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A gradient algorithm for optimal control problems with model-reality differences
1. | Department of Mathematics, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Malaysia |
2. | Department of Mathematics, Universiti Teknologi Malaysia, 81310 UTM, Skudai, Malaysia |
3. | Department of Mathematics and Statistics, Curtin University, Perth, W.A. 6845 |
References:
[1] |
V. M. Becerra and P. D. Roberts, Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems, Int. J. Control, 63 (1996), 257-281.
doi: 10.1080/00207179608921843. |
[2] |
A. E. Bryson and Y. C. Ho, Applied Optimal Control, Hemisphere Publishing Company, New York, 1975. |
[3] |
S. L. Kek, Nonlinear programming approach for optimal control problems, Proceeding of the 2nd International Conference on Global Optimization and Its Applications, (2013), 20-25. |
[4] |
D. E. Kirk, Optimal Control Theory: An Introduction, Mineola, NY: Dover Publications, 2004. |
[5] |
F. L. Lewis and V. L. Syrmos, Optimal Control, 2nd ed, John Wiley & Sons, 1995. |
[6] |
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. |
[7] |
R. Loxton, K. L. Teo and V. Rehbock, Computational method for a class of switched system optimal control problems, IEEE Transactions on Automatic Control, 54 (2009), 2455-2460.
doi: 10.1109/TAC.2009.2029310. |
[8] |
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. |
[9] |
L. F. Lupián and J. R. Rabadán-Martin, LQR control methods for trajectory execution in omnidirectional mobile robots, Recent Advances in Mobile Robotics, (2011), 385-400. |
[10] |
L. H. Nguyen, S. Park, A. Turnip and K. S. Hong, Application of LQR control theory to the design of modified skyhook control gains for semi-active suspension systems, Proceeding of ICROS-SICE International Joint Conference, (2009), 4698-4703. |
[11] |
P. D. Roberts and T. W. C. Williams, On an algorithm for combined system optimization and parameter estimation, Automatica, 17 (1981), 199-209.
doi: 10.1016/0005-1098(81)90095-9. |
[12] |
P. D. Roberts, Optimal control of nonlinear systems with model-reality differences, Proceedings of the 31st IEEE Conference on Decision and Control, 1 (1992), 257-258. |
[13] |
R. C. H. del Rosario and R. C. Smith, LQR control of shell vibrations via piezocreramic actuators, NASA Contractor Report 201673, ICASE Report No. 97-19, 1997. |
[14] |
J. Saak and P. Benner, Application of LQR techniques to the adaptive control of quasilinear parabolic PDEs, Proceedings in Applied Mathematics and Mechanics, 2007. |
[15] |
K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problem, Longman Scientific and Technical, Essex, 1991. |
[16] |
L. X. Wang, A Course in Fuzzy Systems and Control, Upper Saddle River, NJ, 1997. |
[17] |
C. Z. Wu, K. L. Teo and V. Rehbock, Optimal control of piecewise affine systems with piecewise affine state feedback, Journal of Industrial and Management Optimization, 5 (2009), 737-747.
doi: 10.3934/jimo.2009.5.737. |
[18] |
B. Yang and B. Xiong, Application of LQR techniques to the anti-sway controller of overhead crane, Advanced Material Research, 139-141 (2010), 1933-1936. |
show all references
References:
[1] |
V. M. Becerra and P. D. Roberts, Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems, Int. J. Control, 63 (1996), 257-281.
doi: 10.1080/00207179608921843. |
[2] |
A. E. Bryson and Y. C. Ho, Applied Optimal Control, Hemisphere Publishing Company, New York, 1975. |
[3] |
S. L. Kek, Nonlinear programming approach for optimal control problems, Proceeding of the 2nd International Conference on Global Optimization and Its Applications, (2013), 20-25. |
[4] |
D. E. Kirk, Optimal Control Theory: An Introduction, Mineola, NY: Dover Publications, 2004. |
[5] |
F. L. Lewis and V. L. Syrmos, Optimal Control, 2nd ed, John Wiley & Sons, 1995. |
[6] |
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. |
[7] |
R. Loxton, K. L. Teo and V. Rehbock, Computational method for a class of switched system optimal control problems, IEEE Transactions on Automatic Control, 54 (2009), 2455-2460.
doi: 10.1109/TAC.2009.2029310. |
[8] |
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. |
[9] |
L. F. Lupián and J. R. Rabadán-Martin, LQR control methods for trajectory execution in omnidirectional mobile robots, Recent Advances in Mobile Robotics, (2011), 385-400. |
[10] |
L. H. Nguyen, S. Park, A. Turnip and K. S. Hong, Application of LQR control theory to the design of modified skyhook control gains for semi-active suspension systems, Proceeding of ICROS-SICE International Joint Conference, (2009), 4698-4703. |
[11] |
P. D. Roberts and T. W. C. Williams, On an algorithm for combined system optimization and parameter estimation, Automatica, 17 (1981), 199-209.
doi: 10.1016/0005-1098(81)90095-9. |
[12] |
P. D. Roberts, Optimal control of nonlinear systems with model-reality differences, Proceedings of the 31st IEEE Conference on Decision and Control, 1 (1992), 257-258. |
[13] |
R. C. H. del Rosario and R. C. Smith, LQR control of shell vibrations via piezocreramic actuators, NASA Contractor Report 201673, ICASE Report No. 97-19, 1997. |
[14] |
J. Saak and P. Benner, Application of LQR techniques to the adaptive control of quasilinear parabolic PDEs, Proceedings in Applied Mathematics and Mechanics, 2007. |
[15] |
K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problem, Longman Scientific and Technical, Essex, 1991. |
[16] |
L. X. Wang, A Course in Fuzzy Systems and Control, Upper Saddle River, NJ, 1997. |
[17] |
C. Z. Wu, K. L. Teo and V. Rehbock, Optimal control of piecewise affine systems with piecewise affine state feedback, Journal of Industrial and Management Optimization, 5 (2009), 737-747.
doi: 10.3934/jimo.2009.5.737. |
[18] |
B. Yang and B. Xiong, Application of LQR techniques to the anti-sway controller of overhead crane, Advanced Material Research, 139-141 (2010), 1933-1936. |
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