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A gradient algorithm for optimal control problems with modelreality 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. doi: 10.1080/00207179608921843. 
[2] 
A. E. Bryson and Y. C. Ho, Applied Optimal Control,, Hemisphere Publishing Company, (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. 
[4] 
D. E. Kirk, Optimal Control Theory: An Introduction,, Mineola, (2004). 
[5] 
F. L. Lewis and V. L. Syrmos, Optimal Control,, 2nd ed, (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. 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. 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. doi: 10.1016/j.automatica.2009.05.029. 
[9] 
L. F. Lupián and J. R. RabadánMartin, LQR control methods for trajectory execution in omnidirectional mobile robots,, Recent Advances in Mobile Robotics, (2011), 385. 
[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 semiactive suspension systems,, Proceeding of ICROSSICE International Joint Conference, (2009), 4698. 
[11] 
P. D. Roberts and T. W. C. Williams, On an algorithm for combined system optimization and parameter estimation,, Automatica, 17 (1981), 199. doi: 10.1016/00051098(81)900959. 
[12] 
P. D. Roberts, Optimal control of nonlinear systems with modelreality differences,, Proceedings of the 31st IEEE Conference on Decision and Control, 1 (1992), 257. 
[13] 
R. C. H. del Rosario and R. C. Smith, LQR control of shell vibrations via piezocreramic actuators,, NASA Contractor Report 201673, (2016), 97. 
[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, (1991). 
[16] 
L. X. Wang, A Course in Fuzzy Systems and Control,, Upper Saddle River, (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. doi: 10.3934/jimo.2009.5.737. 
[18] 
B. Yang and B. Xiong, Application of LQR techniques to the antisway controller of overhead crane,, Advanced Material Research, 139141 (2010), 139. 
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. doi: 10.1080/00207179608921843. 
[2] 
A. E. Bryson and Y. C. Ho, Applied Optimal Control,, Hemisphere Publishing Company, (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. 
[4] 
D. E. Kirk, Optimal Control Theory: An Introduction,, Mineola, (2004). 
[5] 
F. L. Lewis and V. L. Syrmos, Optimal Control,, 2nd ed, (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. 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. 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. doi: 10.1016/j.automatica.2009.05.029. 
[9] 
L. F. Lupián and J. R. RabadánMartin, LQR control methods for trajectory execution in omnidirectional mobile robots,, Recent Advances in Mobile Robotics, (2011), 385. 
[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 semiactive suspension systems,, Proceeding of ICROSSICE International Joint Conference, (2009), 4698. 
[11] 
P. D. Roberts and T. W. C. Williams, On an algorithm for combined system optimization and parameter estimation,, Automatica, 17 (1981), 199. doi: 10.1016/00051098(81)900959. 
[12] 
P. D. Roberts, Optimal control of nonlinear systems with modelreality differences,, Proceedings of the 31st IEEE Conference on Decision and Control, 1 (1992), 257. 
[13] 
R. C. H. del Rosario and R. C. Smith, LQR control of shell vibrations via piezocreramic actuators,, NASA Contractor Report 201673, (2016), 97. 
[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, (1991). 
[16] 
L. X. Wang, A Course in Fuzzy Systems and Control,, Upper Saddle River, (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. doi: 10.3934/jimo.2009.5.737. 
[18] 
B. Yang and B. Xiong, Application of LQR techniques to the antisway controller of overhead crane,, Advanced Material Research, 139141 (2010), 139. 
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