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

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

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.
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 & Management Optimization, 2016, 12 (2) : 781-810. doi: 10.3934/jimo.2016.12.781
References:
[1]

World Scientific, Singapore, 2006. doi: 10.1142/6262.  Google Scholar

[2]

McGraw-Hill, 1966.  Google Scholar

[3]

Differential Equations and Nonlinear Mechanics, Volume 2007.  Google Scholar

[4]

Orlands, Florida, Academic Press, 1977.  Google Scholar

[5]

Hemisphere Publishing, DC, 1975.  Google Scholar

[6]

C. Buskens, NUDOCCCS, FORTRAN-Subroutine NUDOCCCS (Numerical Discretisation method for Optimal Control problems with Constraints in Controls and States),, 2010. , ().   Google Scholar

[7]

Journal of Optimization Theory and Applications, 107 (2000), 505-527. doi: 10.1023/A:1026491014283.  Google Scholar

[8]

Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4613-8165-5.  Google Scholar

[9]

Control Engineering Practice, 20 (2002), 618-628. doi: 10.1016/j.conengprac.2012.03.001.  Google Scholar

[10]

Springer, The Netherlands, 2005.  Google Scholar

[11]

Chemical Engineering Science, 54 (1999), 2715-2720. doi: 10.1016/S0009-2509(98)00375-3.  Google Scholar

[12]

M. E. Fisher and L. S. Jennings, MATLAB MISER,, , (): 483.   Google Scholar

[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. , ().   Google Scholar

[14]

Research Notes in Mathematics, Vol. 47, Pitman (Advance Publishing Program), London, 1981.  Google Scholar

[15]

Automatica, 24 (1988), 3-18. doi: 10.1016/0005-1098(88)90003-9.  Google Scholar

[16]

Journal of Optimization Theory and Applications, 26 (1978), 395-425. doi: 10.1007/BF00933463.  Google Scholar

[17]

Pacific Journal of Optimization, 6 (2010), 3157-3175.  Google Scholar

[18]

Annals of Operations Research, 98 (2000), 65-87. doi: 10.1023/A:1019235819716.  Google Scholar

[19]

Journal of the Franklin Institute, 339 (2002), 479-498. doi: 10.1016/S0016-0032(02)00028-5.  Google Scholar

[20]

the University of Western Australia, 2004. Google Scholar

[21]

Automatica, 26 (1990), 371-375. doi: 10.1016/0005-1098(90)90131-Z.  Google Scholar

[22]

Journal of Industrial and Management Optimization, 8 (2012), 591-609. doi: 10.3934/jimo.2012.8.591.  Google Scholar

[23]

Automatica, 48 (2012), 660-665. doi: 10.1016/j.automatica.2012.01.019.  Google Scholar

[24]

Journal of Optimization Theory and Applications, 154 (2012), 30-53. doi: 10.1007/s10957-012-0006-9.  Google Scholar

[25]

Journal of Optimization Theory and Applications, 134 (2007), 191-206. doi: 10.1007/s10957-007-9217-x.  Google Scholar

[26]

SIAM Journal on Numerical Analysis, in press, 2008. doi: 10.1137/060675034.  Google Scholar

[27]

North Holland, 1991.  Google Scholar

[28]

Journal of Optimization Theory and Applications, 49 (1986), 47-63. doi: 10.1007/BF00939247.  Google Scholar

[29]

Applied Mathematics and Computation, 224 (2013), 866-875. doi: 10.1016/j.amc.2013.08.092.  Google Scholar

[30]

Journal of Optimization Theory and Applications, 151 (2011), 260-291. doi: 10.1007/s10957-011-9904-5.  Google Scholar

[31]

Discrete and Continuous Dynamical Systems Series B, 16 (2011), 1101-1117. doi: 10.3934/dcdsb.2011.16.1101.  Google Scholar

[32]

International Journal of Innovative Computing, Information and Control, 6 (2010), 521-532. Google Scholar

[33]

