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The control parameterization method for nonlinear optimal control: A survey
1. | Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845 |
2. | Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U 1987, Perth, W.A. 6845 |
References:
[1] |
B. Açikmeşe and L. Blackmore, Lossless convexification of a class of optimal control problems with non-convex control constraints, Automatica J. IFAC, 47 (2011), 341-347.
doi: 10.1016/j.automatica.2010.10.037. |
[2] |
N. U. Ahmed, "Elements of Finite-Dimensional Systems and Control Theory,'' Longman Scientific and Technical, Essex, 1988. |
[3] |
N. U. Ahmed, "Dynamic Systems and Control with Applications,'' World Scientific, Singapore, 2006. |
[4] |
Z. Benayache, G. Besançon and D. Georges, A new nonlinear control methodology for irrigation canals based on a delayed input model, in "Proceedings of the 17th World Congress of the International Federation of Automatic Control,'' 2008. |
[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] |
M. Boccadoro, Y. Wardi, M. Egerstedt and E. Verriest, Optimal control of switching surfaces in hybrid dynamical systems, Discrete Event Dynamic Systems: Theory and Applications, 15 (2005), 433-448.
doi: 10.1007/s10626-005-4060-4. |
[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] |
L. Caccetta, I. Loosen and V. Rehbock, Computational aspects of the optimal transit path problem, Journal of Industrial and Management Optimization, 4 (2008), 95-105.
doi: 10.3934/jimo.2008.4.95. |
[9] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, A max-min control problem arising in gradient elution chromatography, Industrial and Engineering Chemistry Research, 51 (2012), 6137-6144.
doi: 10.1021/ie202475p. |
[10] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, A unified parameter identification method for nonlinear time-delay systems, Journal of Industrial and Management Optimization, 9 (2013), 471-486.
doi: 10.3934/jimo.2013.9.471. |
[11] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, A class of optimal state-delay control problems, Nonlinear Analysis: Real World Applications, 14 (2013), 1536-1550.
doi: 10.1016/j.nonrwa.2012.10.017. |
[12] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, Time-delay estimation for nonlinear systems with piecewise-constant input, Applied Mathematics and Computation, 219 (2013), 9543-9560.
doi: 10.1016/j.amc.2013.03.015. |
[13] |
Q. Q. Chai, C. H. Yang, K. L. Teo and W. H. Gui, Optimal control of an industrial-scale evaporation process: Sodium aluminate solution, Control Engineering Practice, 20 (2012), 618-628.
doi: 10.1016/j.conengprac.2012.03.001. |
[14] |
B. Christiansen, H. Maurer and O. Zirn, Optimal control of a voice-coil-motor with Coulombic friction, in "Proceedings of the 47th IEEE Conference on Decision and Control,'' 2008.
doi: 10.1109/CDC.2008.4739025. |
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M. Chyba, T. Haberkorn, R. N. Smith and S. K. Choi, Design and implementation of time efficient trajectories for autonomous underwater vehicles, Ocean Engineering, 35 (2008), 63-76.
doi: 10.1016/j.oceaneng.2007.07.007. |
[16] |
J. Y. Dieulot and J. P. Richard, Tracking control of a nonlinear system with input-dependent delay, in "Proceedings of the 40th IEEE Conference on Decision and Control,'' 2001. |
[17] |
B. Farhadinia, K. L. Teo and R. Loxton, A computational method for a class of non-standard time optimal control problems involving multiple time horizons, Mathematical and Computer Modelling, 49 (2009), 1682-1691.
doi: 10.1016/j.mcm.2008.08.019. |
[18] |
M. Gerdts and M. Kunkel, A nonsmooth 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. |
[19] |
C. J. Goh and K. L. Teo, Control parametrization: A unified approach to optimal control problems with general constraints, Automatica J. IFAC, 24 (1988), 3-18.
doi: 10.1016/0005-1098(88)90003-9. |
[20] |
P. G. Howlett, P. J. Pudney and X. Vu, Local energy minimization in optimal train control, Automatica J. IFAC, 45 (2009), 2692-2698.
doi: 10.1016/j.automatica.2009.07.028. |
[21] |
L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, "MISER3 Optimal Control Software: Theory and User Manual,'' University of Western Australia, Perth, 2004. |
[22] |
L. S. Jennings and K. L. Teo, A computational algorithm for functional inequality constrained optimization problems, Automatica J. IFAC, 26 (1990), 371-375.
