-
Previous Article
Information diffusion in social sensing
- NACO Home
- This Issue
-
Next Article
Partial fraction expansion based frequency weighted model reduction for discrete-time systems
A new computational strategy for optimal control problem with a cost on changing control
1. | Department of Mathematics and Statistics, Curtin University, Perth, Australia, Australia |
2. | Department of Mathematics , Shanghai University, Shanghai, China |
References:
[1] |
B. Açikmeşe and L. Blackmore, Lossless convexification of a class of nonconvex optimal control problems for linear systems, In Proceedings of the 2010 American control conference, Baltimore, USA, 2010. |
[2] |
B. Açikmeşe and L. Blackmore, Lossless convexification of a class of optimal control problems with non-convex control constraints, Automatica, 47 (2011), 341-347.
doi: 10.1016/j.automatica.2010.10.037. |
[3] |
N. U. Ahmed, Elements of Finite-Dimensional Systems and Control Theory, Essex: Longman Scientific and Technical, 1988. |
[4] |
N. U. Ahmed, Dynamic Systems and Control with Applications, Singapore: World Scientific, 2006.
doi: 10.1142/6262. |
[5] |
J. M. Blatt, Optimal control with a cost of switching control, Journal of the Australian Mathematical Society-Series B: Applied Mathematics, 19 (1976), 316-332. |
[6] |
N. Banihashemi and C. Y. Kaya, Inexact restoration and adaptive mesh refinement for optimal control, Journal of Industrial and Management Optimization, 10 (2014), 521-542.
doi: 10.3934/jimo.2014.10.521. |
[7] |
C. Büskens and H. Maurer, SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis, and real-time control, Journal of Computational and Applied Mathematics, 120 (2000), 85-108.
doi: 10.1016/S0377-0427(00)00305-8. |
[8] |
W. N. Chen, J. Zhang, H. S. H. Chung, W. L. Zhong, W. G. Wu and Y. H. Shi, A novel set-based particle swarm optimization method for discrete optimization problems, IEEE Transactions on Evolutionary Computation, 14 (2010), 278-300. |
[9] |
M. Gerdts, Global convergence of a non-smooth Newton method for control-state constrained optimal control problems, SIAM Journal on Optimization, 19 (2008), 326-350.
doi: 10.1137/060657546. |
[10] |
M. Gerdts and M. Kunkel, A non-smooth Newton's method for discretized optimal control problems with state and control constraints, Journal of Industrial and Management Optimization, 4 (2008), 247-270.
doi: 10.3934/jimo.2008.4.247. |
[11] |
R. F. Hartl, S. P. Sethi and R. G. Vickson, A survey of the maximum principles for optimal control problems with state constraints, SIAM Review, 37 (1995), 181-218.
doi: 10.1137/1037043. |
[12] |
L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, MISER 3 Optimal Control Software: Theory and User Manual, version 3. University of Western Australia, 2004. |
[13] |
L. S. Jennings and K. L. Teo, A numerical algorithm for constrained optimal control problems with applications to harvesting, in "Dynamics of Complex Interconnected Biological Systems", Birkhauser Boston, Boston, (1990), 218-234.
doi: 10.1007/978-1-4684-6784-0_12. |
[14] |
C. H. Jiang, Q. Lin, C. J. Yu, K. L. Teo and G. R. Duan, An exact penalty method for free terminal time optimal control problem with continuous inequality constraints, Journal of Optimization Theory and Applications, 154 (2012), 30-53.
doi: 10.1007/s10957-012-0006-9. |
[15] |
C. Y. Kaya and J. L. Noakes, Computational method for time-optimal switching control, Journal of Optimization Theory and Applications, 117 (2003), 69-92.
doi: 10.1023/A:1023600422807. |
[16] |
H. W. J. Lee, K. L. Teo, V. Rehbock and L. S. Jennings, Control parametrization enhancing technique for time optimal control problems, Dynamic Systems and Applications, 6 (1997), 243-262. |
[17] |
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for a class of free terminal time optimal control problems, Pacific Journal of Optimization, 7 (2011), 63-81. |
[18] |
B. Li, C. Xu, K. L. Teo and J. Chu, Time optimal Zermelo's navigation problem with moving and fixed obstacles, Applied Mathematics and Computation, 224 (2013), 866-875.
doi: 10.1016/j.amc.2013.08.092. |
[19] |
Q. Lin, R. Loxton and K. L. Teo, The control parameterization method for nonlinear optimal control: a survey, Journal of Industrial and Management Optimization, 10 (2014), 275-309.
doi: 10.3934/jimo.2014.10.275. |
[20] |
R. Loxton, Q. Lin, V. Rehbock and K. L. Teo, Control parameterization for optimal control problems with continuous inequality constraints: new convergence results. Numerical Algebra, Control and Optimization, 2 (2012), 571-599.
doi: 10.3934/naco.2012.2.571. |
[21] |
R. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints, Automatica, 44 (2008), 2923-2929.
doi: 10.1016/j.automatica.2008.04.011. |
[22] |
R. Loxton, K. L. Teo, V. Rehbock and K. F. C. Yiu, Optimal control problems with a continuous inequality constraint on the state and the control, Automatica, 45 (2009), 2250-2257.
doi: 10.1016/j.automatica.2009.05.029. |
[23] |
D. G. Luenberger and Y. Y. Ye, Linear and Nonlinear Programming, (3rd ed.). New York: Springer, 2008. |
[24] |
J. Matula, On an extremum problem, Journal of the Australian Mathematical Society-Series B: Applied Mathematics, 28 (1987), 376-392.
doi: 10.1017/S0334270000005464. |
[25] |
J. Nocedal and S. J. Wright, Numerical Optimization, (2nd ed.). New York: Springer, 2006. |
[26] |
H. L. Royden and P. M. Fitzpatrick, Real analysis, (4th ed.). Boston: Prentice Hall, 2010. |
[27] |
Y. Sakawa and Y. Shindo, Optimal control of container cranes, Automatica, 18 (1982), 257-266. |
[28] |
K. Schittkowski, NLPQLP: a fortran implementation of a sequential quadratic programming algorithm with distributed and non-monotone line search, version 2.24. University of Bayreuth, 2007. |
[29] |
D. E. Stewart, A numerical algorithm for optimal control problems with switching costs, Journal of the Australian Mathematical Society-Series B: Applied Mathematics, 34 (1992), 212-228.
doi: 10.1017/S0334270000008730. |
[30] |
K. L. Teo and C. J. Goh, On constrained optimization problems with non-smooth cost functions, Applied Mathematics and Optimization, 17 (1988), 181-190.
doi: 10.1007/BF01443621. |
[31] |
K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, Essex: Longman Scientific and Technical, 1991. |
[32] |
K. L. Teo and L. S. Jennings, Optimal control with a cost on changing control, Journal of Optimization Theory and Applications, 68 (1991), 335-357.
doi: 10.1007/BF00941572. |
[33] |
R. J. Vanderbei, Case studies in trajectory optimization: trains, planes, and other pastimes, Optimization and Engineering, 2 (2001), 215-243.
doi: 10.1023/A:1013145328012. |
[34] |
T. L. Vincent and W. J. Grantham, Optimality in Parametric Systems, New York: John Wiley, 1981. |
[35] |
L. Y. Wang, W. H. Gui, K. L. Teo, R. Loxton and C. H. Yang, Time delayed optimal control problems with multiple characteristic time points: computation and industrial applications, Journal of Industrial and Management Optimization, 5 (2009), 705-718.
doi: 10.3934/jimo.2009.5.705. |
[36] |
Z. Y. Wu, F. S. Bai, H. W. J. Lee and Y. J. Yang, A filled function method for constrained global optimization, Journal of Global Optimization, 39 (2007), 495-507.
doi: 10.1007/s10898-007-9152-2. |
[37] |
X. Xu and P. J. Antsaklis, Optimal control of switched systems based on parameterization of the switching instants, IEEE Transactions on Automatic Control, 49 (2004), 2-16.
doi: 10.1109/TAC.2003.821417. |
[38] |
C. J. Yu, B. Li, R. Loxton and K. L. Teo, Optimal discrete-valued control computation, Journal of Global Optimization, 56 (2013), 503-518.
doi: 10.1007/s10898-012-9858-7. |
[39] |
C. J. Yu, K. L. Teo , L. S. Zhang and Y. Q. Bai, A new exact penalty function method for continuous inequality constrained optimization problems, Journal of Industrial and Management Optimization, 6 (2010), 895-910,
doi: 10.3934/jimo.2010.6.895. |
[40] |
C. J. Yu, K. L. Teo and T. T. Tiow, Optimal control with a cost of changing control, Australian Control Conference (AUCC), (2013), 20-25. |
[41] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem, Journal of Industrial Management and Optimization, 8 (2012), 485-491.
