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A Probabilistic Algorithm for Optimal Control Problem

by Akbar Banitalebi, Mohd Ismail Abd Aziz, Rohanin Ahmad
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 46 - Number 8
Year of Publication: 2012
Authors: Akbar Banitalebi, Mohd Ismail Abd Aziz, Rohanin Ahmad
10.5120/6932-9298

Akbar Banitalebi, Mohd Ismail Abd Aziz, Rohanin Ahmad . A Probabilistic Algorithm for Optimal Control Problem. International Journal of Computer Applications. 46, 8 ( May 2012), 48-55. DOI=10.5120/6932-9298

@article{ 10.5120/6932-9298,
author = { Akbar Banitalebi, Mohd Ismail Abd Aziz, Rohanin Ahmad },
title = { A Probabilistic Algorithm for Optimal Control Problem },
journal = { International Journal of Computer Applications },
issue_date = { May 2012 },
volume = { 46 },
number = { 8 },
month = { May },
year = { 2012 },
issn = { 0975-8887 },
pages = { 48-55 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume46/number8/6932-9298/ },
doi = { 10.5120/6932-9298 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:39:44.967211+05:30
%A Akbar Banitalebi
%A Mohd Ismail Abd Aziz
%A Rohanin Ahmad
%T A Probabilistic Algorithm for Optimal Control Problem
%J International Journal of Computer Applications
%@ 0975-8887
%V 46
%N 8
%P 48-55
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper we present a direct method for the numerical solution of the constrained optimal control problem when the gradient information is not available. At this aim, a new control parameterization based on Bernstein basis functions is suggested to convert control problem into nonlinear programing problem (NLP), and then a recently proposed stochastic algorithm called Probabilistic Global Search Johor (PGSJ) is considered for the solution of resultant NLP. The underlining idea of the PGSJ algorithm is to use probability density functions (PDF) to direct the search while no recombination operator is used. This algorithm along with the new Bernstein-based control parameterization (BCP) is compiled into BCP/PGSJ direct method to be applied to approximate the solution of the control problem up to the accuracy required. This method is lastly implemented while simulating some case studies which illustrate the efficiency of the method.

