In handling textile materials, deformation is very common and is unavoidable. When the fabrics are dispatched for further feature extractions, it's necessary to recover the original shape for comparison with a standard template. This recovery problem is investigated in this paper. By introducing a set of recovered functions, the problem is formulated as a combined optimal control and optimal parameter selection problem, governed by the dynamical system of a set of two-dimensional control functions. After parameterization of the control functions, the problem is transformed into a nonlinear optimization problem, where gradient based optimization methods can be applied. We also analyze the convergence of the parameterization method. Several numerical examples are used to demonstrate the method.
|Number of pages||15|
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|Publication status||Published - 1 Nov 2011|
- Two-dimensional control function
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics