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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.

MSC:
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
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