VISUAL MISER: An efficient user-friendly visual program for solving optimal control problems

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April 2016, 12(2): 781-810. doi: 10.3934/jimo.2016.12.781

VISUAL MISER: An efficient user-friendly visual program for solving optimal control problems

Feng Yang ^1, , Kok Lay Teo ^2, , Ryan Loxton ^3, , Volker Rehbock ^3, , Bin Li ^4, , Changjun Yu ^5, and Leslie Jennings ^6,

1.	School of Automation Engineering, University of Electronic Science and Technology of China, No.2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu, Sichuan, 611731, China
2.	Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U 1987, Perth, W.A. 6845
3.	Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845
4.	Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, WA 6845
5.	School of Business, Central South University, South Lushan Road, Changsha, Hunan, China
6.	Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009, Australia

Received November 2014 Revised April 2015 Published June 2015

Abstract
Related Papers

The FORTRAN MISER software package has been used with great success over the past two decades to solve many practically important real world optimal control problems. However, MISER is written in FORTRAN and hence not user-friendly, requiring FORTRAN programming knowledge. To facilitate the practical application of powerful optimal control theory and techniques, this paper describes a Visual version of the MISER software, called Visual MISER. Visual MISER provides an easy-to-use interface, while retaining the computational efficiency of the original FORTRAN MISER software. The basic concepts underlying the MISER software, which include the control parameterization technique, a time scaling transform, a constraint transcription technique, and the co-state approach for gradient calculation, are described in this paper. The software structure is explained and instructions for its use are given. Finally, an example is solved using the new Visual MISER software to demonstrate its applicability.

Keywords: intel visual fortran, Optimal control, optimization., visual MISER.

Mathematics Subject Classification: Primary: 49M37, 49M25; Secondary: 65K0.

Citation: Feng Yang, Kok Lay Teo, Ryan Loxton, Volker Rehbock, Bin Li, Changjun Yu, Leslie Jennings. VISUAL MISER: An efficient user-friendly visual program for solving optimal control problems. Journal of Industrial and Management Optimization, 2016, 12 (2) : 781-810. doi: 10.3934/jimo.2016.12.781

References:

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[2]	M. Athans and P. L. Falb, Optimal Control, McGraw-Hill, 1966.
[3]	V. Azhmyakov, Optimal control of mechanical systems, Differential Equations and Nonlinear Mechanics, Volume 2007.
[4]	R. Bellman and R. E. Dreyfus, Dynamic Programming and Modern Control Theory, Orlands, Florida, Academic Press, 1977.
[5]	A. E. Jr. Bryson and Y. C. Ho, Applied Optimal Control, Hemisphere Publishing, DC, 1975.
[6]	C. Buskens, NUDOCCCS, FORTRAN-Subroutine NUDOCCCS (Numerical Discretisation method for Optimal Control problems with Constraints in Controls and States), 2010. http://www.swmath.org/software/8606
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[8]	L. Cesari, Optimization: Theory and Applications, Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4613-8165-5.
[9]	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 (2002), 618-628. doi: 10.1016/j.conengprac.2012.03.001.
[10]	B. D. Craven and S. M. N. Islam, Optimization in Economics and Finance, Springer, The Netherlands, 2005.
[11]	M. Fikar, M. A. Latifi and Y. Creff, Optimal Changeover Profiles for an Industrial Depropanizer, Chemical Engineering Science, 54 (1999), 2715-2720. doi: 10.1016/S0009-2509(98)00375-3.
[12]	M. E. Fisher and L. S. Jennings, MATLAB MISER, http://www.acad.polyu.edu.hk/ majlee/AMA483-523/OCTmanual.pdf
[13]	P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright, User's Guide for NPSOL 5.0: Fortran package for nonlinear programming, 1986. http://web.stanford.edu/group/SOL/npsol.htm
[14]	W. E. Gruver and E. Sachs, Algorithmic Methods in Optimal Control, Research Notes in Mathematics, Vol. 47, Pitman (Advance Publishing Program), London, 1981.
[15]	C. J. Goh and K. L. Teo, Control parameterization: a unified approach to optimal control problems with general constraints, Automatica, 24 (1988), 3-18. doi: 10.1016/0005-1098(88)90003-9.
[16]	S. Gonzalez and A. Miele, Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions, Journal of Optimization Theory and Applications, 26 (1978), 395-425. doi: 10.1007/BF00933463.
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[20]	L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, MISER3.3 Optimal Control Software Version: Theory and User Manual, the University of Western Australia, 2004.
[21]	L. S. Jennings and K. L. Teo, A computational algorithm for functional inequality constrained optimization problems, Automatica, 26 (1990), 371-375. doi: 10.1016/0005-1098(90)90131-Z.
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[24]	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.
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[29]	B. Li, C. Xu, K. L. Teo and J. Chu, Time optimal Zermelo's navigation problem with moving and fixed obstacles, Applied Mathematics and Computation, 224 (2013), 866-875. doi: 10.1016/j.amc.2013.08.092.
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[32]	B. Li, K. L. Teo and G. R. Duan, Optimal control computation for discrete time time-delayed optimal control problem with all-time-step inequality constraints, International Journal of Innovative Computing, Information and Control, 6 (2010), 521-532.
[33]	B. Li, K. L. Teo, G. H. Zhao and G. R. Duan, An efficient computational approach to a class of minimax optimal control problems with applications, Australian and New Zealand Industrial and Applied Mathematics Journal, 51 (2009), 162-177. doi: 10.1017/S1446181110000040.
[34]	C. J. Li, K. L Teo, B. Li and G. F. Ma, A constrained optimal pid-like controller design for spacecraft attitude stabilization, Acta Astronautica, 74 (2011), 131-140. doi: 10.1016/j.actaastro.2011.12.021.
[35]	C. C. Lim and K. L. Teo, Optimal insulin infusion control to a mathematical blood glucoregulatory model with fuzzy parameters, Cybernetics and Systems, 22 (1991), 1-16. doi: 10.1080/01969729108902267.
[36]	Q. Lin, R. Loxton and K. L. Teo, The control parameterization for nonlinear optimal control: A survey, Journal of Industrial and Management Optimization, 10 (2014), 275-309. doi: 10.3934/jimo.2014.10.275.
[37]	R. Loxton, K. L. Teo, V. Rehbock and W. K. Ling, Optimal switching instants for a switched-capacitor DC/DC power converter, Automatica, 45 (2009), 973-980. doi: 10.1016/j.automatica.2008.10.031.