Australian and New Zealand Industrial and Applied Mathematics Journal, 51 (2009), 162-177. doi: 10.1017/S1446181110000040.  Google Scholar

[34]

Acta Astronautica, 74 (2011), 131-140. doi: 10.1016/j.actaastro.2011.12.021.  Google Scholar

[35]

Cybernetics and Systems, 22 (1991), 1-16. doi: 10.1080/01969729108902267.  Google Scholar

[36]

Journal of Industrial and Management Optimization, 10 (2014), 275-309. doi: 10.3934/jimo.2014.10.275.  Google Scholar

[37]

Automatica, 45 (2009), 973-980. doi: 10.1016/j.automatica.2008.10.031.  Google Scholar

[38]

Automatica, 45 (2009), 2250-2257. doi: 10.1016/j.automatica.2009.05.029.  Google Scholar

[39]

IEEE Transactions on Automatic Control, 54 (2009), 2455-2460. doi: 10.1109/TAC.2009.2029310.  Google Scholar

[40]

Numerical Algebra, Control and Optimization, 2 (2012), 571-599. doi: 10.3934/naco.2012.2.571.  Google Scholar

[41]

Automatica, 49 (2013), 2652-2664. doi: 10.1016/j.automatica.2013.05.027.  Google Scholar

[42]

Pacific Journal of Optimization, 10 (2014), 537-560.  Google Scholar

[43]

Chapman & Hall/CRC, Boca Raton, 2000. doi: 10.1201/9781420036022.  Google Scholar

[44]

Chemical Engineering Journal, 75 (1999), 1-9. Google Scholar

[45]

World Scientific, 1994, 185pp. Google Scholar

[46]

MATLAB - The Language of Technical Computing, http://mathworks.com/products/matlab/,, 2008., ().   Google Scholar

[47]

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.  Google Scholar

[48]

Numerical Algorithms, 42 (2006), 165-169. doi: 10.1007/s11075-006-9035-5.  Google Scholar

[49]

Journal of Mathematical Analysis and Applications, 119 (1986), 21-54. doi: 10.1016/0022-247X(86)90142-3.  Google Scholar

[50]

Journal of Optimization Theory and Applications, 100 (1999), 1-13. Google Scholar

[51]

R. Petzold and A. C. Hindmarsh, LSODA, Ordinary Differential Equation Solver for Stiff or Non-Stiff System,, 2005., ().   Google Scholar

[52]

CRC Press, 1987. Google Scholar

[53]

Journal of Industrial and Management Optimization, 3 (2007), 331-348. doi: 10.3934/jimo.2007.3.585.  Google Scholar

[54]

Automatica, 18 (1982), 257-266. doi: 10.1016/0005-1098(82)90086-3.  Google Scholar

[55]

K. Schittkowski, NLPQLP: A new fortran implementation of a sequential quadratic programming algorithm for parallel computing,, 2010., ().   Google Scholar

[56]

A. L. Schwartz, RIOTS-A Matlab toolbox for solving general optimal control problems,, 2008. , ().   Google Scholar

[57]

Journal of Optimization Theory and Applications, 46 (1985), 265-293. doi: 10.1007/BF00939285.  Google Scholar

[58]

Springer, 2006.  Google Scholar

[59]

Longman Scientific and Technical, England, 1991.  Google Scholar

[60]

Journal of Australian Mathematical Society, Series B, 40 (1999), 314-335. doi: 10.1017/S0334270000010936.  Google Scholar

[61]

Automatica, 29 (1993), 789-792. doi: 10.1016/0005-1098(93)90076-6.  Google Scholar

[62]

Journal of Australian Mathematical Society, Series B, 33 (1992), 517-530. doi: 10.1017/S0334270000007207.  Google Scholar

[63]

IMA - Journal of Mathematical Control and Information, 6 (1989), 81-95. doi: 10.1093/imamci/6.1.81.  Google Scholar

[64]

Journal of Optimization Theory and Applications, 56 (1988), 145-156. doi: 10.1007/BF00938530.  Google Scholar

[65]

