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Article

Mathematically Grounded Neuro-Fuzzy Control of IoT-Enabled Irrigation Systems

1
CoE “National Center of Mechatronics and Clean Technologies”, 1000 Sofia, Bulgaria
2
Department of Computer Systems, Faculty of Computer Systems and Technologies, Technical University of Sofia, 1000 Sofia, Bulgaria
3
Department of Information Technology in Industry, Faculty of Computer Systems and Technologies, Technical University of Sofia, 1000 Sofia, Bulgaria
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(2), 314; https://doi.org/10.3390/math14020314
Submission received: 12 December 2025 / Revised: 13 January 2026 / Accepted: 15 January 2026 / Published: 16 January 2026
(This article belongs to the Special Issue Advances in Fuzzy Logic and Artificial Neural Networks, 2nd Edition)

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.
Keywords: Adaptive Neuro-Fuzzy Inference Systems (ANFIS); Artificial Neural Networks (ANN); evapotranspiration estimation; fuzzy logic control; IoT-based irrigation; Input-to-State Stability (ISS); Mamdani fuzzy controller; smart agriculture; soil moisture modeling; Takagi–Sugeno (TS) fuzzy model; uniformly ultimately bounded (UUB) systems; water optimization Adaptive Neuro-Fuzzy Inference Systems (ANFIS); Artificial Neural Networks (ANN); evapotranspiration estimation; fuzzy logic control; IoT-based irrigation; Input-to-State Stability (ISS); Mamdani fuzzy controller; smart agriculture; soil moisture modeling; Takagi–Sugeno (TS) fuzzy model; uniformly ultimately bounded (UUB) systems; water optimization

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MDPI and ACS Style

Hinov, N.; Kabakchieva, R.; Gotseva, D.; Stanchev, P. Mathematically Grounded Neuro-Fuzzy Control of IoT-Enabled Irrigation Systems. Mathematics 2026, 14, 314. https://doi.org/10.3390/math14020314

AMA Style

Hinov N, Kabakchieva R, Gotseva D, Stanchev P. Mathematically Grounded Neuro-Fuzzy Control of IoT-Enabled Irrigation Systems. Mathematics. 2026; 14(2):314. https://doi.org/10.3390/math14020314

Chicago/Turabian Style

Hinov, Nikolay, Reni Kabakchieva, Daniela Gotseva, and Plamen Stanchev. 2026. "Mathematically Grounded Neuro-Fuzzy Control of IoT-Enabled Irrigation Systems" Mathematics 14, no. 2: 314. https://doi.org/10.3390/math14020314

APA Style

Hinov, N., Kabakchieva, R., Gotseva, D., & Stanchev, P. (2026). Mathematically Grounded Neuro-Fuzzy Control of IoT-Enabled Irrigation Systems. Mathematics, 14(2), 314. https://doi.org/10.3390/math14020314

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