doi: 10.3934/jimo.2012.8.485. |
[42] |
F. Yang, K. L. Teo, R. Loxton, V. Rehbock, B. Li , C. J. Yu and L. Jennings, Visual MISER: An efficient user-friendly visual program for solving optimal control problems, Journal of Industrial and Management Optimization, doi:10.3934/jimo.2016.12.781, 2016
doi: 10.3934/jimo.2016.12.781. |
[43] |
Y. Zhao and M. A. Stadtherr, Rigorous global optimization for dynamic systems subject to inequality path constraints, Industrial and Engineering Chemistry Research, 50 (2011), 12678-12693. |
show all references
References:
[1] |
B. Açikmeşe and L. Blackmore, Lossless convexification of a class of nonconvex optimal control problems for linear systems, In Proceedings of the 2010 American control conference, Baltimore, USA, 2010. |
[2] |
B. Açikmeşe and L. Blackmore, Lossless convexification of a class of optimal control problems with non-convex control constraints, Automatica, 47 (2011), 341-347.
doi: 10.1016/j.automatica.2010.10.037. |
[3] |
N. U. Ahmed, Elements of Finite-Dimensional Systems and Control Theory, Essex: Longman Scientific and Technical, 1988. |
[4] |
N. U. Ahmed, Dynamic Systems and Control with Applications, Singapore: World Scientific, 2006.
doi: 10.1142/6262. |
[5] |
J. M. Blatt, Optimal control with a cost of switching control, Journal of the Australian Mathematical Society-Series B: Applied Mathematics, 19 (1976), 316-332. |
[6] |
N. Banihashemi and C. Y. Kaya, Inexact restoration and adaptive mesh refinement for optimal control, Journal of Industrial and Management Optimization, 10 (2014), 521-542.
doi: 10.3934/jimo.2014.10.521. |
[7] |
C. Büskens and H. Maurer, SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis, and real-time control, Journal of Computational and Applied Mathematics, 120 (2000), 85-108.
doi: 10.1016/S0377-0427(00)00305-8. |
[8] |
W. N. Chen, J. Zhang, H. S. H. Chung, W. L. Zhong, W. G. Wu and Y. H. Shi, A novel set-based particle swarm optimization method for discrete optimization problems, IEEE Transactions on Evolutionary Computation, 14 (2010), 278-300. |
[9] |
M. Gerdts, Global convergence of a non-smooth Newton method for control-state constrained optimal control problems, SIAM Journal on Optimization, 19 (2008), 326-350.
doi: 10.1137/060657546. |
[10] |
M. Gerdts and M. Kunkel, A non-smooth Newton's method for discretized optimal control problems with state and control constraints, Journal of Industrial and Management Optimization, 4 (2008), 247-270.
doi: 10.3934/jimo.2008.4.247. |
[11] |
R. F. Hartl, S. P. Sethi and R. G. Vickson, A survey of the maximum principles for optimal control problems with state constraints, SIAM Review, 37 (1995), 181-218.
doi: 10.1137/1037043. |
[12] |
L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, MISER 3 Optimal Control Software: Theory and User Manual, version 3. University of Western Australia, 2004. |
[13] |
L. S. Jennings and K. L. Teo, A numerical algorithm for constrained optimal control problems with applications to harvesting, in "Dynamics of Complex Interconnected Biological Systems", Birkhauser Boston, Boston, (1990), 218-234.
doi: 10.1007/978-1-4684-6784-0_12. |
[14] |
C. H. Jiang, Q. Lin, C. J. Yu, K. L. Teo and G. R. Duan, An exact penalty method for free terminal time optimal control problem with continuous inequality constraints, Journal of Optimization Theory and Applications, 154 (2012), 30-53.
doi: 10.1007/s10957-012-0006-9. |
[15] |
C. Y. Kaya and J. L. Noakes, Computational method for time-optimal switching control, Journal of Optimization Theory and Applications, 117 (2003), 69-92.
doi: 10.1023/A:1023600422807. |
[16] |
H. W. J. Lee, K. L. Teo, V. Rehbock and L. S. Jennings, Control parametrization enhancing technique for time optimal control problems, Dynamic Systems and Applications, 6 (1997), 243-262. |
[17] |
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for a class of free terminal time optimal control problems, Pacific Journal of Optimization, 7 (2011), 63-81. |
[18] |
B. Li, C. Xu, K. L. Teo and J. Chu, Time optimal Zermelo's navigation problem with moving and fixed obstacles, Applied Mathematics and Computation, 224 (2013), 866-875.
doi: 10.1016/j.amc.2013.08.092. |
[19] |
Q. Lin, R. Loxton and K. L. Teo, The control parameterization method for nonlinear optimal control: a survey, Journal of Industrial and Management Optimization, 10 (2014), 275-309.
doi: 10.3934/jimo.2014.10.275. |
[20] |
R. Loxton, Q. Lin, V. Rehbock and K. L. Teo, Control parameterization for optimal control problems with continuous inequality constraints: new convergence results. Numerical Algebra, Control and Optimization, 2 (2012), 571-599.