International Journal of Mechanical Sciences, 12 (1970), 973-983. doi: 10.1016/0020-7403(70)90037-8.  Google Scholar

[66]

in Proc. 2nd European Congress on Intelligent Techniques and Soft Computing (EUFIT) (H.J. Zimmermann ed.), Aachen, Germany, pp. 347-351, 1994. Google Scholar

[67]

Journal of Industrial and Management Optimization, 2 (2006), 435-450. doi: 10.3934/jimo.2006.2.435.  Google Scholar

[68]

Institute for Systems Research, University of Maryland, Technical Report SRC-TR-92-107r5, College Park, MD 20742. Google Scholar

show all references

References:
[1]

World Scientific, Singapore, 2006. doi: 10.1142/6262.  Google Scholar

[2]

McGraw-Hill, 1966.  Google Scholar

[3]

Differential Equations and Nonlinear Mechanics, Volume 2007.  Google Scholar

[4]

Orlands, Florida, Academic Press, 1977.  Google Scholar

[5]

Hemisphere Publishing, DC, 1975.  Google Scholar

[6]

C. Buskens, NUDOCCCS, FORTRAN-Subroutine NUDOCCCS (Numerical Discretisation method for Optimal Control problems with Constraints in Controls and States),, 2010. , ().   Google Scholar

[7]

Journal of Optimization Theory and Applications, 107 (2000), 505-527. doi: 10.1023/A:1026491014283.  Google Scholar

[8]

Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4613-8165-5.  Google Scholar

[9]

Control Engineering Practice, 20 (2002), 618-628. doi: 10.1016/j.conengprac.2012.03.001.  Google Scholar

[10]

Springer, The Netherlands, 2005.  Google Scholar

[11]

Chemical Engineering Science, 54 (1999), 2715-2720. doi: 10.1016/S0009-2509(98)00375-3.  Google Scholar

[12]

M. E. Fisher and L. S. Jennings, MATLAB MISER,, , (): 483.   Google Scholar

[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. , ().   Google Scholar

[14]

Research Notes in Mathematics, Vol. 47, Pitman (Advance Publishing Program), London, 1981.  Google Scholar

[15]

Automatica, 24 (1988), 3-18. doi: 10.1016/0005-1098(88)90003-9.  Google Scholar

[16]

Journal of Optimization Theory and Applications, 26 (1978), 395-425. doi: 10.1007/BF00933463.  Google Scholar

[17]

Pacific Journal of Optimization, 6 (2010), 3157-3175.  Google Scholar

[18]

Annals of Operations Research, 98 (2000), 65-87. doi: 10.1023/A:1019235819716.  Google Scholar

[19]

Journal of the Franklin Institute, 339 (2002), 479-498. doi: 10.1016/S0016-0032(02)00028-5.  Google Scholar

[20]

the University of Western Australia, 2004. Google Scholar

[21]

Automatica, 26 (1990), 371-375. doi: 10.1016/0005-1098(90)90131-Z.  Google Scholar

[22]

Journal of Industrial and Management Optimization, 8 (2012), 591-609. doi: 10.3934/jimo.2012.8.591.  Google Scholar

[23]

Automatica, 48 (2012), 660-665. doi: 10.1016/j.automatica.2012.01.019.  Google Scholar

[24]

Journal of Optimization Theory and Applications, 154 (2012), 30-53. doi: 10.1007/s10957-012-0006-9.  Google Scholar

[25]

Journal of Optimization Theory and Applications, 134 (2007), 191-206. doi: 10.1007/s10957-007-9217-x.  Google Scholar

[26]

SIAM Journal on Numerical Analysis, in press, 2008. doi: 10.1137/060675034.  Google Scholar

[27]

North Holland, 1991.  Google Scholar

[28]

Journal of Optimization Theory and Applications, 49 (1986), 47-63. doi: 10.1007/BF00939247.  Google Scholar

[29]

Applied Mathematics and Computation, 224 (2013), 866-875. doi: 10.1016/j.amc.2013.08.092.  Google Scholar