[38]	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.
[39]	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.
[40]	R. Loxton, Q. Lin, V. Rehbock and K. L. Teo, Control parameterization for optimal control problems with continuous inequality constraints: New convergence results, Numerical Algebra, Control and Optimization, 2 (2012), 571-599. doi: 10.3934/naco.2012.2.571.
[41]	R. Loxton, Q. Lin and K. L. Teo, Minimizing control variation in nonlinear optimal control, Automatica, 49 (2013), 2652-2664. doi: 10.1016/j.automatica.2013.05.027.
[42]	R. Loxton, Q. Lin and K. L. Teo, Switching time optimization for nonlinear switched systems: Direct optimization and the time scaling transformation, Pacific Journal of Optimization, 10 (2014), 537-560.
[43]	R. Luus, Iterative Dynamic Programming, Chapman & Hall/CRC, Boca Raton, 2000. doi: 10.1201/9781420036022.
[44]	R. Luus and O. N. Okongwu, Towards practical optimal contorl of batch reactors, Chemical Engineering Journal, 75 (1999), 1-9.
[45]	R. Martin and K. L. Teo, Optimal Control of Drug Administration in Cancer Chemotherapy, World Scientific, 1994, 185pp.
[46]	MATLAB - The Language of Technical Computing, http://mathworks.com/products/matlab/, 2008.
[47]	H. Maurer, C. Buskens and G. Feichtinger, Solution techniques for periodic control problems: a case study in production planning, Optimal Control Applications and Methods, 19 (1998), 185-203. doi: 10.1002/(SICI)1099-1514(199805/06)19:3<185::AID-OCA627>3.0.CO;2-E.
[48]	H. H. Mehne and A. H. Borzabadi, A numerical method for solving optimal control problems using state parametrization, Numerical Algorithms, 42 (2006), 165-169. doi: 10.1007/s11075-006-9035-5.
[49]	A. Miele and T. Wang, Primal-dual properties of sequential gradient-restoration algorithms for optimal control problems, Part 2, General problem, Journal of Mathematical Analysis and Applications, 119 (1986), 21-54. doi: 10.1016/0022-247X(86)90142-3.
[50]	H. J. Oberle and B. Sothmann, Numerical computation of optimal feed rates for a fed-batch fermentation model, Journal of Optimization Theory and Applications, 100 (1999), 1-13.
[51]	R. Petzold and A. C. Hindmarsh, LSODA, Ordinary Differential Equation Solver for Stiff or Non-Stiff System, 2005.
[52]	L. S. Pontryagin, V. G. Boltayanskii, R. V. Gamkrelidze and E. F. Mischenko, Mathematical Theory of Optimal Processes, CRC Press, 1987.
[53]	V. Rehbock and I. Livk, Optimal control of a batch crystallization process, Journal of Industrial and Management Optimization, 3 (2007), 331-348. doi: 10.3934/jimo.2007.3.585.
[54]	Y. Sakawa and Y. Shindo, Optimal control of container cranes, Automatica, 18 (1982), 257-266. doi: 10.1016/0005-1098(82)90086-3.
[55]	K. Schittkowski, NLPQLP: A new fortran implementation of a sequential quadratic programming algorithm for parallel computing, 2010.
[56]	A. L. Schwartz, RIOTS-A Matlab toolbox for solving general optimal control problems, 2008. http://mechatronics.ucmerced.edu/RIOTS
[57]	Y. Shindo and Y. Sakawa, Local convergence of an algorithm for solving optimal control problems, Journal of Optimization Theory and Applications, 46 (1985), 265-293. doi: 10.1007/BF00939285.
[58]	W. Sun and Y. X. Yuan, Optimization Theory and Methods, Springer, 2006.
[59]	K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, Longman Scientific and Technical, England, 1991.
[60]	K. L. Teo, L. S. Jennings, H. W. J. Lee and V. Rehbock, The control parameterization enhancing transform for constrained optimal control problems, Journal of Australian Mathematical Society, Series B, 40 (1999), 314-335. doi: 10.1017/S0334270000010936.
[61]	K. L. Teo, V. Rehbock and L. S. Jennings, A new computational algorithm for functional inequality constrained optimization problems, Automatica, 29 (1993), 789-792. doi: 10.1016/0005-1098(93)90076-6.
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[64]	K. L. Teo and C. C. Lim, Time optimal control computation with application to ship steering, Journal of Optimization Theory and Applications, 56 (1988), 145-156. doi: 10.1007/BF00938530.
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show all references

