Autors: Hinov, N. L., Kabakchieva, R. V., Gotseva, D. A., Stanchev, P. A.
Title: Mathematically Grounded Neuro-Fuzzy Control of IoT-Enabled Irrigation Systems
Keywords: Adaptive Neuro-Fuzzy Inference Systems (ANFIS), Artificial Neural Networks (ANN), evapotranspiration estimation, fuzzy logic control, Input-to-State Stability (ISS), IoT-based irrigation, Mamdani fuzz

Abstract: This paper develops a mathematically grounded neuro-fuzzy control framework for IoT-enabled irrigation systems in precision agriculture. A discrete-time, physically motivated model of soil moisture is formulated to capture the nonlinear water dynamics driven by evapotranspiration, irrigation, and drainage in the crop root zone. A Mamdani-type fuzzy controller is designed to approximate the optimal irrigation strategy, and an equivalent Takagi–Sugeno (TS) representation is derived, enabling a rigorous stability analysis based on Input-to-State Stability (ISS) theory and Linear Matrix Inequalities (LMIs). Online parameter estimation is performed using a Recursive Least Squares (RLS) algorithm applied to real IoT field data collected from a drip-irrigated orchard. To enhance prediction accuracy and long-term adaptability, the fuzzy controller is augmented with lightweight artificial neural network (ANN) modules for evapotranspiration estimation and slow adaptation of membership-function parameters. This work provides one of the first mathematically certified neuro-fuzzy irrigation controllers integrating ANN-based estimation with Input-to-State Stability (ISS) and LMI-based stability guarantees. Under mild Lipschitz continuity and boundedness assumptions, the resulting neuro-fuzzy closed-loop system is proven to be uniformly ultimately bounded. Experimental validation in an operational IoT setup demonstrates accurate soil-moisture regulation, with a tracking error below 2%, and approximately 28% reduction in water consumption compared to fixed-schedule irrigation. The proposed framework is validated on a real IoT deployment and positioned relative to existing intelligent irrigation approaches.