[30]

Journal of Optimization Theory and Applications, 151 (2011), 260-291. doi: 10.1007/s10957-011-9904-5.  Google Scholar

[31]

Discrete and Continuous Dynamical Systems Series B, 16 (2011), 1101-1117. doi: 10.3934/dcdsb.2011.16.1101.  Google Scholar

[32]

International Journal of Innovative Computing, Information and Control, 6 (2010), 521-532. Google Scholar

[33]

Australian and New Zealand Industrial and Applied Mathematics Journal, 51 (2009), 162-177. doi: 10.1017/S1446181110000040.  Google Scholar

[34]

Acta Astronautica, 74 (2011), 131-140. doi: 10.1016/j.actaastro.2011.12.021.  Google Scholar

[35]

Cybernetics and Systems, 22 (1991), 1-16. doi: 10.1080/01969729108902267.  Google Scholar

[36]

Journal of Industrial and Management Optimization, 10 (2014), 275-309. doi: 10.3934/jimo.2014.10.275.  Google Scholar

[37]

Automatica, 45 (2009), 973-980. doi: 10.1016/j.automatica.2008.10.031.  Google Scholar

[38]

Automatica, 45 (2009), 2250-2257. doi: 10.1016/j.automatica.2009.05.029.  Google Scholar

[39]

IEEE Transactions on Automatic Control, 54 (2009), 2455-2460. doi: 10.1109/TAC.2009.2029310.  Google Scholar

[40]

Numerical Algebra, Control and Optimization, 2 (2012), 571-599. doi: 10.3934/naco.2012.2.571.  Google Scholar

[41]

Automatica, 49 (2013), 2652-2664. doi: 10.1016/j.automatica.2013.05.027.  Google Scholar

[42]

Pacific Journal of Optimization, 10 (2014), 537-560.  Google Scholar

[43]

Chapman & Hall/CRC, Boca Raton, 2000. doi: 10.1201/9781420036022.  Google Scholar

[44]

Chemical Engineering Journal, 75 (1999), 1-9. Google Scholar

[45]

World Scientific, 1994, 185pp. Google Scholar

[46]

MATLAB - The Language of Technical Computing, http://mathworks.com/products/matlab/,, 2008., ().   Google Scholar

[47]

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.  Google Scholar

[48]

Numerical Algorithms, 42 (2006), 165-169. doi: 10.1007/s11075-006-9035-5.  Google Scholar

[49]

Journal of Mathematical Analysis and Applications, 119 (1986), 21-54. doi: 10.1016/0022-247X(86)90142-3.  Google Scholar

[50]

Journal of Optimization Theory and Applications, 100 (1999), 1-13. Google Scholar

[51]

R. Petzold and A. C. Hindmarsh, LSODA, Ordinary Differential Equation Solver for Stiff or Non-Stiff System,, 2005., ().   Google Scholar

[52]

CRC Press, 1987. Google Scholar

[53]

Journal of Industrial and Management Optimization, 3 (2007), 331-348. doi: 10.3934/jimo.2007.3.585.  Google Scholar

[54]

Automatica, 18 (1982), 257-266. doi: 10.1016/0005-1098(82)90086-3.  Google Scholar

[55]

K. Schittkowski, NLPQLP: A new fortran implementation of a sequential quadratic programming algorithm for parallel computing,, 2010., ().   Google Scholar

[56]

A. L. Schwartz, RIOTS-A Matlab toolbox for solving general optimal control problems,, 2008. , ().   Google Scholar

[57]

Journal of Optimization Theory and Applications, 46 (1985), 265-293. doi: 10.1007/BF00939285.  Google Scholar

[58]

Springer, 2006.  Google Scholar

[59]

Longman Scientific and Technical, England, 1991.  Google Scholar

[60]

Journal of Australian Mathematical Society, Series B, 40 (1999), 314-335. doi: 10.1017/S0334270000010936.  Google Scholar

[61]

