A space of filters for the consistent initialization of differential-algebraic equations in optimization tasks

Abstract

In this article, a new approach to determining consistent initial conditions for an optimization task with differential-algebraic equations (DAEs) is presented. The work is motivated by the fact that initial conditions have a significant impact on both the obtained state trajectories, as well as the progress of the optimization procedure. In the first step of the designed approach, an α-parametrization of the DAE model takes place. This gives the possibility of influencing the dynamics of the system, and in particular its total reduction. When the initial values of the differential state variables are given, then the solution of the DAE system depends only on the algebraic state variables and the input function, which should have the character of the consistent initial conditions. To obtain the consistent initial conditions and, at the same time, to optimize the considered process, in the second step of the procedure a filter space is defined and applied. The filter space is an innovative extension of Fletcher's filter method. It is built from a finite number of filters, and the dimension of the filter space depends on the input function parametrization approach. As a result of using the filter space, it is possible to obtain a reasonable initial solution to the whole optimization problem, which can be improved by available exact local algorithms. The operation of the new method is tested in the heat and mass transfer optimization task, which is described by a system of nonlinear differential-algebraic equations.