You are here

Hybridization of Neural Nets and Genetic Algorithms to Compute the Boundary Control for Controlled Heat Equation

Journal Name:

Publication Year:

AMS Codes:

Abstract (2. Language): 
This paper presents a computational method for boundary control of controlled heat equation. The proposed method relies upon the function approximation capability of feedforward neural network and global optimization power of genetic algorithm.
117-128

REFERENCES

References: 

[1] Y Arfiadi and M N S Hadi. Optimal Direct (Static) Output Feedback Controller using
Real Coded Genetic Algorithms. Computers and Structures, 79:1625–1634, 2001.
[2] C Carthel, R Glowinski, and J L Lions. On Exact and Approximate Boundary Controllabilities
for the Heat Equation: A Numerical Approach. Journal of Optimization Theory
and Applications, 82(2):429–484, 1994.
[3] W D Chang. Nonlinear System Identification and Control using a Real-Coded Genetic
Algorithm. Applied Mathematical Modelling, 31:541–550, 2007.
[4] J M Coron and E Trelat. Global Steady-state Controllability of One-dimensional Semilinear
Heat Equation. SIAM J. Control, 43(2):549–569, 2004.
[5] K Deep, K P Singh, M L Kansal, and C Mohan. A real coded genetic algorithm for solving
integer and mixed integer optimization problems. Applied Mathematics and Computation,
212(2):505–518, 2009.
[6] C Fabre, J P Puel, and E Zuazua. Approximate Controllability of the Semilinear Heat
Equation. Proceedings of the Royal Society of Edinburgh, 125A:31–61, 1995.
[7] P J Fleming and R C Purshouse. Evolutionary Algorithms in Control Systems Engineering:
A Survey. Control Engineering Practice, 10:1233–1241, 2002.
[8] A Friedman and L S Jiang. Nonlinear Optimal Control in Heat Conduction. SIAM Journal
on Control and Optimization, 21(6):940–951, 1983.
[9] R Glowinski. Boundary controllability problems for wave and heat equations. In J P
Zelensio, editor, Boundary Control and Boundary Variation, Lecture Notes in Control and
Information Sciences., volume 178, pages 221–237. Springer Verlag, Berlin, Germany,
1992.
[10] K Krishnakumar and D E Goldberg. Control System Optimization using Genetic Algorithms.
J Guidance, Control and Dynamics, 15(3):735–742, 1992.
[11] I E Lagaris, A C Likas, and D I Fotiadis. Artificial Neural Networks for Solving Ordinary
and Partial Differential Equations. IEEE Transactions on Neural Networks, 9(5):987–
1000, 1998.
[12] I E Lagaris, A C Likas, and D G Papageorgiou. Neural Network Methods for Boundary
Value Problems with Irregular Boundaries. IEEE Transactions on Neural Networks,
11(5):1041–1049, 2000.
[13] Z Michalewicz, C Z Janikow, and J B Krawczyk. A Modified Genetic Algorithm for
Optimal Control Problems. Computers Math. Applic., 23(12):83–94, 1992.
[14] M Sirbu. Feedback Null Controllability of the Semilinear Heat Equation. Differential and
Integral Equation, 15(1):115–128, 2002.
[15] N Sukavanam and V Panwar. Computation of boundary control of controlled heat equation
using artificial neural networks. Int. Comm. Heat Mass Transfer, 30(8):1137–1146,
2003.
[16] N Sukavanam and N K Tomar. Approximate Controllability of Semilinear Delay Control
Systems. Nonlinear Functional Analysis and Applications, 12(1):53–59, 2007.
[17] L D Teresa. Approximate Controllability of a Semilinear Heat Equation. SIAM Journal
on Control and Optimization, 36(6):2128–2147, 1998.
[18] Y Yamashita and M Shima. Numerical Computational Method using Genetic Algorithm
for the Optimal Control Problem with Terminal Constraints and Free Parameters. Nonlinear
Analysis, Theory, Method and Applications, 30(4):2285–2290, 1997.
[19] H X Zhou. A Note on Approximate Controllability for Semilinear One-dimensional Heat
Equation. Appl. Math. Optim., 8:275–285, 1982.

Thank you for copying data from http://www.arastirmax.com