Article

Multidimensional Systems and Signal Processing

, Volume 24, Issue 4, pp 657-665

Open Access This content is freely available online to anyone, anywhere at any time.

On the existence of an optimal solution of the Mayer problem governed by 2D continuous counterpart of the Fornasini-Marchesini model

  • Dorota BorsAffiliated withFaculty of Mathematics and Computer Science, University of Lodz
  • , Marek MajewskiAffiliated withFaculty of Mathematics and Computer Science, University of Lodz Email author 

Abstract

In the paper the optimization problem described by some nonlinear hyperbolic equation being continuous counterpart of the Fornasini-Marchesini model is considered. A theorem on the existence of at least one solution to this hyperbolic PDE is proved and some properties of the set of all solutions are established. The existence of a solution to an optimization problem under appropriate assumptions is the main result of this paper. Some application of the obtained results to the process of gas filtration is also presented.

Keywords

Mayer problem Continuous counterpart of the Fornasini-Marchesini model Existence of optimal solutions