Generalized Predictive Control Based on Interval Gray Model with Adaptive Buffer Operator for a Class of 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. Encountering difficulties in delineating the statistical properties of such systems through deterministic variables like state or output variables, existing control techniques tend to either bypass these systems or address them as systems impacted by stochastic perturbations. To reveal system’s inherent statistical characteristics, this work proposed a novel Interval Grey Adaptive Buffer Generalized Predictive Control (IGAB-GPC) scheme, which employs the bidirectional mapping framework under pattern mpving 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 IGM(1,2)-based prediction model for robust uncertainty quantification, and (3) a GPC framework incorporating receding horizon optimization and feedback correction for enhanced control accuracy. The workflow involves constructing a pattern-moving space through data-driven quantization, applying the adaptive buffer operator to smooth time-series fluctuations, developing the IGM(1,2) model, and implementing the IGAB-GPC strategy. Numerical simulations demonstrate that IGAB-GPC outperforms benchmark methods like CARIMA-GPC and IG-GPC, achieving superior tracking accuracy, smoother pattern transitions, and robust stability, making it highly suitable for complex industrial processes