Studies in approximation methods—I: Splines and control via discrete dynamic programming |
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Authors: | Irving Birnbaum Leon Lapidus |
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Affiliation: | Department of Chemical Engineering, Princeton University, Princeton, NJ 08540, U.S.A. |
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Abstract: | A novel approach is suggested for alleviating the curse of dimensionality in discrete dynamic programming as applied to optimal control problems. By using multidimensional B-splines to approximate the overall minimum objective and optimal control function, a significant reduction of computer storage is made. The ease and accuracy of this approach is demonstrated on a two-dimensional control problem. Extensions of this procedure are also proposed that result in increased accuracy. |
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