keywords: Cost functional, nodal points, optimal control, optimal state, wave equation
The fourier solution proposed by Duchateau and Zachmann for deriving the general equations for states and controls was applied to the problems of one dimensional quadratic functionalMin ∫ [z,u] =Min 01 01 dxdt and the finite element technique used on the resulting system to obtain the states, controls and the cost functional at different levels of discretization up to ten nodal points. The numerical solutions depict increase in the cost functional as the space dimension increases while as the number of elements increase, the controls get smaller among other things.
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