Skip to main content
SpringerLink
Log in

Dynamic Programming: Optimal Control Applications

  • Reference work entry
Encyclopedia of Optimization

Article Outline

Keywords

Optimal Control Problem

Iterative Dynamic Programming

Early Applications of IDP

Choice of Candidates for Control

Piecewise Linear Continuous Control

Algorithm for IDP

Time-Delay Systems

State Constraints

Singular Control Problems

Sensitivity of Control Policy

Use of Variable Stage-Lengths

Nonseparable Problems

Future Directions

See also

References

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bellman R (1957) Dynamic programming. Princeton Univ. Press, Princeton

    Google Scholar 

  2. Bellman R, Dreyfus S (1962) Applied dynamic programming. Princeton Univ. Press, Princeton

    MATH  Google Scholar 

  3. Bojkov B, Luus R (1992) Use of random admissible values for control in iterative dynamic programming. Ind Eng Chem Res 31:1308–1314

    Article  Google Scholar 

  4. Bojkov B, Luus R (1993) Evaluation of the parameters used in iterative dynamic programming. Canad J Chem Eng 71:451–459

    Google Scholar 

  5. Bojkov B, Luus R (1994) Time-optimal control by iterative dynamic programming. Ind Eng Chem Res 33:1486–1492

    Article  Google Scholar 

  6. Bojkov B, Luus R (1995) Time optimal control of high dimensional systems by iterative dynamic programming. Canad J Chem Eng 73:380–390

    Article  Google Scholar 

  7. Bojkov B, Luus R (1996) Optimal control of nonlinear systems with unspecified final times. Chem Eng Sci 51:905–919

    Article  Google Scholar 

  8. Dadebo S, Luus R (1992) Optimal control of time-delay systems by dynamic programming. Optimal Control Appl Meth 13:29–41

    Article  MATH  MathSciNet  Google Scholar 

  9. Dadebo SA, McAuley KB (1995) Dynamic optimization of constrained chemical engineering problems using dynamic programming. Comput Chem Eng 19:513–525

    Article  Google Scholar 

  10. DeTremblay M, Luus R (1989) Optimization of non-steady-state operation of reactors. Canad J Chem Eng 67:494–502

    Google Scholar 

  11. Hartig F, Keil FJ, Luus R (1995) Comparison of optimization methods for a fed-batch reactor. Hungarian J Ind Chem 23:141–148

    Google Scholar 

  12. Lapidus L, Luus R (1967) Optimal control of engineering processes. Blaisdell, Waltham, pp 84–86

    Google Scholar 

  13. Li D, Haimes YY (1990) New approach for nonseparable dynamic programming problems. JOTA 66:311–330

    Article  MathSciNet  Google Scholar 

  14. Luus R (1989) Optimal control by dynamic programming using accessible grid points and region reduction. Hungarian J Ind Chem 17:523–543

    Google Scholar 

  15. Luus R (1990) Application of dynamic programming to high-dimensional nonlinear optimal control problems. Internat J Control 52:239–250

    Article  MATH  MathSciNet  Google Scholar 

  16. Luus R (1990) Optimal control by dynamic programming using systematic reduction in grid size. Internat J Control 19:995–1013

    Article  MathSciNet  Google Scholar 

  17. Luus R (1991) Application of iterative dynamic programming to state constrained optimal control problems. Hungarian J Ind Chem 19:245–254

    Google Scholar 

  18. Luus R (1991) Effect of the choice of final time in optimal control of nonlinear systems. Canad J Chem Eng 69:144–151

    Article  Google Scholar 

  19. Luus R (1992) On the application of iterative dynamic programming to singular optimal control problems. IEEE Trans Autom Control 37:1802–1806

    Article  MATH  MathSciNet  Google Scholar 

  20. Luus R (1993) Application of dynamic programming to differential-algebraic process systems. Comput Chem Eng 17:373–377

    Article  Google Scholar 

  21. Luus R (1993) Application of iterative dynamic programming to very high-dimensional systems. Hungarian J Ind Chem 21:243–250

    Google Scholar 

  22. Luus R (1993) Optimization of fed-batch fermentors by iterative dynamic programming. Biotechnol and Bioengin 41:599–602

    Article  Google Scholar 

  23. Luus R (1993) Piecewise linear continuous control by iterative dynamic programming. Ind Eng Chem Res 32:859–865

    Article  Google Scholar 

  24. Luus R (1994) Optimal control of batch reactors by iterative dynamic programming. J Process Control 4:218–226

    Article  Google Scholar 

  25. Luus R (1995) Sensitivity of control policy on yield of a fed-batch reactor. Proc. IASTED Internat. Conf. on Modelling and Simulation, Pittsburgh, PA, April 27-29, 1995, pp 224–226

