanehiro, J. P. Laumond and A. Monin, On human motion imitation by humanoid robot, in "Proc. IEEE ICRA," (2008), 2697-2704. |
[49] |
E. Todorov, Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system, Neural. Comput., 17 (2005), 1084-1108.
doi: 10.1162/0899766053491887. |
[50] |
E. Todorov, Optimality principles in sensorimotor control, Nature Neurosci., 7 (2004), 907-915.
doi: 10.1038/nn1309. |
[51] |
Y. Uno, M. Kawato and R. Suzuki, Formation and control of optimal trajectory in human multijoint arm movement, Biol. Cybern., 61 (1989), 89-101.
doi: 10.1007/BF00204593. |
[52] |
Y. Uno, R. Suzuki and M. Kawato, Minimum muscle-tension-change model which reproduces human arm movement, in "Proc. 4th Symp. Biol. Physiol. Eng.," (1989), 299-302. |
[53] |
L. N. Vicente and P. H. Calamai, Bilevel and multilevel programming: a bibliography review, J Global. Optim., 5 (1994), 291-306.
doi: 10.1007/BF01096458. |
[54] |
A. Wächter and L.T. Biegler, Line search filter methods for nonlinear programming: motivation and global convergence, SIAM J. Optim., 16 (2005), 1-31. |
[55] |
A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program., 106 (2006), 25-57. |
[56] |
D. A. Winter, "Biomechanics and Motor Control of Human Movement," Third Edition, Wiley, New York, 2005. |
[57] |
J. M. Winters and L. Stark, Analysis of fundamental human movement patterns through the use of in-depth antagonistic muscle models, IEEE Trans. Biomedical Eng., 10 (1985), 826-839.
doi: 10.1109/TBME.1985.325498. |
[58] |
J. J. Ye and D. L. Zhu, Optimality conditions for bilevel programming problems, Optimization, 33 (1995), 9-27.
doi: 10.1080/02331939508844060. |
[59] |
T. Yoshikawa, "Foundations of Robotics: Analysis and Control," MIT Press, Cambridge, 1990. |
[1] |
Marcus Wagner. A direct method for the solution of an optimal control problem arising from image registration. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 487-510. doi: 10.3934/naco.2012.2.487 |
[2] |
Mohamed Aliane, Mohand Bentobache, Nacima Moussouni, Philippe Marthon. Direct method to solve linear-quadratic optimal control problems. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 645-663. doi: 10.3934/naco.2021002 |
[3] |
Mohammad Hadi Noori Skandari, Marzieh Habibli, Alireza Nazemi. A direct method based on the Clenshaw-Curtis formula for fractional optimal control problems. Mathematical Control and Related Fields, 2020, 10 (1) : 171-187. doi: 10.3934/mcrf.2019035 |
[4] |
Dan Li, Li-Ping Pang, Fang-Fang Guo, Zun-Quan Xia. An alternating linearization method with inexact data for bilevel nonsmooth convex optimization. Journal of Industrial and Management Optimization, 2014, 10 (3) : 859-869. doi: 10.3934/jimo.2014.10.859 |
[5] |
Zahra Al Helal, Volker Rehbock, Ryan Loxton. Modelling and optimal control of blood glucose levels in the human body. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1149-1164. doi: 10.3934/jimo.2015.11.1149 |
[6] |
Jianxiong Ye, An Li. Necessary optimality conditions for nonautonomous optimal control problems and its applications to bilevel optimal control. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1399-1419. doi: 10.3934/jimo.2018101 |
[7] |
Max Gunzburger, Sung-Dae Yang, Wenxiang Zhu. Analysis and discretization of an optimal control problem for the forced Fisher equation. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 569-587. doi: 10.3934/dcdsb.2007.8.569 |
[8] |
Martin Bauer, Markus Eslitzbichler, Markus Grasmair. Landmark-guided elastic shape analysis of human character motions. Inverse Problems and Imaging, 2017, 11 (4) : 601-621. doi: 10.3934/ipi.2017028 |
[9] |
Jean-Pierre de la Croix, Magnus Egerstedt. Analyzing human-swarm interactions using control Lyapunov functions and optimal control. Networks and Heterogeneous Media, 2015, 10 (3) : 609-630. doi: 10.3934/nhm.2015.10.609 |
[10] |
Matthias Gerdts, Martin Kunkel. Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation. Journal of Industrial and Management Optimization, 2014, 10 (1) : 311-336. doi: 10.3934/jimo.2014.10.311 |
[11] |
Qun Lin, Ryan Loxton, Kok Lay Teo. The control parameterization method for nonlinear optimal control: A survey. Journal of Industrial and Management Optimization, 2014, 10 (1) : 275-309. doi: 10.3934/jimo.2014.10.275 |
[12] |
Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control and Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019 |
[13] |
Enkhbat Rentsen, J. Zhou, K. L. Teo. A global optimization approach to fractional optimal control. Journal of Industrial and Management Optimization, 2016, 12 (1) : 73-82. doi: 10.3934/jimo.2016.12.73 |
[14] |
Yibing Lv, Zhongping Wan. Linear bilevel multiobjective optimization problem: Penalty approach. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1213-1223. doi: 10.3934/jimo.2018092 |
[15] |
Evelyn Herberg, Michael Hinze. Variational discretization of one-dimensional elliptic optimal control problems with BV functions based on the mixed formulation. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022013 |
[16] |
N. U. Ahmed. Existence of optimal output feedback control law for a class of uncertain infinite dimensional stochastic systems: A direct approach. Evolution Equations and Control Theory, 2012, 1 (2) : 235-250. doi: 10.3934/eect.2012.1.235 |
[17] |
Canghua Jiang, Cheng Jin, Ming Yu, Zongqi Xu. Direct optimal control for time-delay systems via a lifted multiple shooting algorithm. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021135 |
[18] |
Karl Kunisch, Markus Müller. Uniform convergence of the POD method and applications to optimal control. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4477-4501. doi: 10.3934/dcds.2015.35.4477 |
[19] |
Kaifang Liu, Lunji Song, Shan Zhao. A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2411-2428. doi: 10.3934/dcdsb.2020184 |
[20] |
Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2581-2598. doi: 10.3934/dcdsb.2020196 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]