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Asymptotic problems in optimal control with a vanishing Lagrangian and unbounded data
Adaptive time--mesh refinement in optimal control problems with state constraints
1. | SYSTEC-ISR, Faculdade de Engenharia, Universidade do Porto, 4200-465, Porto, Portugal |
2. | ISR-Porto, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal |
References:
[1] |
J. T. Betts, Practical Methods for Optimal Control Using Nonlinear Programming, SIAM, 2001. |
[2] |
J. T. Betts, N. Biehn, S. L. Campbell and W. P. Huffman, Compensating for order variation in mesh refinement for direct transcription methods, Journal of Computational and Applied Mathematics, 125 (2000), 147-158.
doi: 10.1016/S0377-0427(00)00465-9. |
[3] |
J. T. Betts and W. P. Huffman, Mesh refinement in direct transcription methods for optimal control, Optimal Control Applications and Methods, 19 (1998), 1-21.
doi: 10.1002/(SICI)1099-1514(199801/02)19:1<1::AID-OCA616>3.0.CO;2-Q. |
[4] |
M. H. A. Biswas, L. T. Paiva and M. d. R. de Pinho, A SEIR model for control of infectious diseases with constraints, Mathematical Biosciences and Engineering, 11 (2014), 761-784.
doi: 10.3934/mbe.2014.11.761. |
[5] |
P. Falugi, E. Kerrigan and E. Van Wyk, Imperial College London Optimal Control Software. User Guide (ICLOCS), Department of Electrical Engineering, Imperial College London, London, UK, 2010. |
[6] |
F. A. C. C. Fontes, A general framework to design stabilizing nonlinear model predictive controllers, Systems and Control Letters, 42 (2001), 127-143.
doi: 10.1016/S0167-6911(00)00084-0. |
[7] |
F. A. C. C. Fontes and H. Frankowska, Normality and nondegeneracy for optimal control problems with state constraints, Journal of Optimization Theory and Applications, 22 (2015), p30.
doi: 10.1007/s10957-015-0704-1. |
[8] |
F. A. C. C. Fontes and S. O. Lopes, Normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints, Journal of Mathematical Analysis and Applications, 399 (2013), 27-37.
doi: 10.1016/j.jmaa.2012.09.049. |
[9] |
I. Kolmanovsky and N. McClamroch, Developments in nonholonomic control problems, IEEE Control Systems, 15 (1995), 20-36.
doi: 10.1109/37.476384. |
[10] |
I. Kornienko, L. T. Paiva and M. d. R. d. Pinho, Introducing state constraints in optimal control for health problems, Procedia Technology, 17 (2014), 415-422.
doi: 10.1016/j.protcy.2014.10.249. |
[11] |
S. O. Lopes, F. A. Fontes and M. d. R. de Pinho, On constraint qualifications for nondegenerate necessary conditions of optimality applied to optimal control problems, Discrete and Continuous Dynamical Systems (DCDS-A), 29 (2011), 559-575.
doi: 10.3934/dcds.2011.29.559. |
[12] |
R. M. Neilan and S. Lenhart, An introduction to optimal control with an application in disease modeling, Modeling paradigms and analysis of disease transmission models, 75 (2010), 67-81. |
[13] |
L. T. Paiva, Optimal Control in Constrained and Hybrid Nonlinear System: Solvers and Interfaces, Technical report, Faculdade de Engenharia, Universidade do Porto, 2013. |
[14] |
L. T. Paiva and F. A. C. C. Fontes, Mesh refinement strategy for optimal control problems, AIP Conference Proceedings, 1558 (2013), 590-593, Proceding of the ICNAAM 2013 - 11th International Conference on Numerical Analysis and Applied Mathematics.
doi: 10.1063/1.4825560. |
[15] |
L. T. Paiva and F. A. C. C. Fontes, Time-mesh refinement in optimal control problems for nonholonomic vehicles, Procedia Technology, 17 (2014), 178-185.
doi: 10.1016/j.protcy.2014.10.226. |
[16] |
M. A. Patterson, W. W. Hager and A. V. Rao, A ph mesh refinement method for optimal control, Optimal Control Applications and Methods, Doi:10.1002/oca.2114. |
[17] | |
[18] |
A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming, 106 (2006), 25-57.
doi: 10.1007/s10107-004-0559-y. |
[19] |
Y. Zhao and P. Tsiotras, Density functions for mesh refinement in numerical optimal control, Journal of Guidance, Control, and Dynamics, 34 (2011), 271-277.
