A Method for Solving Optimal Control Problems Using Genetic Programming

Authors

Department of Mathematics, Gomishan Center, Gorgan Branch, Islamic Azad University, Gomishan, Iran.

Abstract

This paper deals with a novel method for solving optimal control problems based on genetic programming. This approach produces some trial solutions and seeks the best of them. If the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. Using numerical examples, we will demonstrate how to use the results.

Keywords


1. A. Brabazon, M.O. Neill, A grammar model for foreign-exchange trading, in Proceedings of the International conference on Artificial Intelligence, volume II, H. R. Arabnia et al. (eds.), CSREA Press, 492-498, 23-26 June (2003).

2. DN. Burghes, A. Graham, Introduction to Control Theory, Including Optimal Control, E. Horwood, Halsted Press, New Yourk (1980).

3. J.J. Collins, C. Ryan, Automatic generation of robot behaviors using grammatical evolution, in Proc. of AROB 2000, the Fifth International Symposium on Artificial Life and Robotics (2000).

4. O.S. Fard and A.H. Borzabadi, Optimal control problem, quasi-assignment problem and genetic algorithm, Proc. World. Acad. Sci. Eng. Tech., 21, 70-73 (2007).

5. M. Keyanpour, M. Azizsefat, Numerical solution of optimal control problems by an iterative scheme, Advanced Modeling and Optimization, 13(1), 25-37 (2011).

6. J.R. Koza, Genetic Programming: On the Programming of Computer by Means of Natural Selection, MIT Press, Cambridge, MA (1992).

7. M.O. Neill, Automatic Programming in an Arbitrary Language: Evolving Programs with Grammatical Evolution, PhD Thesis, University Of Limerick, Ireland, August (2001).

8. M.O. Neill, C. Ryan, Grammatical Evolution: Evolutionary Automatic Programming in a Arbitrary Language, Volume 4 of Genetic programming, Kluwer Academic Publishers (2003).

9. M.O. Neill, C. Ryan, Grammatical evolution, IEEE Trans. Evolutionary Computation, 5, 349-358 (2001).

10. C. Ryan, J.J. Collins, and M.O. Neill, Evolving programs for an arbitrary language, in Proceedings of the First European Workshop on Genetic Programming, volume 1391 of LNCS, W. Banzhaf, Ri. Poli, M. Schoenauer and T.C. Fogarty, (eds.), Springer-Verlag, 83{95, Paris, 14-15 April (1998).

11. M.O. Neill, J.J. Collins, and C. Ryan, Automatic generation of caching algorithms, in Evolutionary Algorithms in Engineering and Computer Science, Kaisa Miettinen, Marko M. Mkel, Pekka Neittaanmki, and Jacques Periaux (eds.), 127-134, Jyvskyl, Finland, 30 May-3 June (1999).

12. C. Ryan, M.O. Neill, and J.J. Collins, Grammatical evolution: Solving trigonometric identities, in Proceedings of Mendel 1998: 4th International Mendel Conference on Genetic Algorithms, Optimization Problems, Fuzzy Logic, Neural Networks, Rough Sets., Technical University of Brno, Faculty of Mechanical Engineering, 111{119, Brno, Czech Republic, June 24-26 (1998).

13. I.G. Tsoulos, I.E. Lagaris, Solving differential equations with genetic programming, Genetic Programming and Evolvable Machines, 7(1), 33-54 (2006).