References
  1. Bellman, R. E. 1957. Dynamic Programming. Princeton University Press, New Jersey.
  2. Howard, R. A. 1960. Dynamic programming and Markova processes. The MIT Press, Massachusetts.
  3. Bellman, R. 1971. Introduction to mathematical theory of control processes. vol. 2. Academic Press, New York.
  4. Luus, R. 2000. Iterative Dynamic Programming. Chapman and Hall CRC Press, Florida.
  5. Pontryagin, L. S. , Boltyanskii, V. G. , Gamkrelidze, R. V. , and Mischenko, E. F. 1962. The mathematical theory of optimal processes (Translation by Neustadt L. W. ). Macmillan, New York.
  6. Hartl, R. F. 1984. A survey of the optimality conditions for optimal control problems with state variable inequality constraints. In Brans, J. P. (Ed. ) Operational research '84. (pp. 423-433). North-Holland, Amsterdam.
  7. Hartl, R. F. , Sethi, S. P. , and Vickson, R. G. 1995. A Survey of the Maximum Principles for Optimal Control Problems with State Constraints. SIAM Review, 37(2), 181-218.
  8. Carrillo-Ureta, G. E. , Roberts, P. D. , and Becema, V. M. 2001. Genetic algorithms for optimal control of beer fermentation. Proceedings of the 2001 IEEE, International Symposium on Intelligent Control September 5-7, 2001 Mexico City, Mexico.
  9. GirirajKumar, S. M. , Rakesh, B. , Anantharaman, N. 2010. Design of controller using simulated annealing for a real time process. International Journal of Computer Applications, 6(2), 20–25.
  10. Babaeizadeh, S. , Banitalebi, A. , Rohanin, A. , and Mohd-Ismail B. A. A. 2011. An ant colony approach to optimal control problem. International Seminar on the Application of Science & Mathematics 2011. PWTC, Kuala Lumpur, Malaysia.
  11. Ali, M. M. , Khompatraporn, C. , and Zabinsky, Z. B. 2005. A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems. Journal of Global Optimization, 31, 635–672.
  12. Modares, H. , Sistani, M. B. N, 2011. Solving nonlinear optimal control problems using a hybrid IPSO–SQP algorithm. Engineering Applications of Artificial Intelligence, 24, 476–484.
  13. Kumar, R. K. , Anand, S. and Sydulu, M. 2012. A Novel Multi agent based PSO approaches for security Constrained Optimal Power Flows using smooth and non-smooth cost functions. International Journal of Computer Applications, 41(3), 14-21.
  14. Cruz, I. L. L. , Willigenburg, L. G. V. , and Straten, G. V. 2003. Efficient Differential Evolution algorithms for multimodal optimal control problems. Applied Soft Computing, 3, 97–122.
  15. Sun, D. Y. , Lin, P. M. , Lin, S. P. 2008. Integrating controlled random search into the line-up competition algorithm to solve unsteady operation problems. Industrial & Engineering Chemistry Research, 47, 8869–8887.
  16. Ghosh, A. , Das, S. , Chowdhury, A. , Giri, R. 2011. An ecologically inspired direct search method for solving optimal control problems with Bezier parameterization. Engineering Applications of Artificial Intelligence, 24, 1195–1203.
  17. Banitalebi, A. , Mohd-Ismail B. A. A. , and Rohanin, A. 2011. A new probabilistic global search algorithm. Regional Annual Fundamental Science Symposium 2011, Thistle Hotel, Johor, Malaysia.
  18. Biegler, L. T. 2007. An overview of simultaneous strategies for dynamic optimization. Chemical Engineering and Processing, 46, 1043–1053.
  19. Loxton. R. C. , Teo, K. L. Rehbock, V. , and Yiu, K. F. C. , 2009. Optimal control problems with a continuous inequality constraint on the state and the control. Automatica, 45, 2250-2257.
  20. Goh. J. , Teo, K. L. , 1988. Control parameterization: a unified approach to optimal control problems with general constraints. Automatica, 24(1), 3–18.
  21. Vlassenbroeck, J. 1988. A Chebyshev Polynomial Method for Optimal Control with State Constraints. Automatica, ( 24) 4, 499-506.
  22. Schlegel, M. , Stockmann, K. , Binder, T. , Marquardt, W. 2005. Dynamic optimization using adaptive control vector parameterization. Computers and Chemical Engineering (29) 1731–1751.
  23. Biegler, L. , 1984. Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation. Computers and Chemical Engineering. 8 (3–4), 243–248.
  24. Sadek, I. , Abualrub, T. , Abukhaled, M. 2007. A computational method for solving optimal control of a system of parallel beams using Legendre wavelets. Mathematical and Computer Modeling, 45, 1253–1264.
  25. Farouki, R. T. , and Rajan, V. T. l988. Algorithms for polynomials in Bernstein form. Computer Aided Geometric Design, 5, l-26.
  26. Tsitouras, Ch. 2011. Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption. Computers and Mathematics with Applications. 62, 770-775.
  27. Lenhart, S. and Workman, J. T. 2007. Optimal control applied to biological models. Mathematical and Computational Biology Series. Chapman and Hall, CRC Press, Boca Raton.
  28. Kirk, D. E. 1970. Optimal Control Theory: An Introduction. Prentice Hall Inc. New Jersey.
  29. Floudas, Christodoulos A. 1999. Handbook of test problems in local and global optimization. Kluwer Academic Publishers. Dordrecht.
  30. Neuman, C. P. and Sen, A. 1973. A suboptimal control algorithm for constrained problems using cubic splines. Automatica, 9, 601.
Index Terms

Computer Science
Information Sciences

Keywords

Optimal Control Problem Constraints Direct Methods Stochastic Algorithm.

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