MATLAB Implementation of Generalized Predictive Control for CARIMA Model

This program implements Generalized Predictive Control (GPC) for CARIMA (Controlled Auto-Regressive Integrated Moving Average) models. GPC represents an advanced control methodology rooted in control theory, effectively addressing predictive control challenges in multivariate, nonlinear, and time-varying systems. The core principle integrates predictive models with control strategies, enabling precise system output regulation and optimization through real-time parameter adjustments. The implementation employs key algorithmic components including: - Diophantine equation solutions for multi-step output predictions - Recursive least squares for online parameter estimation - Cost function minimization using receding horizon optimization - Control increment calculation with weighting factors for stability Through real-time optimization and adjustment of model parameters, the program achieves accurate output prediction and control enhancement, significantly improving prediction accuracy and control performance for dynamic systems. The code structure features modular design with separate functions for prediction, optimization, and control law computation.