Abstract
In a previous study, the authors developed the planning of the water used in the irrigation systems of a given farmland in order to ensure that the field cultivation is in a good state of preservation. This planning was modelled and tackled as an optimal control problem: minimize the water flow (control) so that the extent water amount in the soil (trajectory) fulfils the cultivation water requirements. In this paper, we characterize the solution of our problem guaranteeing the existence of the solution and applying the necessary and sufficient conditions of optimality. We validate the numerical results obtained previously, comparing the analytical and numerical solutions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Betts, J.B.: Pratical methods for optimal control using nonlinear programming. SIAM, Philadelphia (1943)
Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley-Interscience, New York (1983)
Lopes, S., Fontes, F.A.C.C.: Normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints. Journal of Mathematical Analysis and Applications 399, 27–37 (2013)
Horton, R.E.: An approach toward a physical interpretation of infiltration capacity. Soil Sci. Soc. Am. Proc. 5, 300–417 (1940)
Elliott, R., Itenfisu, D., Brown, P., Jensen, M.E., Mecham, B., Howell, T.A., Snyder, R.L., Eching, S., Spofford, T., Hattendorf, M., Martin, D., Cuenca, R.H., Walter, I.A., Allen, R.G., Wright, J.L.: The ASCE standardized reference evapotranspiration equation. Rep. Task Com. on Standardized Reference Evapotranspiration (2002)
Gaspar, J., Machado, A.A., Haie, R.M.: Pereira. Analysis of effective effciency in decision making for irrigation interventions. Water Resources 39, 700–707 (2012)
Pereira, L.S.: Necessidades de água e métodos de rega. Publicações Europa - América (2004)
Rampazzo, F., Vinter, R.B.: A theorem on the existence of neighbouring feasible trajectories with aplication to optimal control 16, 335–351 (1999)
Raposo, J.R.: A REGA — dos primitivos regadios às modernas técnicas de rega. Fundação Calouste Gulbenkian (1996)
Pereira, R., Lopes, S., Fontes, F., Machado, G.J.: Irrigation planning in the context of climate change. In: Mathematical Models for Engineering Science, MMES 2011, pp. 239–244 (2011)
Pereira, R., Gonçalves, M., Lopes, S., Fontes, F., Machado, G.J.: Irrigation planning: an optimal control approach. In: International Conference of Numerical Analysis and Applied Mathematics, AIP Conference Proceedings, vol. 1558, pp. 622–626 (2013)
Pereira, R., Gonçalves, M., Lopes, S., Fontes, F., Machado, G.J.: An optimal control approach to the irrigation planning problem. Submitted to Conferência Brasileira de Dinâmica, Controle e Aplicações (2013)
Vinter, R.: Optimal control. Birkhauser, Boston (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Lopes, S.O., Fontes, F.A.C.C., Pereira, R.M.S., de Pinho, M.d.R., Ribeiro, C. (2015). Optimal Control for an Irrigation Planning Problem: Characterisation of Solution and Validation of the Numerical Results. In: Moreira, A., Matos, A., Veiga, G. (eds) CONTROLO’2014 – Proceedings of the 11th Portuguese Conference on Automatic Control. Lecture Notes in Electrical Engineering, vol 321. Springer, Cham. https://doi.org/10.1007/978-3-319-10380-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-10380-8_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10379-2
Online ISBN: 978-3-319-10380-8
eBook Packages: EngineeringEngineering (R0)