doi: 10.3934/naco.2012.2.571. |
[21] |
R. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints, Automatica, 44 (2008), 2923-2929.
doi: 10.1016/j.automatica.2008.04.011. |
[22] |
R. Loxton, K. L. Teo, V. Rehbock and K. F. C. Yiu, Optimal control problems with a continuous inequality constraint on the state and the control, Automatica, 45 (2009), 2250-2257.
doi: 10.1016/j.automatica.2009.05.029. |
[23] |
D. G. Luenberger and Y. Y. Ye, Linear and Nonlinear Programming, (3rd ed.). New York: Springer, 2008. |
[24] |
J. Matula, On an extremum problem, Journal of the Australian Mathematical Society-Series B: Applied Mathematics, 28 (1987), 376-392.
doi: 10.1017/S0334270000005464. |
[25] |
J. Nocedal and S. J. Wright, Numerical Optimization, (2nd ed.). New York: Springer, 2006. |
[26] |
H. L. Royden and P. M. Fitzpatrick, Real analysis, (4th ed.). Boston: Prentice Hall, 2010. |
[27] |
Y. Sakawa and Y. Shindo, Optimal control of container cranes, Automatica, 18 (1982), 257-266. |
[28] |
K. Schittkowski, NLPQLP: a fortran implementation of a sequential quadratic programming algorithm with distributed and non-monotone line search, version 2.24. University of Bayreuth, 2007. |
[29] |
D. E. Stewart, A numerical algorithm for optimal control problems with switching costs, Journal of the Australian Mathematical Society-Series B: Applied Mathematics, 34 (1992), 212-228.
doi: 10.1017/S0334270000008730. |
[30] |
K. L. Teo and C. J. Goh, On constrained optimization problems with non-smooth cost functions, Applied Mathematics and Optimization, 17 (1988), 181-190.
doi: 10.1007/BF01443621. |
[31] |
K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, Essex: Longman Scientific and Technical, 1991. |
[32] |
K. L. Teo and L. S. Jennings, Optimal control with a cost on changing control, Journal of Optimization Theory and Applications, 68 (1991), 335-357.
doi: 10.1007/BF00941572. |
[33] |
R. J. Vanderbei, Case studies in trajectory optimization: trains, planes, and other pastimes, Optimization and Engineering, 2 (2001), 215-243.
doi: 10.1023/A:1013145328012. |
[34] |
T. L. Vincent and W. J. Grantham, Optimality in Parametric Systems, New York: John Wiley, 1981. |
[35] |
L. Y. Wang, W. H. Gui, K. L. Teo, R. Loxton and C. H. Yang, Time delayed optimal control problems with multiple characteristic time points: computation and industrial applications, Journal of Industrial and Management Optimization, 5 (2009), 705-718.
doi: 10.3934/jimo.2009.5.705. |
[36] |
Z. Y. Wu, F. S. Bai, H. W. J. Lee and Y. J. Yang, A filled function method for constrained global optimization, Journal of Global Optimization, 39 (2007), 495-507.
doi: 10.1007/s10898-007-9152-2. |
[37] |
X. Xu and P. J. Antsaklis, Optimal control of switched systems based on parameterization of the switching instants, IEEE Transactions on Automatic Control, 49 (2004), 2-16.
doi: 10.1109/TAC.2003.821417. |
[38] |
C. J. Yu, B. Li, R. Loxton and K. L. Teo, Optimal discrete-valued control computation, Journal of Global Optimization, 56 (2013), 503-518.
doi: 10.1007/s10898-012-9858-7. |
[39] |
C. J. Yu, K. L. Teo , L. S. Zhang and Y. Q. Bai, A new exact penalty function method for continuous inequality constrained optimization problems, Journal of Industrial and Management Optimization, 6 (2010), 895-910,
doi: 10.3934/jimo.2010.6.895. |
[40] |
C. J. Yu, K. L. Teo and T. T. Tiow, Optimal control with a cost of changing control, Australian Control Conference (AUCC), (2013), 20-25. |
[41] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem, Journal of Industrial Management and Optimization, 8 (2012), 485-491.
