Articles

Conceptualization of Markov Processes in Cyber-Physical Systems: Modelling, Prediction, and Control

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Cyber-Physical Systems (CPS) bring together physical processes with computing, communication, and control. They often operate in environments full of uncertainty, noise, and constant change, which makes traditional deterministic models struggle to capture how these systems really behave. This work introduces a more flexible framework based on Markov processes that helps model, predict, and control CPS in a more realistic way. By viewing system behaviour as probabilistic transitions between states, it becomes easier to analyze uncertainty and understand how the system evolves over time. The study looks at discrete-time Markov chains and expands the discussion to Hidden Markov Models (HMMs) and Markov Decision Processes (MDPs), allowing both visible and hidden aspects of system dynamics to be represented. It outlines a well-defined process for defining states, calculating transition probabilities, and making forecasts. The paper explores, in addition to that, the use of control techniques based on the use of probability theory and shows that these methods have a greater level of robustness compared to traditional control techniques. An example is given to show how this model improves performance and flexibility. All in all, Markov modelling is a good starting point for dealing with the challenges in CPSs, paving the way for integration with other tools.

A Hybrid “ARIMA–ML Regression” Model for Enhanced Predictive Analysis in Cyber-Physical Systems: Conceptual framework and Simulation Evaluation

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This paper presents a hybrid ARIMA–machine learning (ARIMA–ML) regression framework designed to improve predictive accuracy in cyber‑physical systems (CPS). The approach brings together the strengths of classical statistical time‑series modelling and modern data‑driven techniques, allowing the model to capture both linear structures and nonlinear dynamics that commonly arise in CPS environments. A simulation‑based evaluation was conducted using a multivariate dataset generated from a MATLAB/Simulink CPS model, complemented by Python‑based machine learning components. The results show that the hybrid model consistently outperforms standalone ARIMA and ML approaches across multiple operational scenarios, including normal operation, peak load, and early‑stage failure conditions. Improvements were observed not only in RMSE and MAE but also in residual stability, prediction interval reliability, and statistical significance as confirmed by the Diebold–Mariano test. These findings suggest that hybrid modelling offers a practical and effective pathway for enhancing predictive maintenance, anomaly detection, and decision‑support capabilities in complex CPS environments. Future work will explore real‑time deployment, integration with edge computing platforms, and the use of more advanced learning architectures to further strengthen model adaptability and performance.