Generalized Predictive Control

This program utilizes the generalized predictive control (GPC) algorithm for modeling and analyzing CARIMA models. GPC represents an advanced control technique applicable across multiple domains including finance, engineering, and logistics. The implementation employs key computational components: - Recursive parameter estimation using recursive least squares (RLS) for model adaptation - Diophantine equation solutions for optimal predictor derivation - Quadratic cost function minimization with receding horizon strategy - Implementation of control increment constraints through optimization techniques Through this algorithm, we achieve enhanced understanding of CARIMA model dynamics and improve future behavior prediction capabilities. The codebase enables systematic exploration of model parameters and assumptions, facilitating deeper interpretation of model implications and impacts. The program specifically focuses on improving CARIMA model accuracy and reliability through: - Real-time parameter tuning mechanisms - Robustness enhancement via weighted control sequences - Numerical stability improvements in matrix inversion operations These implementations ensure practical applicability to real-world problems while maintaining computational efficiency through optimized prediction horizon handling and constraint management.