References:

[1]	N. U. Ahmed, Dynamic Systems and Control with Applications, World Scientific, Singapore, 2006. doi: 10.1142/6262.
[2]	M. Athans and P. L. Falb, Optimal Control, McGraw-Hill, 1966.
[3]	V. Azhmyakov, Optimal control of mechanical systems, Differential Equations and Nonlinear Mechanics, Volume 2007.
[4]	R. Bellman and R. E. Dreyfus, Dynamic Programming and Modern Control Theory, Orlands, Florida, Academic Press, 1977.
[5]	A. E. Jr. Bryson and Y. C. Ho, Applied Optimal Control, Hemisphere Publishing, DC, 1975.
[6]	C. Buskens, NUDOCCCS, FORTRAN-Subroutine NUDOCCCS (Numerical Discretisation method for Optimal Control problems with Constraints in Controls and States), 2010. http://www.swmath.org/software/8606
[7]	C. Buskens and H. Maurer, Nonlinear programming methods for real-time control of an industrial robot, Journal of Optimization Theory and Applications, 107 (2000), 505-527. doi: 10.1023/A:1026491014283.
[8]	L. Cesari, Optimization: Theory and Applications, Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4613-8165-5.
[9]	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 (2002), 618-628. doi: 10.1016/j.conengprac.2012.03.001.
[10]	B. D. Craven and S. M. N. Islam, Optimization in Economics and Finance, Springer, The Netherlands, 2005.
[11]	M. Fikar, M. A. Latifi and Y. Creff, Optimal Changeover Profiles for an Industrial Depropanizer, Chemical Engineering Science, 54 (1999), 2715-2720. doi: 10.1016/S0009-2509(98)00375-3.
[12]	M. E. Fisher and L. S. Jennings, MATLAB MISER, http://www.acad.polyu.edu.hk/ majlee/AMA483-523/OCTmanual.pdf
[13]	P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright, User's Guide for NPSOL 5.0: Fortran package for nonlinear programming, 1986. http://web.stanford.edu/group/SOL/npsol.htm
[14]	W. E. Gruver and E. Sachs, Algorithmic Methods in Optimal Control, Research Notes in Mathematics, Vol. 47, Pitman (Advance Publishing Program), London, 1981.
[15]	C. J. Goh and K. L. Teo, Control parameterization: a unified approach to optimal control problems with general constraints, Automatica, 24 (1988), 3-18. doi: 10.1016/0005-1098(88)90003-9.
[16]	S. Gonzalez and A. Miele, Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions, Journal of Optimization Theory and Applications, 26 (1978), 395-425. doi: 10.1007/BF00933463.
[17]	G. R. Duan, D. K. Gu and B. Li, Optimal control for final approach of rendezvous with non-cooperative target, Pacific Journal of Optimization, 6 (2010), 3157-3175.
[18]	P. Howlett, The optimal control of a train, Annals of Operations Research, 98 (2000), 65-87. doi: 10.1023/A:1019235819716.
[19]	H. Jaddu, Direct solution of nonlinear optimal control problems using quasilinearization and Chebyshev polynomials, Journal of the Franklin Institute, 339 (2002), 479-498. doi: 10.1016/S0016-0032(02)00028-5.
[20]	L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, MISER3.3 Optimal Control Software Version: Theory and User Manual, the University of Western Australia, 2004.
[21]	L. S. Jennings and K. L. Teo, A computational algorithm for functional inequality constrained optimization problems, Automatica, 26 (1990), 371-375. doi: 10.1016/0005-1098(90)90131-Z.
[22]	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.
[23]	C. Jiang, K. L. Teo and G. R. Duan, A suboptimal feedback control for nonlinear time-varying systems with continuous inequality constraints, Automatica, 48 (2012), 660-665. doi: 10.1016/j.automatica.2012.01.019.
[24]	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.
[25]	C. Y. Kaya and J. M. Martnez, Euler discretization and inexact restoration for optimal control, Journal of Optimization Theory and Applications, 134 (2007), 191-206. doi: 10.1007/s10957-007-9217-x.
[26]	C. Y. Kaya and J. L. Noakes, Leapfrog for Optimal Control, SIAM Journal on Numerical Analysis, in press, 2008. doi: 10.1137/060675034.
[27]	M. I. Kamien and N. L. Schwartz, Dynamic Optimization - The Calculus of Variations and Optimal Control in Economics and Management, North Holland, 1991.
[28]	T. T. Lam and Y. Bayazitoglu, Application of the sequential gradient restoration algorithm to terminal convective instability problems, Journal of Optimization Theory and Applications, 49 (1986), 47-63. doi: 10.1007/BF00939247.
[29]	B. Li, C. Xu, K. L. Teo and J. Chu, Time optimal Zermelo's navigation problem with moving and fixed obstacles, Applied Mathematics and Computation, 224 (2013), 866-875. doi: 10.1016/j.amc.2013.08.092.
[30]	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.
[31]	B. Li, K. L. Teo, C. C. Lim and G. R. Duan, An optimal PID controller design for nonlinear constrained optimal control problems, Discrete and Continuous Dynamical Systems Series B, 16 (2011), 1101-1117. doi: 10.3934/dcdsb.2011.16.1101.
[32]	B. Li, K. L. Teo and G. R. Duan, Optimal control computation for discrete time time-delayed optimal control problem with all-time-step inequality constraints, International Journal of Innovative Computing, Information and Control, 6 (2010), 521-532.
