Optimal control and numerical software: An overview

Systems Theory: Perspectives, Applications and Developments

Volumn , Issue , 2014, Pages 93-110

  Rodrigues, Helena Sofia ^a   Monteiro, M Teresa T ^b   Torres, Delfim F M ^c  

^a INSTITUTO POLITÉCNICO DE VIANA DO CASTELO   (Portugal)

^b UNIVERSITY OF MINHO   (Portugal)

^c UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Direct methods; Indirect methods; Numerical software; Pptimal control; Rubella

Indexed keywords

EID: 84919381995     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (39)

1. Bryson Jr., A. E. (1996). Optimal control 1950 to 1985. IEEE Control Systems Magazine, 26-33.
2. Sussmann, H. J., Willems, J. C. (1997). 300 years of optimal control: from the Brachystochrone to the Maximum Principle. IEEE Control Systems Magazine, 32-44.
3. Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., Mishchenko, E. F. (1962). The Mathematical Theory of Optimal Processes. Translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt. Interscience Publishers John Wiley & Sons, Inc. New York-London.
4. Leitmann, G. (1997). The calculus of variations and optimal control. An introduction. Mathematical Concepts and Methods in Science and Engineering 24, New York:Plenum Press.
5. Kirk, D. E. (1998). Optimal Control Theory: An Introduction. Dover Publications.
6. Goh, B. S. (July 2008). Optimal singular rocket and aircraft trajectories. In: Control and Decision Conference 2008 (CCDC 2008), 1531-1536.
7. Molavi, R., Khaburi, D. A. (2008). Optimal control strategies for speed control of permanent-magnet synchronous motor drives. In: Proceedings of World Academy of Science, Engineering and Technology, 44, 428-432.
8. Bonnard, B., Janin, G. (2008). Geometric orbital transfer using averaging techniques. J. Dyn. Control Syst., 14(2), 145-167.
9. Hermant, A. (2010). Optimal control of the atmospheric reentry of a space shuttle by an homotopy method. Optimal Control Applications and Methods, 32(6), 627-646.
10. Munteanu, I., Bratcu, A. I., Cutululis, N. A., Ceanga, E. (2008). Optimal Control of Wind Energy Systems: Towards a Global Approach. Volume XXII of Advances in Industrial Control. Springer.
11. Sun, Z., Li, S. (2008). Optimal control of dynamic investment on inventory with stochastic demand. In: Control and Decision Conference, 2008 (CCDC 2008), 3200-3203.
12. Joshi, H. R. (2002). Optimal control of an HIV immunology model. Optimal Control Appl. Methods, 23(4), 199-213.
13. Joshi, H. R., Lenhart, S., Li,M. Y.,Wang, L. (2006). Optimal control methods applied to disease models. In: Mathematical studies on human disease dynamics. Volume 410 of Contemp. Math., 187-207. Amer. Math. Soc., Providence, RI.
14. Lenhart, S., Workman, J. T. (2007). Optimal Control Applied to Biological Models. Chapman & Hall/CRC Mathematical and Computational Biology Series. Chapman & Hall/CRC, Boca Raton, FL.
15. Nanda, S., Moore, H., Lenhart, S. (2007). Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Math. Biosci., 210(1), 143-156.
16. Chachuat, B. (2007). Nonlinear and Dynamic Optimization: From Theory to Practice. Automatic Control Laboratory, EPFL, Switzerland.
17. Zabczyk, J. (2008). Mathematical Control Theory. Modern Birkhäuser Classics. Birkhäuser Boston Inc., Boston, MA. Reprint of the 1995 edition.
18. Lewis, F. L., Syrmos, V. L. (1995). Optimal Control. Wiley: New York, 2nd ed edition.
19. Clarke, F. H. (1990). Optimization and Nonsmooth Analysis, volume 5 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, second edition.
20. Fleming, W. H., Rishel, R. W. (1975). Deterministic and Stochastic Optimal Control. Springer-Verlag.
21. Kamien, M. I., Schwartz, N. L. (1991). Dynamic Optimization: The Calulus of Variations and Optimal Control in Economics and Management. North-Holland.
22. Macki, J., Strauss, A. (1982). Introduction to Optimal Control Theory. Springer-Verlag.
23. Sarychev, A. V., Torres, D. F. M. (2000). Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics. Appl. Math. Optim., 41(2), 237-254.
24. Torres, D. F. M. (2003). Lipschitzian regularity of the minimizing trajectories for nonlinear optimal control problems. Math. Control Signals Systems, 16(2-3), 158-174.
25. Buonomo, B. (2011). On the optimal vaccination strategies for horizontally and vertically transmitted infectious diseases. Journal of Biological Systems, 19(2), 263-279.
26. Wang., X. (2009). Solving optimal control problems with MATLAB: Indirect methods. Technical report, ISE Dept., NCSU.
27. Houcque, D., Applications of MATLAB: Ordinary differential equations (ODE). Technical report, Robert R. McCormick School of Engineering and Applied Science-Northwestern University, Evanston.
28. Rodrigues, H. S. https://sites.google.com/site/hsofiarodrigues, PhD codes, 2012.
29. Betts, J. (2001). Practical Methods for Optimal Control Using Nonlinear Programming. SIAM: Advances in Design and Control.
30. Gerdts, M. (May 2009). User's guide OC-ODE (version 1.4). Technical report, Universit ät Würzburg.
31. Hirmajer, T., Balsa-Canto, E., Banga, J. R. (2009). DOTcvpSB, a software toolbox for dynamic optimization in systems biology. Bioinformatics, 10, 199-213.
32. Hindmarsh, A. C., et al. (2005). Sundials: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software, 31(3), 363-396.
33. NEOS. http://neos.mcs.anl.gov/neos.
34. Kühl, P., et al. (June 2007). MUSCOD-II Users Manual. University of Heidelberg.
35. Fourer, R., Gay, D. M., Kernighan, B. W. (2002). AMPL: A Modeling Language for Mathematical Programming. Duxbury Press/Brooks/Cole Publishing Company.
36. Wächter, A., Biegler, L. T. (2006). On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming:Series A and B, 106(1), 25-57.
37. Byrd, R. H., Nocedal, J., Waltzy, R. A. (2006). Large-Scale Nonlinear Optimization, chapter Knitro: An Integrated Package for Nonlinear Optimization, 35-59. Springer-Verlag.
38. Gill, P. E., Murray, M. A., Sauders, W. (2005). Snopt: An SQP algorithm for largescale constrained optimization. SIAM, 47(1), 99-131.
39. Rao, A. V. (2009). A survey of numerical method for optimal control. Technical Report AAS, 09-334, Dep. of Mechanical and Aerospace Engineering, University of Florida.