A Solution Method for an Optimal Controlled Vibrating Circle Shell by Measure and Classical Trajectory

Abstract:

Article Preview

The mean idea of this paper is to present a new combinatorial solution technique for the controlled vibrating circle shell systems. Based on the classical results of the wave equations on circle domains, the trajectory is considered as a finite trigonometric series with unknown coefficients in polar coordinates. Then, the problem is transferred to one in which its unknowns are a positive Radon measure and some positive coefficients. Extending the underlying space helps us to prove the existence of the solution. By using the density properties and some approximation schemes, the problem is deformed into a finite linear programming and the nearly optimal trajectory and control are identified simultaneously. A numerical example is also given.

Info:

Periodical:

Edited by:

Zhou Mark

Pages:

1855-1860

DOI:

10.4028/www.scientific.net/AMM.52-54.1855

Citation:

J.A. Fakharzadeh and F.N. Jafarpoor, "A Solution Method for an Optimal Controlled Vibrating Circle Shell by Measure and Classical Trajectory", Applied Mechanics and Materials, Vols. 52-54, pp. 1855-1860, 2011

Online since:

March 2011

Export:

Price:

$38.00

[1] Borzabadi, A. H., Farahi, M. H., Kamyad, A. V. and Mehne, H. H.: Optimal Control of the Heat Equation in an Inhomogeneous Body. Journal of Applied Mathematics and Computing. Springer, Berlin, Vol. 15, pp.127-146(2008).

DOI: 10.1007/bf02935750

[2] Conway, J. B.: A Course in Functional Analysis, University Of Tennessee, Springer(1990).

[3] Fakharzadeh, J. A. and Rubio, J.E.: Shape-Measure Method for Solving Elliptic Optimal Shape Problems, Bulletin of the Iranian Mathematical Society , Vol. 27, pp.41-64(2001).

[4] Fakharzadeh J., A.: Determining the best domain for a nonlinear wave system, JAMC J. of Applied Mathematics and computations, 1-2(13), pp.183-194(2003).

[5] Farahi, M. H., The Boundary Control of the Wave Equation. PhD thesis, Dept. of Applied Mathematical Studies, Leeds University, April (1996).

[6] Kamyad, A. V., Keyanpour, M. and Farahi, M. H.: A New Approach for Solving of Optimal Nonlinear Control Problems. Appl. Math. and Computations(2007).

[7] Kreyszing, E.: Advance Engineering Mathematics. John Wiley and Sons (4thedition)(1979).

[8] Mehne, H. H.: On Solving Constrained Shape Optimization Problems for Finding the Optimum Shape of a Bar Cross-Section. Elsevier Science Publishers B. V. Amesterdam, pp.1129-1141(2008).

DOI: 10.1016/j.apnum.2007.04.019

[9] Mikhailov, V. P.: Partial Differential Equations. MIR, Moscow(1978).

[10] Royden, H. L.: Real Analysis. Prentice-Hall, India, (3th edition)(2005).

[11] Rubio, J. E.: Control and Optimization: the linear treatment of nonlinear problems. Manchester University Press, Manchester, (1986).

[12] Rubio, J. E., The Global Control of Nonlinear Elliptic Equation. Journal of Franklin Institute, 1(330), pp.29-35(1993).

[13] Porbadakhshan, A. V., Kamyad, A. V., and Farahi, A. H. Numerical Solution of Nonlinear Wave Problems Applying Nonlinear Programming. WSEAS Tromactions on Circuits on Circuits and system, Vol. 147. pp.423-437(2004).

In order to see related information, you need to Login.