References

  1. García L. Parra L. Jimenez J.M. Lloret J. Lorenz P. IoT-Based Smart Irrigation Systems: An Overview on the Recent Trends on Sensors and IoT Systems for Irrigation in Precision Agriculture Sensors 2020 20 1042 10.3390/s20041042
  2. Pascoal D. Adão T. Chojka A. Silva N. Rodrigues S. Peres E. Morais R. Democratizing IoT for Smart Irrigation: A Cost-Effective DIY Solution Proposal Evaluated in an Actinidia Orchard Algorithms 2025 18 563 10.3390/a18090563
  3. Artetxe E. Barambones O. Martín Toral I. Uralde J. Calvo I. del Rio A. Smart IoT Irrigation System Based on Fuzzy Logic, LoRa, and Cloud Integration Electronics 2024 13 1949 10.3390/electronics13101949
  4. Hoque M.J. Islam M.S. Khaliluzzaman M. A Fuzzy Logic- and Internet of Things-Based Smart Irrigation System Eng. Proc. 2023 58 93 10.3390/ecsa-10-16243
  5. Bin L. Shahzad M. Khan H. Bashir M.M. Ullah A. Siddique M. Sustainable Smart Agriculture Farming for Cotton Crop: A Fuzzy Logic Rule Based Methodology Sustainability 2023 15 13874 10.3390/su151813874
  6. Singh A.K. Tariq T. Ahmer M.F. Sharma G. Bokoro P.N. Shongwe T. Intelligent Control of Irrigation Systems Using Fuzzy Logic Controller Energies 2022 15 7199 10.3390/en15197199
  7. Maya Olalla E. Lopez Flores A. Zambrano M. Domínguez Limaico M. Diaz Iza H. Vasquez Ayala C. Fuzzy Control Application to an Irrigation System of Hydroponic Crops under Greenhouse: Case Cultivation of Strawberries (Fragaria vesca) Sensors 2023 23 4088 10.3390/s23084088
  8. Prasad R. Srivastava A.K. Tiwari R. Fuzzy Logic-Based Sprinkler Controller for a Precision Irrigation System: A Case Study of Semi-Arid Regions in India Eng. Proc. 2024 82 103 10.3390/ecsa-11-20504
  9. Neugebauer M. Akdeniz C. Demir V. Yurdem H. Fuzzy Logic Control for Watering System Sci. Rep. 2023 13 18485 10.1038/s41598-023-45203-2
  10. Benzaouia M. Hajji B. Mellit A. Rabhi A. Fuzzy-IoT Smart Irrigation System for Precision Scheduling and Monitoring Comput. Electron. Agric. 2023 215 108407 10.1016/j.compag.2023.108407
  11. Taheri M. Bigdeli M. Imanian H. Mohammadian A. An Overview of Evapotranspiration Estimation Models Utilizing Artificial Intelligence Water 2025 17 1384 10.3390/w17091384
  12. Karahan H. Cetin M. Can M.E. Alsenjar O. Developing a New ANN Model to Estimate Daily Actual Evapotranspiration Using Limited Climatic Data and Remote Sensing Techniques for Sustainable Water Management Sustainability 2024 16 2481 10.3390/su16062481
  13. Phesa M. Mbatha N. Ikudayisi A. MODIS Evapotranspiration Forecasting Using ARIMA and ANN Approach at a Water-Stressed Irrigation Scheme in South Africa Hydrology 2024 11 176 10.3390/hydrology11100176
  14. Skhiri A. Ferhi A. Bousselmi A. Khlifi S. Mattar M.A. Artificial Neural Network for Forecasting Reference Evapotranspiration in Semi-Arid Bioclimatic Regions Water 2024 16 602 10.3390/w16040602
  15. Adnan R.M. Mostafa R.R. Islam A.R.M.d.T. Kisi O. Kuriqi A. Heddam S. Estimating Reference Evapotranspiration Using Hybrid Adaptive Fuzzy Inferencing Coupled with Heuristic Algorithms Comput. Electron. Agric. 2021 191 106541 10.1016/j.compag.2021.106541
  16. Laaboudi A. Slama A. Using Neuro-fuzzy and linear models to estimate reference Evapotranspiration in South region of Algeria (A comparative study) Ital. J. Agrometeorol. 2020 2 55 64 10.13128/ijam-971
  17. Gökkuş M.K. ANFIS Based Reference Evapotranspiration (ET0) Estimation Using Limited and Different Climate Parameters ISPEC J. Agric. Sci. 2024 8 1022 1033 10.5281/zenodo.13761632
  18. Akiner M.E. Ghasri M. Comparative Assessment of Deep Belief Network and Hybrid Adaptive Neuro-Fuzzy Inference System Model Based on a Meta-Heuristic Optimization Algorithm for Precise Predictions of the Potential Evapotranspiration Environ. Sci. Pollut. Res. 2024 31 42719 42749 10.1007/s11356-024-33987-3 38879646
  19. Gutiérrez-Magaña S.-M. García-Díaz N. Soriano-Equigua L. Mata-López W.A. García-Virgen J. Brizuela-Ramírez J.-E. Neuro-Fuzzy System to Predict Timely Harvest in Stevia Crops Agriculture 2025 15 840 10.3390/agriculture15080840
  20. Elsayed S. El-Hendawy S. Khadr M. Elsherbiny O. Al-Suhaibani N. Dewir Y.H. Tahir M.U. Mubushar M. Darwish W. Integration of Spectral Reflectance Indices and Adaptive Neuro-Fuzzy Inference System for Assessing the Growth Performance and Yield of Potato under Different Drip Irrigation Regimes Chemosensors 2021 9 55 10.3390/chemosensors9030055
  21. Enemegio R. Jurado F. Villanueva-Tavira J. Experimental Evaluation of a Takagi–Sugeno Fuzzy Controller for an EV3 Ballbot System Appl. Sci. 2024 14 4103 10.3390/app14104103
  22. Song R. Huang S. Xiong L. Zhou Y. Li T. Tan P. Sun Z. Takagi–Sugeno Fuzzy Parallel Distributed Compensation Control for Low-Frequency Oscillation Suppression in Wind Energy-Penetrated Power Systems Electronics 2024 13 3795 10.3390/electronics13193795
