On the existence of an optimal solution of the Mayer problem governed by 2D continuous counterpart of the Fornasini-Marchesini model
- 605 Downloads
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.
KeywordsMayer problem Continuous counterpart of the Fornasini-Marchesini model Existence of optimal solutions
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
- Cesari L. (1983) Optimization—theory and application. Springer, BerlinGoogle Scholar
- Fornasini, E.& Marchesini, G. (1976). State space realization of two dimensional filters. IEEE Transactions on Automatic Control, AC-21(4), 484–491.Google Scholar
- Fornasini, E. & Marchesini, G. (1978/1979). Doubly-indexed dynamical systems: State-space models and structural properties. Mathematical Systems Theory, 12, 59–72.Google Scholar
- Kisielewicz, M. (1991). Differential inclusions and optimal control, volume 44. Kluwer, Dordrecht, Boston, London, Higher School of Engineering, Zielona Góra, Poland.Google Scholar
- Tikhonov A. N., Samarski A. A. (1990) Equations of mathematical physics. Dover Publications, Inc., New YorkGoogle Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.