Abstract
Problem of soil acidity regularization is modeled as stochastic adaptive control problem with a linear difference equation of the dynamics of a field pH level. Stochastic component in the equation represents an individual time variability of soil acidity of an elementary section. We use Bayesian approach to determine a posteriori probability density function of the unknown parameters of the stochastic transition process. The Kullback–Leibler information divergence is used as a measure of difference between true distribution and its estimation. Algorithm for the construction of an adaptive stabilizing control in such a linear control system is proposed in the paper. Numerical realization of the algorithm is represented for a problem of a field soil acidity control.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aoki M (1989) Optimization of stochastic systems. Academic Press, California
Boland JW, Filar JA, Howlett PG (2010) Environmental problems, uncertainty, and mathematical modeling. Notices AMS 57(10):1286–1294
Bole B, Goebel K, Field M (2012) Using Markov model of fault growth physics and environmental stresses to optimize control actions, American Institute of Aeronautics and Astronautics 1–7
Dinkin EB, Ushkevich AA (1975) Controlled Markov processes and their applications, 338 p. Nauka, Moscow
Guo X, Hernandez-del-Valle A, Hernandez-Lerma O (2012) First passage problems for nonstationary discrete-time stochastic control systems. Eur J Control 6:528–538
Hernandez-Lerma O, Marcus SI (1987) Adaptive policies for discrete-time stochastic control systems with unknown disturbance distribution. Syst Control Lett 9:307–315
Jorgensen S, Martin-Herran G, Zaccour G (2010) Dynamic games in the economics and management of pollution. Environ Model Assess 15:433–467
Karelin VV (1991) Adaptive optimal strategies in controlled Markov processes, Advances in Optimization Proceedings of 6 the French-German Colloquium of Optimization, pp 518–525
Kros J, Mol-Dijkstra JP, Pebesma EJ (2002) Assessment of the prediction error in a large-scale application of a dynamic soil acidification model. Stoch Environ Res Risk Assess 16:279–306
Kullback S, Leibler RA (1951) On information and sufficiency. Annals Math Stat 22(1):79–86
Nebolsin AN, Nebolsina ZP (2010) Soil liming. RASHN, GNU LNIISCH, Saint Petersburg
Schmieman E, de Vries W, Hordijk L, Kroeze C, Posch M, Reinds GJ, van Ierland E (2002) Dynamic cost-effective reduction strategies for acidification in Europe: an application to Ireland and the United Kingdom. Environ Model Assess 7:163–178
Shilnikov IA, Akanova NI, Barinov VN (2003) The method of soil acidity predicting and calculation of calcium balance in agriculture of Nechernozemie in Russian Federation. In: Pryanishnikov DA, VNII of agricultural chemistry, Moscow, p 24
Yakushev VP, Bure VM, Yakushev VV, Bure AV (2012) Stochastic modeling and optimal solutions on soil liming. Agrophysics 2:24–29
Yakushev VP, Karelin VV, Bure VM (2013) Bayesian approach for soil acidity control, vol 10, 3. Vestnik St. Petersburg University, Saint Petersburg, pp 168–179
Acknowledgments
We thank two anonymous referees for helpful comments and remarks. The work of the fourth author was partly supported by research project 9.38.245.2014 of Saint Petersburg State University.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yakushev, V.P., Karelin, V.V., Bure, V.M. et al. Soil acidity adaptive control problem. Stoch Environ Res Risk Assess 29, 1671–1677 (2015). https://doi.org/10.1007/s00477-014-0965-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-014-0965-5