doi: 10.1016/0005-1098(90)90131-Z. |
[23] |
C. Jiang, Q. Lin, C. 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. |
[24] |
C. Jiang, K. L. Teo, R. Loxton and G. R. Duan, A neighboring extremal solution for an optimal switched impulsive control problem, Journal of Industrial and Management Optimization, 8 (2012), 591-609.
doi: 10.3934/jimo.2012.8.591. |
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K. Kaji and K. H. Wong, Nonlinearly constrained time-delayed optimal control problems, Journal of Optimization Theory and Applications, 82 (1994), 295-313.
doi: 10.1007/BF02191855. |
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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. |
[27] |
H. W. J. Lee, K. L. Teo and X. Q. Cai, An optimal control approach to nonlinear mixed integer programming problems, Computers and Mathematics with Applications, 36 (1998), 87-105.
doi: 10.1016/S0898-1221(98)00131-X. |
[28] |
H. W. J. Lee, K. L. Teo and A. E. B. Lim, Sensor scheduling in continuous time, Automatica J. IFAC, 37 (2001), 2017-2023.
doi: 10.1016/S0005-1098(01)00159-5. |
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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), 243-261. |
[30] |
H. W. J. Lee, K. L. Teo, V. Rehbock and L. S. Jennings, Control parametrization enhancing technique for optimal discrete-valued control problems, Automatica J. IFAC, 35 (1999), 1401-1407.
doi: 10.1016/S0005-1098(99)00050-3. |
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H. W. J. Lee and K. L. Teo, Control parametrization enhancing technique for solving a special ODE class with state dependent switch, Journal of Optimization Theory and Applications, 118 (2003), 55-66.
doi: 10.1023/A:1024735407694. |
[32] |
H. W. J. Lee and K. H. Wong, Semi-infinite programming approach to nonlinear time-delayed optimal control problems with linear continuous constraints, Optimization Methods and Software, 21 (2006), 679-691.
doi: 10.1080/10556780500142306. |
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R. Li, K. L. Teo, K. H. Wong and G. R. Duan, Control parameterization enhancing transform for optimal control of switched systems, Mathematical and Computer Modelling, 43 (2006), 1393-1403.
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B. Li, C. J. Yu, K. L. Teo and G. R. Duan, An exact penalty function method for continuous inequality constrained optimal control problem, Journal of Optimization Theory and Applications, 151 (2011), 260-291.
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show all references
References:
[1] |
B. Açikmeşe and L. Blackmore, Lossless convexification of a class of optimal control problems with non-convex control constraints, Automatica J. IFAC, 47 (2011), 341-347.
doi: 10.1016/j.automatica.2010.10.037. |
[2] |
N. U. Ahmed, "Elements of Finite-Dimensional Systems and Control Theory,'' Longman Scientific and Technical, Essex, 1988. |
[3] |
N. U. Ahmed, "Dynamic Systems and Control with Applications,'' World Scientific, Singapore, 2006. |
[4] |
Z. Benayache, G. Besançon and D. Georges, A new nonlinear control methodology for irrigation canals based on a delayed input model, in "Proceedings of the 17th World Congress of the International Federation of Automatic Control,'' 2008. |
[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] |
M. Boccadoro, Y. Wardi, M. Egerstedt and E. Verriest, Optimal control of switching surfaces in hybrid dynamical systems, Discrete Event Dynamic Systems: Theory and Applications, 15 (2005), 433-448.
doi: 10.1007/s10626-005-4060-4. |
[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] |
L. Caccetta, I. Loosen and V. Rehbock, Computational aspects of the optimal transit path problem, Journal of Industrial and Management Optimization, 4 (2008), 95-105.
doi: 10.3934/jimo.2008.4.95. |
[9] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, A max-min control problem arising in gradient elution chromatography, Industrial and Engineering Chemistry Research, 51 (2012), 6137-6144.
doi: 10.1021/ie202475p. |
[10] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, A unified parameter identification method for nonlinear time-delay systems, Journal of Industrial and Management Optimization, 9 (2013), 471-486.
doi: 10.3934/jimo.2013.9.471. |
[11] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, A class of optimal state-delay control problems, Nonlinear Analysis: Real World Applications, 14 (2013), 1536-1550.