doi: 10.3934/jimo.2012.8.485. |
[42] |
F. Yang, K. L. Teo, R. Loxton, V. Rehbock, B. Li , C. J. Yu and L. Jennings, Visual MISER: An efficient user-friendly visual program for solving optimal control problems, Journal of Industrial and Management Optimization, doi:10.3934/jimo.2016.12.781, 2016
doi: 10.3934/jimo.2016.12.781. |
[43] |
Y. Zhao and M. A. Stadtherr, Rigorous global optimization for dynamic systems subject to inequality path constraints, Industrial and Engineering Chemistry Research, 50 (2011), 12678-12693. |
[1] |
Di Wu, Yanqin Bai, Fusheng Xie. Time-scaling transformation for optimal control problem with time-varying delay. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1683-1695. doi: 10.3934/dcdss.2020098 |
[2] |
Takeshi Ohtsuka, Ken Shirakawa, Noriaki Yamazaki. Optimal control problem for Allen-Cahn type equation associated with total variation energy. Discrete and Continuous Dynamical Systems - S, 2012, 5 (1) : 159-181. doi: 10.3934/dcdss.2012.5.159 |
[3] |
Ying Zhang, Changjun Yu, Yingtao Xu, Yanqin Bai. Minimizing almost smooth control variation in nonlinear optimal control problems. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1663-1683. doi: 10.3934/jimo.2019023 |
[4] |
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 |
[5] |
M. Alipour, M. A. Vali, A. H. Borzabadi. A hybrid parametrization approach for a class of nonlinear optimal control problems. Numerical Algebra, Control and Optimization, 2019, 9 (4) : 493-506. doi: 10.3934/naco.2019037 |
[6] |
Hang-Chin Lai, Jin-Chirng Lee, Shuh-Jye Chern. A variational problem and optimal control. Journal of Industrial and Management Optimization, 2011, 7 (4) : 967-975. doi: 10.3934/jimo.2011.7.967 |
[7] |
Changjun Yu, Shuxuan Su, Yanqin Bai. On the optimal control problems with characteristic time control constraints. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1305-1320. doi: 10.3934/jimo.2021021 |
[8] |
Sören Bartels, Marijo Milicevic. Iterative finite element solution of a constrained total variation regularized model problem. Discrete and Continuous Dynamical Systems - S, 2017, 10 (6) : 1207-1232. doi: 10.3934/dcdss.2017066 |
[9] |
Florian Krügel. Some properties of minimizers of a variational problem involving the total variation functional. Communications on Pure and Applied Analysis, 2015, 14 (1) : 341-360. doi: 10.3934/cpaa.2015.14.341 |
[10] |
Konstantinos Papafitsoros, Kristian Bredies. A study of the one dimensional total generalised variation regularisation problem. Inverse Problems and Imaging, 2015, 9 (2) : 511-550. doi: 10.3934/ipi.2015.9.511 |
[11] |
Bin Li, Xiaolong Guo, Xiaodong Zeng, Songyi Dian, Minhua Guo. An optimal pid tuning method for a single-link manipulator based on the control parametrization technique. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1813-1823. doi: 10.3934/dcdss.2020107 |
[12] |
Giulia Cavagnari. Regularity results for a time-optimal control problem in the space of probability measures. Mathematical Control and Related Fields, 2017, 7 (2) : 213-233. doi: 10.3934/mcrf.2017007 |
[13] |
Qing Tang. On an optimal control problem of time-fractional advection-diffusion equation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : 761-779. doi: 10.3934/dcdsb.2019266 |
[14] |
Jingtao Shi, Juanjuan Xu, Huanshui Zhang. Stochastic recursive optimal control problem with time delay and applications. Mathematical Control and Related Fields, 2015, 5 (4) : 859-888. doi: 10.3934/mcrf.2015.5.859 |
[15] |
Jiongmin Yong. A deterministic linear quadratic time-inconsistent optimal control problem. Mathematical Control and Related Fields, 2011, 1 (1) : 83-118. doi: 10.3934/mcrf.2011.1.83 |
[16] |
Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. An optimal control problem in HIV treatment. Conference Publications, 2013, 2013 (special) : 311-322. doi: 10.3934/proc.2013.2013.311 |
[17] |
Andrea Bacchiocchi, Germana Giombini. An optimal control problem of monetary policy. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5769-5786. doi: 10.3934/dcdsb.2021224 |
[18] |
Xiaoqun Zhang, Tony F. Chan. Wavelet inpainting by nonlocal total variation. Inverse Problems and Imaging, 2010, 4 (1) : 191-210. doi: 10.3934/ipi.2010.4.191 |
[19] |
Zhen-Zhen Tao, Bing Sun. Space-time spectral methods for a fourth-order parabolic optimal control problem in three control constraint cases. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022080 |
[20] |
Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. Parametrization of the attainable set for a nonlinear control model of a biochemical process. Mathematical Biosciences & Engineering, 2013, 10 (4) : 1067-1094. doi: 10.3934/mbe.2013.10.1067 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]