Generalized Predictive Control Algorithm for TS Fuzzy Models

The Generalized Predictive Control (GPC) algorithm for TS (Takagi-Sugeno) fuzzy models represents an advanced control strategy that combines fuzzy logic with predictive control techniques. The TS fuzzy model employs local linear models and fuzzy rules to describe complex nonlinear systems, enabling the control algorithm to maintain excellent nonlinear approximation capabilities while ensuring computational efficiency.

Generalized Predictive Control (GPC) is a model-based predictive control method that optimizes control input sequences over a future time horizon to achieve optimal dynamic system response. When the prediction model utilizes TS fuzzy identification, the system can adaptively adjust local linear prediction models according to different operating states, thereby providing more accurate descriptions of nonlinear dynamic behaviors.

The key to TS fuzzy identification lies in rule base construction and parameter optimization. Implementation typically involves using clustering algorithms or neural networks to partition input-output data, followed by parameter optimization for local linear models through methods like least squares or gradient descent. Within the predictive control framework, the TS model's predictive output synthesizes contributions from all local models via fuzzy inference mechanisms, while closed-loop control is achieved through rolling optimization and feedback correction mechanisms.

This algorithm is particularly suitable for complex nonlinear systems such as industrial process control and robotic trajectory tracking. It effectively balances robustness with control precision while mitigating the rule explosion problem commonly encountered in traditional fuzzy control systems.