  23. Nonlinear Systems: Khalil, Hassan: 9780130673893: Amazon.Com: Books Available online: https://www.amazon.com/Nonlinear-Systems-3rd-Hassan-Khalil/dp/0130673897 (accessed on 1 November 2025)
  24. Chao C.-T. Chen D.-H. Chiou J.-S. Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems Mathematics 2021 9 2441 10.3390/math9192441
  25. Meredef I.e. Hammoudi M.Y. Betka A. Hamiane M. Mimoune K. Stability and Stabilization of TS Fuzzy Systems via Line Integral Lyapunov Fuzzy Function Electronics 2022 11 3136 10.3390/electronics11193136
  26. Kolev S. Design of a System for Intelligent Agriculture and Monitoring of the Optimal Parameters of Agricultural Crops Proceedings of the 2021 29th National Conference with International Participation (TELECOM) Sofia, Bulgaria 28–29 October 2021 43 46 10.1109/TELECOM53156.2021.9659656
  27. Remya S. Sasikala R. Performance evaluation of optimized and adaptive neuro fuzzy inference system for predictive modeling in agriculture Comput. Electr. Eng. 2020 86 106718 10.1016/j.compeleceng.2020.106718
  28. Tyokighir S.S. Mom J. Ukhurebor K.E. Igwue G. An Adaptive Neuro-Fuzzy Inference System-Based Irrigation Sprinkler System for Dry Season Farming Bull. Electr. Eng. Inform. 2024 13 2434 2441 10.11591/eei.v13i4.7834
  29. Shah M.I. Abunama T. Javed M.F. Bux F. Aldrees A. Tariq M.A.U.R. Mosavi A. Modeling Surface Water Quality Using the Adaptive Neuro-Fuzzy Inference System Aided by Input Optimization Sustainability 2021 13 4576 10.3390/su13084576
  30. Kayhomayoon Z. Bahmani M.J. Milan S.G. Bazrafshan O. Berndtsson R. Integration of the Reptile Search Algorithm and the Adaptive Neuro-Fuzzy Inference System Enhances Standardized Precipitation Evapotranspiration Index Forecasting Sci. Rep. 2025 15 14647 10.1038/s41598-025-98772-9
  31. Quy V.K. Van Hau N. Van Anh D. Quy N.M. Ban N.T. Lanza S. Randazzo G. Muzirafuti A. IoT-Enabled Smart Agriculture: Architecture, Applications, and Challenges Appl. Sci. 2022 12 3396 10.3390/app12073396
  32. Kolev S. Design of a New Version of a System for Intelligent Agriculture Proceedings of the 2022 V International Conference on High Technology for Sustainable Development (HiTech) Sofia, Bulgaria 6–7 October 2022 1 5 10.1109/HiTech56937.2022.10145541
  33. Fereres E. Soriano M.A. Deficit Irrigation for Reducing Agricultural Water Use J. Exp. Bot. 2006 58 147 159 10.1093/jxb/erl165 17088360
  34. Ahsen R. Khan Z.M. Farid H.U. Shakoor A. Ali I. Estimation of cropped area and irrigation water requirement using remote sensing and gis J. Anim. Plant Sci. 2020 30 876 884 10.36899/JAPS.2020.4.0103
  35. Mohamed A. Anuar N.F. Mutalib S. Yusoff M. Abdul-Rahman S. Turf Grass Irrigation Using Neuro-Fuzzy System Lecture Notes in Computer Science Springer Berlin/Heidelberg, Germany 2012 644 651
  36. Ezenne G.I. Jupp L. Mantel S.K. Tanner J.L. Current and Potential Capabilities of UAS for Crop Water Productivity in Precision Agriculture Agric. Water Manag. 2019 218 158 164 10.1016/j.agwat.2019.03.034
  37. Achite M. Jehanzaib M. Sattari M.T. Toubal A.K. Elshaboury N. Wałęga A. Krakauer N. Yoo J.-Y. Kim T.-W. Modern Techniques to Modeling Reference Evapotranspiration in a Semiarid Area Based on ANN and GEP Models Water 2022 14 1210 10.3390/w14081210
  38. Qazi S. Khawaja B.A. Farooq Q.U. IoT-Equipped and AI-Enabled Next Generation Smart Agriculture: A Critical Review, Current Challenges and Future Trends IEEE Access 2022 10 21219 21235 10.1109/ACCESS.2022.3152544
  39. Boughamsa M. Ramdani M. Adaptive Fuzzy Control Strategy for Greenhouse Micro-Climate Int. J. Autom. Control 2017 12 108 10.1504/IJAAC.2018.088604
  40. Bushnag A. Chaabane S.B. Harrabi R. Alharbi L.A. Alshmrani M. Abuzneid S. Smart Agriculture: IoT-Based Smart Irrigation with Advanced Fuzzy Logic Control Expert Syst. Appl. 2025 299 130168 10.1016/j.eswa.2025.130168
  41. Escobar L.M. Aguilar J. Garces-Jimenez A. De Mesa J.A.G. Gomez-Pulido J.M. Advanced Fuzzy-Logic-Based Context-Driven Control for HVAC Management Systems in Buildings IEEE Access 2020 8 16111 16126 10.1109/ACCESS.2020.2966545
  42. Simpkins A. System Identification: Theory for the User, 2nd Edition (Ljung, L.; 1999) [On the Shelf] IEEE Robot. Autom. Mag. 2012 19 95 96 10.1109/MRA.2012.2192817
  43. D’Aniello G. Fuzzy logic for situation awareness: A systematic review J Ambient Intell Hum. Comput 2023 14 4419 4438 10.1007/s12652-023-04560-6
  44. Villarrubia G. Paz J.F.D. Iglesia D.H.D.L. Bajo J. Combining Multi-Agent Systems and Wireless Sensor Networks for Monitoring Crop Irrigation Sensors 2017 17 1775 10.3390/s17081775
  45. Kireva R. Markov E. Petrova-Branicheva V. Irrigation scheduling of apple in drip irrigation J. Mt. Agric. Balk. 2017 20 275 282 Available online: https://www.cabidigitallibrary.org/doi/full/10.5555/20183199805 (accessed on 1 November 2025)

Issue

Mathematics, vol. 14, 2026, Albania, https://doi.org/10.3390/math14020314

Вид: статия в списание, публикация в реферирано издание, индексирана в Scopus и Web of Science