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Control parametrization and finite element method for controlling multi-species reactive transport in a circular pool
1. | Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China, China |
2. | School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa, South Africa |
References:
[1] |
R. C. Borden, C. A. Gomez and M. T. Becker, Geochemical indicators of intrinsic bioremediation, Ground Water, 33 (1995), 180-189.
doi: 10.1111/j.1745-6584.1995.tb00272.x. |
[2] |
T. P. Clement, Generalized solution to multispecies transport equations coupled with a first-order reaction network, Water Resources Research, 37 (2001), 157-163.
doi: 10.1029/2000WR900239. |
[3] |
T. P. Clement, C. D. Johnson, Y. Sun, G. M. Klecka and C. Bartlett, Natural attenuation of chlorinated ethene compounds: model development and field-scale application at the Dover site, Journal of Contaminant Hydrology, 42 (2000), 113-140.
doi: 10.1016/S0169-7722(99)00098-4. |
[4] |
T. P. Clement, Y. Sun, B. S. Hooker and J. N. Petersen, Modeling multispecies reactive transport in ground water, Ground Water Monitoring & Remediation, 18 (1998), 79-92.
doi: 10.1111/j.1745-6592.1998.tb00618.x. |
[5] |
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. |
[6] |
L. S. Jennings, K. L. Teo, M. E. Fisher and C. J. Goh, MISER3 version 3, Optimal control software : Theory and user manual, Centre for Applied Dynamics and Optimization, The University of Western Australia, 2004. http://school.maths.uwa.edu.au/les/miser/manual.html. |
[7] |
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. |
[8] |
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. |
[9] |
M. S. Lee, K. K. Lee, Y. Hyun, T. P. Clement and D. Hamilton, Nitrogen transformation and transport modeling in groundwater aquifers, Ecological Modelling, 192 (2006), 143-159.
doi: 10.1016/j.ecolmodel.2005.07.013. |
[10] |
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.
doi: 10.1007/s10957-011-9904-5. |
[11] |
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. |
[12] |
R. C. 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. |
[13] |
M. Lunn, R. J. Lunn and R. Mackayb, Determining analytic solutions of multiple species contaminant transport, with sorption and decay, Journal of Hydrology, 180 (1996), 195-210.
doi: 10.1016/0022-1694(95)02891-9. |
[14] |
H. Maurer, C. Büshens, J. H. R. Kim and C. Y. Kaya, Optimization methods for the verification of second order sufficient conditions for bang-bang controls, Optimal Control Applications and Methods, 26 (2005), 129-156.
doi: 10.1002/oca.756. |
[15] |
D. E. Rice, R. D. Grose, J. C. Michaelsen, B. P. Dooher, D. H. Macqueen, S. J. Cullen, W. E. Kastenberg, L. G. Everett and M. S. Marino, "California Leaking Underground Fuel Tank (LUFT) Historical Case Analyses," California State Water Resources Publication, UCRL-AR-122206, 1995. |
[16] |
L. Semprini, P. K. Kitanidis, D. H. Kampbell and J. T. Wilson, Anaerobic transformation of chlorinated aliphatic hydrocarbons in a sand aquifer based on spatial chemical distributions, Water Resources Research, 31 (1995), 1051-1062.
doi: 10.1029/94WR02380. |
[17] |
H. Tao and X. Liu, An improved control parameterization method for chemical dynamic optimization problems, World Congress on Intelligent Control and Automation, WCICA, (2006), 1650-1653. |
[18] |
K. L. Teo, C. J. Goh and K. H. Wong, "A Unified Computational Approach to Optimal Control Problems," Pitman Monographs and Surveys in Pure and Applied Mathematics 55, Longman Scientific & Technical, 1991. |
[19] |
K. L. Teo, L. S. Jennings, H. W. J. Lee and V. Rehbock, The control parameterization enhancing transform for constrained optimal control problems, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 40 (1999), 314-335.
doi: 10.1017/S0334270000010936. |
[20] |
K. L. Teo, H. W. J. Lee and V. Rehbock, Control parametrization enhancing technique for time optimal control and optimal three-valued control problems, Dynamics of Continuous, Discrete and Impulsive Systems, 4 (1998), 617-631. |
[21] |
K. L. Teo, K. H. Wong and D. J. Clements, Optimal control computation for linear time-lag systems with linear terminal constraints, Journal of Optimization Theory and Applications, 44 (1984), 509-526.
doi: 10.1007/BF00935465. |
[22] |
L. Y. Wang, W. H. Gui, K. L. Teo, R. C. Loxton and C. H. Yang, Time-delay 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. |
[23] |
K. H. Wong, D. J. Clements and K. L. Teo, Optimal control computation for nonlinear time-lag systems, Journal of Optimization Theory and Applications, 47 (1985), 91-107.
doi: 10.1007/BF00941318. |
[24] |
K. H. Wong, L. S. Jennings and F. Benyah, Control parametrization method for free planning time optimal control problems with time-delayed arguments, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 47 (2001), 5679-5690.
doi: 10.1016/S0362-546X(01)00669-1. |
[25] |
K. H. Wong, H. W. J. Lee and C. K. Chan, Control parametrization and finite element method for controlling multi-species reactive transport in a rectangular diffuser unit, Journal of Optimization Theory and Applications, 150 (2011), 118-141.
