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Research Papers

Symbolic and Numeric Computation of Optimal Initial Velocity in a Wave Equation

[+] Author and Article Information
Yeşim Saraç

Atatürk Üniversitesi,
Fen Fakültesi,
Matematik Bölümü,
25240, Erzurum, Turkeye-mail: ysarac@atauni.edu.tr

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 3, 2011; final manuscript received April 13, 2012; published online August 31, 2012. Assoc. Editor: Carmen M. Lilley.

J. Comput. Nonlinear Dynam 8(1), 011018 (Aug 31, 2012) (4 pages) Paper No: CND-11-1125; doi: 10.1115/1.4006786 History: Received August 03, 2011; Revised April 13, 2012

We get symbolic and numeric solutions developing a MAPLE® program which uses the initial velocity on the state variable of a wave equation as control function. Solution of this problem implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and a given target. An iterative algorithm is constructed to compute the required optimal control as the limit of a suitable subsequence of controls. Results are tested with some numerical examples.

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Figures

Grahic Jump Location
Fig. 1

The graphs of Jα1(ψ*) and Jα2(ψ*) for different α

Grahic Jump Location
Fig. 2

The graphs of Jα1(ψ*) and Jα2(ψ*) for different α

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