Automatica, 29 (1993), 789-792. doi: 10.1016/0005-1098(93)90076-6.  Google Scholar

[62]

Journal of Australian Mathematical Society, Series B, 33 (1992), 517-530. doi: 10.1017/S0334270000007207.  Google Scholar

[63]

IMA - Journal of Mathematical Control and Information, 6 (1989), 81-95. doi: 10.1093/imamci/6.1.81.  Google Scholar

[64]

Journal of Optimization Theory and Applications, 56 (1988), 145-156. doi: 10.1007/BF00938530.  Google Scholar

[65]

International Journal of Mechanical Sciences, 12 (1970), 973-983. doi: 10.1016/0020-7403(70)90037-8.  Google Scholar

[66]

in Proc. 2nd European Congress on Intelligent Techniques and Soft Computing (EUFIT) (H.J. Zimmermann ed.), Aachen, Germany, pp. 347-351, 1994. Google Scholar

[67]

Journal of Industrial and Management Optimization, 2 (2006), 435-450. doi: 10.3934/jimo.2006.2.435.  Google Scholar

[68]

Institute for Systems Research, University of Maryland, Technical Report SRC-TR-92-107r5, College Park, MD 20742. Google Scholar

[1]

Hui Xu, Guangbin Cai, Xiaogang Yang, Erliang Yao, Xiaofeng Li. Stereo visual odometry based on dynamic and static features division. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021059

[2]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399

[3]

Tobias Geiger, Daniel Wachsmuth, Gerd Wachsmuth. Optimal control of ODEs with state suprema. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021012

[4]

Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437

[5]

Lorenzo Freddi. Optimal control of the transmission rate in compartmental epidemics. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021007

[6]

Marzia Bisi, Maria Groppi, Giorgio Martalò, Romina Travaglini. Optimal control of leachate recirculation for anaerobic processes in landfills. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2957-2976. doi: 10.3934/dcdsb.2020215

[7]

Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183

[8]

Xiaohong Li, Mingxin Sun, Zhaohua Gong, Enmin Feng. Multistage optimal control for microbial fed-batch fermentation process. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021040

[9]

John T. Betts, Stephen Campbell, Claire Digirolamo. Examination of solving optimal control problems with delays using GPOPS-Ⅱ. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 283-305. doi: 10.3934/naco.2020026

[10]

Livia Betz, Irwin Yousept. Optimal control of elliptic variational inequalities with bounded and unbounded operators. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021009

[11]

Christian Meyer, Stephan Walther. Optimal control of perfect plasticity part I: Stress tracking. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021022

[12]

Shi'an Wang, N. U. Ahmed. Optimal control and stabilization of building maintenance units based on minimum principle. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1713-1727. doi: 10.3934/jimo.2020041

[13]

Changjun Yu, Lei Yuan, Shuxuan Su. A new gradient computational formula for optimal control problems with time-delay. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021076

[14]

Vladimir Gaitsgory, Ilya Shvartsman. Linear programming estimates for Cesàro and Abel limits of optimal values in optimal control problems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021102

[15]

Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521

[16]

Andrea Signori. Penalisation of long treatment time and optimal control of a tumour growth model of Cahn–Hilliard type with singular potential. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2519-2542. doi: 10.3934/dcds.2020373

[17]

Fabio Camilli, Serikbolsyn Duisembay, Qing Tang. Approximation of an optimal control problem for the time-fractional Fokker-Planck equation. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021013

[18]

Xianbang Chen, Yang Liu, Bin Li. Adjustable robust optimization in enabling optimal day-ahead economic dispatch of CCHP-MG considering uncertainties of wind-solar power and electric vehicle. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1639-1661. doi: 10.3934/jimo.2020038

[19]

Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021014

[20]

Bernard Bonnard, Jérémy Rouot. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model. Journal of Geometric Mechanics, 2021, 13 (1) : 1-23. doi: 10.3934/jgm.2020032

2019 Impact Factor: 1.366

Metrics

  • PDF downloads (129)
  • HTML views (0)
  • Cited by (3)

[Back to Top]