Residual-Regime Markov Modelling for Predictive Control in Cyber-Physical Systems

Cyber-physical systems operate through a continuous interaction between physical processes, computational intelligence, communication networks and control mechanisms. Their behaviour is rarely fully deterministic: sensor noise, delayed communication, nonlinear dynamics, regime changes and early-stage failures create uncertainty that cannot be adequately represented by a single forecasting or control method. This paper proposes an original Residual-Regime Markov Forecast–Control Framework for cyber-physical systems. The framework brings together three modelling layers that play different roles. The ARIMA component handles the basic linear time‑series structure and keeps the model interpretable. On top of that, a machine‑learning layer works on the residuals to capture the nonlinear behaviour that ARIMA cannot. The final layer uses a Markov‑style state representation, turning the forecast errors, system signals and operating conditions into probabilistic regimes that describe how the system is likely to evolve. Unlike classical hybrid forecasting models that stop at prediction, the proposed approach links prediction to decision-making by using Markov transition probabilities, hidden-state belief updates and risk-aware policy selection. The main idea is that forecast errors are not treated only as modelling imperfections; instead, they are interpreted as early indicators of changing system regimes. A simulation-oriented evaluation design is presented for an industrial cyber-physical process with normal operation, peak load and degradation conditions. The proposed framework is expected to improve predictive maintenance, anomaly anticipation and control-policy selection by connecting statistical forecasting, data-driven correction and probabilistic decision logic in a single pipeline. The contribution of the paper lies in transforming hybrid forecasting into a regime-aware forecast–control architecture suitable for intelligent CPS monitoring and adaptive technical management.