doi: 10.2514/1.45852. |
show all references
References:
[1] |
J. T. Betts, Practical Methods for Optimal Control Using Nonlinear Programming, SIAM, 2001. |
[2] |
J. T. Betts, N. Biehn, S. L. Campbell and W. P. Huffman, Compensating for order variation in mesh refinement for direct transcription methods, Journal of Computational and Applied Mathematics, 125 (2000), 147-158.
doi: 10.1016/S0377-0427(00)00465-9. |
[3] |
J. T. Betts and W. P. Huffman, Mesh refinement in direct transcription methods for optimal control, Optimal Control Applications and Methods, 19 (1998), 1-21.
doi: 10.1002/(SICI)1099-1514(199801/02)19:1<1::AID-OCA616>3.0.CO;2-Q. |
[4] |
M. H. A. Biswas, L. T. Paiva and M. d. R. de Pinho, A SEIR model for control of infectious diseases with constraints, Mathematical Biosciences and Engineering, 11 (2014), 761-784.
doi: 10.3934/mbe.2014.11.761. |
[5] |
P. Falugi, E. Kerrigan and E. Van Wyk, Imperial College London Optimal Control Software. User Guide (ICLOCS), Department of Electrical Engineering, Imperial College London, London, UK, 2010. |
[6] |
F. A. C. C. Fontes, A general framework to design stabilizing nonlinear model predictive controllers, Systems and Control Letters, 42 (2001), 127-143.
doi: 10.1016/S0167-6911(00)00084-0. |
[7] |
F. A. C. C. Fontes and H. Frankowska, Normality and nondegeneracy for optimal control problems with state constraints, Journal of Optimization Theory and Applications, 22 (2015), p30.
doi: 10.1007/s10957-015-0704-1. |
[8] |
F. A. C. C. Fontes and S. O. Lopes, Normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints, Journal of Mathematical Analysis and Applications, 399 (2013), 27-37.
doi: 10.1016/j.jmaa.2012.09.049. |
[9] |
I. Kolmanovsky and N. McClamroch, Developments in nonholonomic control problems, IEEE Control Systems, 15 (1995), 20-36.
doi: 10.1109/37.476384. |
[10] |
I. Kornienko, L. T. Paiva and M. d. R. d. Pinho, Introducing state constraints in optimal control for health problems, Procedia Technology, 17 (2014), 415-422.
doi: 10.1016/j.protcy.2014.10.249. |
[11] |
S. O. Lopes, F. A. Fontes and M. d. R. de Pinho, On constraint qualifications for nondegenerate necessary conditions of optimality applied to optimal control problems, Discrete and Continuous Dynamical Systems (DCDS-A), 29 (2011), 559-575.
doi: 10.3934/dcds.2011.29.559. |
[12] |
R. M. Neilan and S. Lenhart, An introduction to optimal control with an application in disease modeling, Modeling paradigms and analysis of disease transmission models, 75 (2010), 67-81. |
[13] |
L. T. Paiva, Optimal Control in Constrained and Hybrid Nonlinear System: Solvers and Interfaces, Technical report, Faculdade de Engenharia, Universidade do Porto, 2013. |
[14] |
L. T. Paiva and F. A. C. C. Fontes, Mesh refinement strategy for optimal control problems, AIP Conference Proceedings, 1558 (2013), 590-593, Proceding of the ICNAAM 2013 - 11th International Conference on Numerical Analysis and Applied Mathematics.
doi: 10.1063/1.4825560. |
[15] |
L. T. Paiva and F. A. C. C. Fontes, Time-mesh refinement in optimal control problems for nonholonomic vehicles, Procedia Technology, 17 (2014), 178-185.
doi: 10.1016/j.protcy.2014.10.226. |
[16] |
M. A. Patterson, W. W. Hager and A. V. Rao, A ph mesh refinement method for optimal control, Optimal Control Applications and Methods, Doi:10.1002/oca.2114. |
[17] | |
[18] |
A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming, 106 (2006), 25-57.
doi: 10.1007/s10107-004-0559-y. |
[19] |
Y. Zhao and P. Tsiotras, Density functions for mesh refinement in numerical optimal control, Journal of Guidance, Control, and Dynamics, 34 (2011), 271-277.
doi: 10.2514/1.45852. |
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