doi: 10.1016/j.nonrwa.2012.10.017. |
[12] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, Time-delay estimation for nonlinear systems with piecewise-constant input, Applied Mathematics and Computation, 219 (2013), 9543-9560.
doi: 10.1016/j.amc.2013.03.015. |
[13] |
Q. Q. Chai, C. H. Yang, K. L. Teo and W. H. Gui, Optimal control of an industrial-scale evaporation process: Sodium aluminate solution, Control Engineering Practice, 20 (2012), 618-628.
doi: 10.1016/j.conengprac.2012.03.001. |
[14] |
B. Christiansen, H. Maurer and O. Zirn, Optimal control of a voice-coil-motor with Coulombic friction, in "Proceedings of the 47th IEEE Conference on Decision and Control,'' 2008.
doi: 10.1109/CDC.2008.4739025. |
[15] |
M. Chyba, T. Haberkorn, R. N. Smith and S. K. Choi, Design and implementation of time efficient trajectories for autonomous underwater vehicles, Ocean Engineering, 35 (2008), 63-76.
doi: 10.1016/j.oceaneng.2007.07.007. |
[16] |
J. Y. Dieulot and J. P. Richard, Tracking control of a nonlinear system with input-dependent delay, in "Proceedings of the 40th IEEE Conference on Decision and Control,'' 2001. |
[17] |
B. Farhadinia, K. L. Teo and R. Loxton, A computational method for a class of non-standard time optimal control problems involving multiple time horizons, Mathematical and Computer Modelling, 49 (2009), 1682-1691.
doi: 10.1016/j.mcm.2008.08.019. |
[18] |
M. Gerdts and M. Kunkel, A nonsmooth 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. |
[19] |
C. J. Goh and K. L. Teo, Control parametrization: A unified approach to optimal control problems with general constraints, Automatica J. IFAC, 24 (1988), 3-18.
doi: 10.1016/0005-1098(88)90003-9. |
[20] |
P. G. Howlett, P. J. Pudney and X. Vu, Local energy minimization in optimal train control, Automatica J. IFAC, 45 (2009), 2692-2698.
doi: 10.1016/j.automatica.2009.07.028. |
[21] |
L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, "MISER3 Optimal Control Software: Theory and User Manual,'' University of Western Australia, Perth, 2004. |
[22] |
L. S. Jennings and K. L. Teo, A computational algorithm for functional inequality constrained optimization problems, Automatica J. IFAC, 26 (1990), 371-375.
doi: 10.1016/0005-1098(90)90131-Z. |
[23] |
C. Jiang, Q. Lin, C. 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. |
[24] |
C. Jiang, K. L. Teo, R. Loxton and G. R. Duan, A neighboring extremal solution for an optimal switched impulsive control problem, Journal of Industrial and Management Optimization, 8 (2012), 591-609.
doi: 10.3934/jimo.2012.8.591. |
[25] |
K. Kaji and K. H. Wong, Nonlinearly constrained time-delayed optimal control problems, Journal of Optimization Theory and Applications, 82 (1994), 295-313.
doi: 10.1007/BF02191855. |
[26] |
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. |
[27] |
H. W. J. Lee, K. L. Teo and X. Q. Cai, An optimal control approach to nonlinear mixed integer programming problems, Computers and Mathematics with Applications, 36 (1998), 87-105.
doi: 10.1016/S0898-1221(98)00131-X. |
[28] |
H. W. J. Lee, K. L. Teo and A. E. B. Lim, Sensor scheduling in continuous time, Automatica J. IFAC, 37 (2001), 2017-2023.
doi: 10.1016/S0005-1098(01)00159-5. |
[29] |
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), 243-261. |
[30] |
H. W. J. Lee, K. L. Teo, V. Rehbock and L. S. Jennings, Control parametrization enhancing technique for optimal discrete-valued control problems, Automatica J. IFAC, 35 (1999), 1401-1407.
doi: 10.1016/S0005-1098(99)00050-3. |
[31] |
H. W. J. Lee and K. L. Teo, Control parametrization enhancing technique for solving a special ODE class with state dependent switch, Journal of Optimization Theory and Applications, 118 (2003), 55-66.
doi: 10.1023/A:1024735407694. |
[32] |
H. W. J. Lee and K. H. Wong, Semi-infinite programming approach to nonlinear time-delayed optimal control problems with linear continuous constraints, Optimization Methods and Software, 21 (2006), 679-691.
doi: 10.1080/10556780500142306. |
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