doi: 10.1007/s10957-011-9826-2. |
show all references
References:
[1] |
R. C. Borden, C. A. Gomez and M. T. Becker, Geochemical indicators of intrinsic bioremediation, Ground Water, 33 (1995), 180-189.
doi: 10.1111/j.1745-6584.1995.tb00272.x. |
[2] |
T. P. Clement, Generalized solution to multispecies transport equations coupled with a first-order reaction network, Water Resources Research, 37 (2001), 157-163.
doi: 10.1029/2000WR900239. |
[3] |
T. P. Clement, C. D. Johnson, Y. Sun, G. M. Klecka and C. Bartlett, Natural attenuation of chlorinated ethene compounds: model development and field-scale application at the Dover site, Journal of Contaminant Hydrology, 42 (2000), 113-140.
doi: 10.1016/S0169-7722(99)00098-4. |
[4] |
T. P. Clement, Y. Sun, B. S. Hooker and J. N. Petersen, Modeling multispecies reactive transport in ground water, Ground Water Monitoring & Remediation, 18 (1998), 79-92.
doi: 10.1111/j.1745-6592.1998.tb00618.x. |
[5] |
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. |
[6] |
L. S. Jennings, K. L. Teo, M. E. Fisher and C. J. Goh, MISER3 version 3, Optimal control software : Theory and user manual, Centre for Applied Dynamics and Optimization, The University of Western Australia, 2004. http://school.maths.uwa.edu.au/les/miser/manual.html. |
[7] |
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. |
[8] |
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. |
[9] |
M. S. Lee, K. K. Lee, Y. Hyun, T. P. Clement and D. Hamilton, Nitrogen transformation and transport modeling in groundwater aquifers, Ecological Modelling, 192 (2006), 143-159.
doi: 10.1016/j.ecolmodel.2005.07.013. |
[10] |
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.
doi: 10.1007/s10957-011-9904-5. |
[11] |
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. |
[12] |
R. C. 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. |
[13] |
M. Lunn, R. J. Lunn and R. Mackayb, Determining analytic solutions of multiple species contaminant transport, with sorption and decay, Journal of Hydrology, 180 (1996), 195-210.
doi: 10.1016/0022-1694(95)02891-9. |
[14] |
H. Maurer, C. Büshens, J. H. R. Kim and C. Y. Kaya, Optimization methods for the verification of second order sufficient conditions for bang-bang controls, Optimal Control Applications and Methods, 26 (2005), 129-156.
doi: 10.1002/oca.756. |
[15] |
D. E. Rice, R. D. Grose, J. C. Michaelsen, B. P. Dooher, D. H. Macqueen, S. J. Cullen, W. E. Kastenberg, L. G. Everett and M. S. Marino, "California Leaking Underground Fuel Tank (LUFT) Historical Case Analyses," California State Water Resources Publication, UCRL-AR-122206, 1995. |
[16] |
L. Semprini, P. K. Kitanidis, D. H. Kampbell and J. T. Wilson, Anaerobic transformation of chlorinated aliphatic hydrocarbons in a sand aquifer based on spatial chemical distributions, Water Resources Research, 31 (1995), 1051-1062.
doi: 10.1029/94WR02380. |
[17] |
H. Tao and X. Liu, An improved control parameterization method for chemical dynamic optimization problems, World Congress on Intelligent Control and Automation, WCICA, (2006), 1650-1653. |
[18] |
K. L. Teo, C. J. Goh and K. H. Wong, "A Unified Computational Approach to Optimal Control Problems," Pitman Monographs and Surveys in Pure and Applied Mathematics 55, Longman Scientific & Technical, 1991. |
[19] |
K. L. Teo, L. S. Jennings, H. W. J. Lee and V. Rehbock, The control parameterization enhancing transform for constrained optimal control problems, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 40 (1999), 314-335.
doi: 10.1017/S0334270000010936. |
[20] |
K. L. Teo, H. W. J. Lee and V. Rehbock, Control parametrization enhancing technique for time optimal control and optimal three-valued control problems, Dynamics of Continuous, Discrete and Impulsive Systems, 4 (1998), 617-631. |
[21] |
K. L. Teo, K. H. Wong and D. J. Clements, Optimal control computation for linear time-lag systems with linear terminal constraints, Journal of Optimization Theory and Applications, 44 (1984), 509-526.
doi: 10.1007/BF00935465. |
[22] |
L. Y. Wang, W. H. Gui, K. L. Teo, R. C. Loxton and C. H. Yang, Time-delay 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. |
[23] |
K. H. Wong, D. J. Clements and K. L. Teo, Optimal control computation for nonlinear time-lag systems, Journal of Optimization Theory and Applications, 47 (1985), 91-107.
doi: 10.1007/BF00941318. |
[24] |
K. H. Wong, L. S. Jennings and F. Benyah, Control parametrization method for free planning time optimal control problems with time-delayed arguments, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 47 (2001), 5679-5690.
doi: 10.1016/S0362-546X(01)00669-1. |
[25] |
K. H. Wong, H. W. J. Lee and C. K. Chan, Control parametrization and finite element method for controlling multi-species reactive transport in a rectangular diffuser unit, Journal of Optimization Theory and Applications, 150 (2011), 118-141.
doi: 10.1007/s10957-011-9826-2. |
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