Explicit Solution Method for Generalized Predictive Control

This program is developed in MATLAB to simulate the explicit solution method for Generalized Predictive Control (GPC). GPC is a model-based control strategy that optimizes controller predictive performance to achieve enhanced control effectiveness. The implementation features a CARIMA (Controlled Auto-Regressive Integrated Moving Average) model for system representation, with key algorithmic components including: Diophantine equation solving for output prediction, cost function minimization using quadratic programming, and receding horizon control implementation. The explicit solution approach adopted in this simulation employs matrix operations for efficient prediction horizon calculations and control law derivation, significantly improving computational efficiency while maintaining algorithmic accuracy. The code structure demonstrates practical implementation of GPC fundamentals through systematic steps: model identification, prediction vector computation, optimized control sequence generation, and real-time control application. This program serves both as an educational tool for understanding GPC theoretical foundations and as a reference design for practical control system engineering applications.