OPTIMAL CONTROL OF A TWO-DIMENSIONAL RICHARDS-KLUTE EQUATION
Abstract
This article demonstrates an approach to optimal control of humidity using point sources for the two-dimensional problem. The mathematical model is based on Richards-Klute equation. The desired humidity state at the last moment is set and the solution should reach it from the known initial state by optimal source power. The moisture is assumed incompressible, the temperature and external pressure are constant.
References
Pullan A. J. The Quasilinear Approximation for Unsaturated Porous Media Flow. Water resources research. 1990. Vol. 26. No. 6. P. 1219-1234.
Novoselskiy S. N. Solution of some Boundary Value Problems of Moisture Transport with Irrigation Sources. Candidate thesis in Mathematics and Physics: 01.02.05. Kalinin Polytechnic Institute. Kalinin, 1981. (in Russian)
Gajevskiy H., Groger K., Zaharias K. Nonlinear operator equations and operator differential equations. Moscow: MIR. 336 p. (in Russian)
Van Genuchten M. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Soc. Am. J. 1980. Vol. 44. P. 892-898.
Kashenko N. M. Processes of moisture transport in porous media. Vestnir Ros. gos. univ. im. I. Kanta. 2010. No. 10. P. 56-58. (in Russian)
Shatkovskiy A.P. Scientific Basics of Intensive Technologies for Drip Irrigation of Cultivated Plants Under Conditions of Ukrainian Steppes. Doctor thesis of Agricultural Sciences: 06.01.02. National Academy of Agrarian Sciences of Ukraine. Kyiv, 2016. 496 p. (in Ukrainian)
Samarskiy A. A., Nikolaev E. S. Methods for solving grid equations. Moscow: Science. 1978. 588 p.
Samarskiy A. A., Gulin A. V. Numerical methods. Moscow: Science. 1989. 432 p.
Arbogast T. An error analysis for Galerkin approximations to an equation of mixed elliptic-parabolic type. Technical Report TR90-33, Department of Computational and Applied Mathematics, Rice University. Houston, TX. 1990. 28 p.
Ginting V. Time integration techniques for Richards equation. Procedia Computer Science 9. 2012. P. 670-678. doi: https://doi.org/10.1016/j.procs.2012.04.072
Pop I. S. Error estimates for a time discretization method for the Richards’ equation. Comput. Geosci. 6. 2002. P. 141-160.
Lions J.-L. Optimal control of systems, described by partial differential equations. Moscow: MIR. 1972. 416 p. (in Russian)
Kirk D. E. Optimal control theory. An Introduction. New Jersey: Dover Books on Electrical Engineering, 1971. 472 p. doi: https://doi.org/10.1002/aic.690170452
Lyashko S., Klyushin D., Semenov V., Shevchenko K. Identification of point contamination source in ground water. International Journal of Ecology and Development. Fall 2006. Vol. 5. No. 6. P. 36-43.
Lyashko S. I. Generalized control of linear systems. Kyiv: Nauk. dumka. 1998. 470 p. (in Russian)
Vabishchevich P. N. Numerical Solution of the Problem of the Identification of the Right-hand Side of a Parabolic Equation. Russian Math. Iz. VUZ. 2003. 47:1. P. 29-37. (in Russian)
Marchuk G. I. Conjugate equations and their application. Tr. IMM UrO RAN. 2006. Vol 12. No 1. P. 184-195. (in Russian)
Marchuk G. I., Shutyaev V. P. Conjugate equations and iterational algorythms in problems of variational data assimilation. Tr. IMM UrO RAN. 2011. Vol. 17. No. 2. P. 136-150. (in Russian)
Marchuk G. I. About some approaches to building conjugate operators in nonlinear tasks. Tr. MIAN. 1994. Vol. 203. P. 126-134. (in Russian)
Marchuk G. I. Construction of conjugate operators in nonlinear problems of mathematical physics. Matem. sb. 1998. Vol. 189. No 10, P. 75-88. (in Russian)