[33]	B. Li, K. L. Teo, G. H. Zhao and G. R. Duan, An efficient computational approach to a class of minimax optimal control problems with applications, Australian and New Zealand Industrial and Applied Mathematics Journal, 51 (2009), 162-177. doi: 10.1017/S1446181110000040.
[34]	C. J. Li, K. L Teo, B. Li and G. F. Ma, A constrained optimal pid-like controller design for spacecraft attitude stabilization, Acta Astronautica, 74 (2011), 131-140. doi: 10.1016/j.actaastro.2011.12.021.
[35]	C. C. Lim and K. L. Teo, Optimal insulin infusion control to a mathematical blood glucoregulatory model with fuzzy parameters, Cybernetics and Systems, 22 (1991), 1-16. doi: 10.1080/01969729108902267.
[36]	Q. Lin, R. Loxton and K. L. Teo, The control parameterization for nonlinear optimal control: A survey, Journal of Industrial and Management Optimization, 10 (2014), 275-309. doi: 10.3934/jimo.2014.10.275.
[37]	R. Loxton, K. L. Teo, V. Rehbock and W. K. Ling, Optimal switching instants for a switched-capacitor DC/DC power converter, Automatica, 45 (2009), 973-980. doi: 10.1016/j.automatica.2008.10.031.
[38]	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.
[39]	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.
[40]	R. Loxton, Q. Lin, V. Rehbock and K. L. Teo, Control parameterization for optimal control problems with continuous inequality constraints: New convergence results, Numerical Algebra, Control and Optimization, 2 (2012), 571-599. doi: 10.3934/naco.2012.2.571.
[41]	R. Loxton, Q. Lin and K. L. Teo, Minimizing control variation in nonlinear optimal control, Automatica, 49 (2013), 2652-2664. doi: 10.1016/j.automatica.2013.05.027.
[42]	R. Loxton, Q. Lin and K. L. Teo, Switching time optimization for nonlinear switched systems: Direct optimization and the time scaling transformation, Pacific Journal of Optimization, 10 (2014), 537-560.
[43]	R. Luus, Iterative Dynamic Programming, Chapman & Hall/CRC, Boca Raton, 2000. doi: 10.1201/9781420036022.
[44]	R. Luus and O. N. Okongwu, Towards practical optimal contorl of batch reactors, Chemical Engineering Journal, 75 (1999), 1-9.
[45]	R. Martin and K. L. Teo, Optimal Control of Drug Administration in Cancer Chemotherapy, World Scientific, 1994, 185pp.
[46]	MATLAB - The Language of Technical Computing, http://mathworks.com/products/matlab/, 2008.
[47]	H. Maurer, C. Buskens and G. Feichtinger, Solution techniques for periodic control problems: a case study in production planning, Optimal Control Applications and Methods, 19 (1998), 185-203. doi: 10.1002/(SICI)1099-1514(199805/06)19:3<185::AID-OCA627>3.0.CO;2-E.
[48]	H. H. Mehne and A. H. Borzabadi, A numerical method for solving optimal control problems using state parametrization, Numerical Algorithms, 42 (2006), 165-169. doi: 10.1007/s11075-006-9035-5.
[49]	A. Miele and T. Wang, Primal-dual properties of sequential gradient-restoration algorithms for optimal control problems, Part 2, General problem, Journal of Mathematical Analysis and Applications, 119 (1986), 21-54. doi: 10.1016/0022-247X(86)90142-3.
[50]	H. J. Oberle and B. Sothmann, Numerical computation of optimal feed rates for a fed-batch fermentation model, Journal of Optimization Theory and Applications, 100 (1999), 1-13.
[51]	R. Petzold and A. C. Hindmarsh, LSODA, Ordinary Differential Equation Solver for Stiff or Non-Stiff System, 2005.
[52]	L. S. Pontryagin, V. G. Boltayanskii, R. V. Gamkrelidze and E. F. Mischenko, Mathematical Theory of Optimal Processes, CRC Press, 1987.
[53]	V. Rehbock and I. Livk, Optimal control of a batch crystallization process, Journal of Industrial and Management Optimization, 3 (2007), 331-348. doi: 10.3934/jimo.2007.3.585.
[54]	Y. Sakawa and Y. Shindo, Optimal control of container cranes, Automatica, 18 (1982), 257-266. doi: 10.1016/0005-1098(82)90086-3.
[55]	K. Schittkowski, NLPQLP: A new fortran implementation of a sequential quadratic programming algorithm for parallel computing, 2010.
[56]	A. L. Schwartz, RIOTS-A Matlab toolbox for solving general optimal control problems, 2008. http://mechatronics.ucmerced.edu/RIOTS
[57]	Y. Shindo and Y. Sakawa, Local convergence of an algorithm for solving optimal control problems, Journal of Optimization Theory and Applications, 46 (1985), 265-293. doi: 10.1007/BF00939285.
[58]	W. Sun and Y. X. Yuan, Optimization Theory and Methods, Springer, 2006.
[59]	K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, Longman Scientific and Technical, England, 1991.
[60]	K. L. Teo, L. S. Jennings, H. W. J. Lee and V. Rehbock, The control parameterization enhancing transform for constrained optimal control problems, Journal of Australian Mathematical Society, Series B, 40 (1999), 314-335. doi: 10.1017/S0334270000010936.
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