    Google Scholar 

  26. Luus R (1996) Numerical convergence properties of iterative dynamic programming when applied to high dimensional systems. Chem Eng Res Des 74:55–62

    Google Scholar 

  27. Luus R (1996) Use of iterative dynamic programming with variable stage lengths and fixed final time. Hungarian J Ind Chem 24:279–284

    Google Scholar 

  28. Luus R (1997) Application of iterative dynamic programming to optimal control of nonseparable problems. Hungarian J Ind Chem 25:293–297

    Google Scholar 

  29. Luus R (1997) Use of iterative dynamic programming for optimal singular control problems. Proc. IASTED Internat. Conf. on Control, Cancun, Mexico, May 28-31, 1997, pp 286–289

    Google Scholar 

  30. Luus R (1997) Use of variable stage-lengths for constrained optimal control problems. Hungarian J Ind Chem 25:299–304

    Google Scholar 

  31. Luus R (1998) Direct approach to time optimal control by iterative dynamic programming. Proc. IASTED Internat. Conf. on Intelligent Systems and Control, Halifax, Nova Scotia, Canada, June 1-4, 1998, pp 121–125

    Google Scholar 

  32. Luus R (1998) Iterative dynamic programming: from curiosity to a practical optimization procedure. Control and Intelligent Systems 26:1–8

    Google Scholar 

  33. Luus R (2000) Iterative dynamic programming. Chapman and Hall/CRC, London

    MATH  Google Scholar 

  34. Luus R, Bojkov B (1994) Global optimization of the bifunctional catalyst problem. Canad J Chem Eng 72:160–163

    Google Scholar 

  35. Luus R, Dittrich J, Keil FJ (1992) Multiplicity of solutions in the optimization of a bifunctional catalyst blend in a tubular reactor. Canad J Chem Eng 70:780–785

    Google Scholar 

  36. Luus R, Galli M (1991) Multiplicity of solutions in using dynamic programming for optimal control. Hungarian J Ind Chem 19:55–62

    Google Scholar 

  37. Luus R, Jaakola THI (1973) Optimization by direct search and systematic reduction of the size of search region. AIChE J 19:760–766

    Article  Google Scholar 

  38. Luus R, Okongwu ON (1999) Towards practical optimal control of batch reactors. Chem Eng 75:1–9

    Article  Google Scholar 

  39. Luus R, Rosen O (1991) Application of iterative dynamic programming to final state constrained optimal control problems. Ind Eng Chem Res 30:1525–1530

    Article  Google Scholar 

  40. Luus R, Smith SG (1991) Application of dynamic programming to high-dimensional systems described by difference equations. Chem Eng Techn 14:122–126

    Article  Google Scholar 

  41. Luus R, Storey C (1997) Optimal control of final state constrained systems. Proc. IASTED Internat. Conf. on Modelling, Simulation and Control, Singapore, Aug. 11-13, 1997, pp 245–249

    Google Scholar 

  42. Luus R, Tassone V (1992) Optimal control of nonseparable problems by iterative dynamic programming. Proc. 42nd Canad. Chemical Engin. Conf., Toronto, Canada, October, 18-21, 1992, pp 81–82

    Google Scholar 

  43. Luus R, Zhang X, Hartig F, Keil FJ (1995) Use of piecewise linear continuous control for time-delay systems. Ind Eng Chem Res 34:4136–4139

    Article  Google Scholar 

  44. Marroquin G, Luyben WL (1973) Practical control studies of batch reactors using realistic mathematical models. Chem Eng Sci 28:993–1003

    Article  Google Scholar 

  45. Mekarapiruk W, Luus R (1997) Optimal control of final state constrained systems. Canad J Chem Eng 25:806–811

    Google Scholar 

  46. Mekarapiruk W, Luus R (1997) Optimal control of inequality state constrained systems. Ind Eng Chem Res 36:1686–1694

    Article  Google Scholar 

  47. Tassone V, Luus R (1993) Reduction of allowable values for control in iterative dynamic programming. Chem Eng Sci 48:3864–3867

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department Chemical Engineering, University Toronto, Toronto, Canada

    Rein Luus

Authors
  1. Rein Luus
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Luus, R. (2008). Dynamic Programming: Optimal Control Applications . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_151

Download citation

Publish with us

Policies and ethics

Search

Navigation