Document Type : Review Article

Authors

Departmen of Electrical Engineering, University of Science and Technology, Tehran, Iran

Abstract

Many real-world applications require minimization of a cost function. This function is the criterion that figures out optimality. In control engineering, this criterion is used in the design of optimal controllers. Cost function optimization has difficulties including calculating gradient function and lack of information about the system and the control loop. In this article, gradient memetic evolutionary programming is proposed for minimization of non-convex cost functions that have been defined in control engineering for the first time. Moreover, stability and convergence of the proposed algorithm are proved. Besides, it is modified to be used in online optimization. To achieve this, the sign of the gradient function is utilized. For calculating the sign of gradient, there is no need to know the cost function shape. The gradient function is estimated by the algorithm. The proposed algorithm is used to design a PI controller for nonlinear benchmark system CSTR (Continuous Stirred Tank Reactor) by online and off-line approaches.

Keywords

[1] B. D. Anderson, J. B. Moore, Linear Optimal Control, Prentice-Hall Inc, New Jersey, 1971.
[2] M. S. Arumugam, M. V. Rao, R. Palaniappan, “New Hybrid genetic operators for real coded genetic algorithm to compute optimal control of a class of hybrid systems”, Applied Soft Computing 6, 38-52, 2005.
[3] K. Nikolos, “EVolutionary algorithm based offline/online path planner for UAV navigation”, IEEE Transactions on systems, man, and Cybernetics, Vol 33, No 6, 898-912, 2003.
[4] P. J. Fleming, R. C. Purshouse, “Evolutionary algorithm in control systems engineering: a survey”, Control Engineering Practice 10, 1223-1241, 2002.
[5] R. L. Haupt, S. E. Haupt, Practical Genetic Algorithms, A John Wiley & Sons Inc., second edition, 2004.
[6] L. J. Fogel, Artificial intelligence through simulated evolution, Wiley, New York, 1966.
[7] I. Rechenberg, Evolutionsstrategie: optimierung technischer systeme nach PrinzISien der biologischen evolution, Frommann- Holzboog, Stuttgar, 1973.
[8] J. H. Holland, Adaptation in natural and artificial systems, University of Michigan Press, Ann Harbor, 1975.
[9] J. Koza, Genetic programming: on the programming of computers by means of natural selection, MIT Press, Cambridge, 1992.
[10] H. Narihisa, K. Kohmoto, T. Taniguchi, M. Ohta, K. Katayama, "Evolutionary Programming With Only Using Exponential Mutation", IEEE Congress on Evolutionary Computations, Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada July 16-21, 2006.
[11] X. Yao, Y. Liu, G. Lin, “Evolutionary Programming Made Faster”, IEEE Trans. on Evolutionary Computation, vol. 3,no. 2, 1999.
[12] H. Narihisa, K. Kohmoto, K. Katayama, “Evolutionary Programming with Double Exponential Probability Distribution”, Proc. of The Second International Association of Science and Technology for Development (IASTED) International Conference on Artificial Intelligence and Applications (AIA2002), pp.358-363, 2002.
[13] K. Kohmoto, H. Narihisa, K. Katayama, “Evolutionary Programming Using Exponential Mutation”, Proc. of the 6th World Multi conference on Systematics, Cybernetics and Informatics, vol.11, Computer Science 2, July 14-18, USA, pp.405-410, 2002.
[14] C.Y. Lee, Y. Song, “Evolutionary Programming using the Levy probability Distribution”, Proc. of Genetic and Evolutionary Computation Conference (GECCO’99), Morgan Kaufman, pp.886-893, 1999.
[15] Yo. Alipouri, J. Poshtan, Ya. Alipouri, M. R. Alipour, Momentum coefficient for promoting accuracy and convergence speed of evolutionary programming. Applied Soft Computing 12, 1765–1786, 2012.
[16] Yo. Alipouri, J. Poshtan, Ya. Alipouri, “A modification to classical evolutionary programming by shifting strategy parameters”, applied Intelligence, DOI 10.1007/s10489-012-0364-x, 2012.
[17] H. Einar, R.S. Phillips, Functional analysis and semi-groups, AMS Colloquium Publications, 31, American Mathematical Society, p. 300–327, 1957.
[18] W. Feller, An introduction to probability theory and its applications, Volume 2 (3rd ed.), Wiley, pp. 230–232, 1971.
[19] F. J. Doyle, A. Packard, M. Morari, “Robust controller design for a nonlinear CSTR”, Chemical Engineering Science 44, 1929-1947, 1989.
[20] T. D. Knapp, H.M. Budman, “Robust control design of non-linear processes using empirical state affine models”, Int. J. Control 73 (17), pp. 1525-1535, 2000.
[21] W. Yu, “Variance Analysis for Nonlinear Systems”, PHD thesis, Queen's University Kingston, Ontario, Canada October, 2007.