Hereditary optimal control problems: Numerical method based upon a padé approximation
| ISSN: |
1573-2878
|
|---|---|
| Keywords: |
Padé approximation ; hereditary optimal control problems ; nonlinear time-lag systems ; computational schemes ; two-sided Laplace transform ; gradient algorithms
|
| Source: |
Springer Online Journal Archives 1860-2000
|
| Topics: |
Mathematics
|
| Notes: |
Abstract In this paper, 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 argumentx(t − τ). In our approximation scheme, we first replace the variable with an augmented statey(t) ≜x(t - τ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(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 problems are solved to illustrate the validity and usefulness of this technique.
|
| Type of Medium: |
Electronic Resource
|
| URL: |