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Hereditary optimal control problems: Numerical method based upon a Padé approximation. (English) Zbl 0617.49013
We consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argument x(t-\(\tau)\). In our approximation scheme, we first replace the variable with an augmented state \(y(t)\underline\triangle x(t-\tau)\). The two-sided Laplace transform of y(t) is a product of the Laplace transform of x(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation for y(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four example problems are solved to illustrate the validity and usefulness of this technique.

90C52 Methods of reduced gradient type
34K35 Control problems for functional-differential equations
41A21 Padé approximation
44A10 Laplace transform
65K10 Numerical optimization and variational techniques
93B40 Computational methods in systems theory (MSC2010)
93C10 Nonlinear systems in control theory
Full Text: DOI
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