Multidimensional Systems and Signal Processing

, Volume 24, Issue 4, pp 657–665

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

Open AccessArticle

DOI: 10.1007/s11045-012-0207-2

Cite this article as:
Bors, D. & Majewski, M. Multidim Syst Sign Process (2013) 24: 657. doi:10.1007/s11045-012-0207-2


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.


Mayer problemContinuous counterpart of the Fornasini-Marchesini modelExistence of optimal solutions
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Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceUniversity of LodzLodzPoland