Generalized predictive control based on interval gray model with adaptive buffer operator for pattern-moving systems

The pattern-moving systems, as a kind of complex nonlinear systems that governed by statistical laws, are commonly found in industrial production processes such as sintering machines and cement rotary kiln. Current control methods face challenges in capturing the statistical properties of these systems using deterministic variables such as states or outputs. As a result, previous approaches often overlook such systems or treat them as being influenced by stochastic disturbances. To reveal the system's inherent statistical attributes, this work proposed a novel interval grey adaptive buffer generalized predictive control (IGAB-GPC), which employs the bidirectional mapping framework under pattern moving theory (PMT) to quantify pattern category variables, enabling precise tracking of dynamic pattern transitions. Key innovations include: (1) an adaptive buffer operator that mitigates oscillations in pattern class sequences based on their monotonicity, (2) an interval grey model IGM(1,2)-based prediction model was developed for uncertainty analysis, and (3) a GPC control scheme incorporating receding horizon optimization and feedback correction for enhanced tracking accuracy. The workflow involves constructing a pattern-moving space through data-driven quantization, applying the adaptive buffer operator to smooth time-series variances, developing the IGM(1,2), and implementing the IGAB-GPC strategy. Experimental findings reveal that IGAB-GPC outperforms other controllers such as controlled autoregressive integrated moving average generalized predictive control (CARIMA-GPC) and interval Grey generalized predictive control (IG-GPC) in terms of tracking results. Specifically, it reduces tracking errors by roughly two orders of magnitude, yielding Mean Absolute Error (MAE) of 0.0056 and Root Mean Squared Error (RMSE) of 0.0074. In short, the primary innovation of this method is the integration an adaptive buffer operator into the grey system modeling and generalized predictive control for handling system uncertainty, which provides enhanced disturbance rejection capabilities for complicated uncertain systems from a pattern dynamic perspective.