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:
http://dx.doi.org/10.1007/BF00938531
Permalink