Abstract: This paper presents a novel computational framework for autonomous photovoltaic (PV) data acquisition and optimization, combining real-time Internet of Things (IoT) monitoring with advanced mathematical tools from matrix theory, tensor analysis, and numerical linear algebra. Building upon a dual-microcontroller standalone solar system, the proposed approach models electrical and environmental data streams as multidimensional structures, enabling efficient representation, correlation analysis, and predictive modeling. Nonnegative matrix techniques and tensor decompositions are employed to capture inherent patterns in irradiance, temperature, voltage, and current dynamics. Iterative numerical methods and Markov chain–based formulations are further applied to enhance forecasting accuracy and system stability under uncertain operating conditions. Convex optimization strategies are integrated into the control layer to improve energy management and reduce processing overhead, ensuring long-term autonomy. The developed methodology bridges experimental IoT-based solar monitoring with recent advances in multilinear algebra and computational mathematics, providing new insights into large-scale energy systems, reliability analysis, and scalable optimization.

Keywords: Photovoltaic monitoring, Tensor analysis, Nonnegative matrices, Iterative methods, Convex optimization, Numerical linear algebra, IoT-enabled systems, Markov chains, Autonomous solar systems

Pages: 286-294

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