Fuzzy T-S Predictive Control: Algorithm and MATLAB Implementation

Fuzzy T-S predictive control is an advanced control strategy that combines fuzzy modeling with generalized predictive control, particularly suitable for nonlinear systems. Its core concept involves using T-S fuzzy models to achieve local linearization of complex nonlinear systems, followed by designing predictive controllers based on these linear models.

The implementation process consists of three stages: Fuzzy Model Identification: Utilize fuzzy clustering algorithms (such as FCM implemented via MATLAB's fcm function) to partition input-output data spaces, establishing linear ARX models for each local region. Rule consequent parameters are determined using least squares estimation, achievable through MATLAB's arx function or pinv for pseudo-inverse calculations. Prediction Model Construction: The weighted fusion of outputs from all T-S model rules leads to a global multi-step ahead prediction equation. This requires handling coupling relationships between fuzzy rules, typically implemented through weighted sum calculations with normalization of membership degrees. Rolling Optimization Solution: At each sampling period, a constrained quadratic programming problem is solved to minimize the error between predicted outputs and reference trajectories. MATLAB's quadprog function can efficiently handle this optimization, with proper configuration of constraint matrices and cost function weights.

Key Implementation Details: Model update mechanisms must account for time-varying system characteristics, potentially requiring recursive least squares algorithms When using Gaussian membership functions for weight calculation, normalization of rule activation levels is crucial to maintain consistency The selection of control horizon and prediction horizon significantly impacts system stability and computational load, often determined through simulation studies

This method's advantage lies in its ability to handle nonlinear characteristics while maintaining predictive control's constraint handling capabilities, making it highly valuable for industrial process control applications. MATLAB implementation typically involves System Identification Toolbox for model estimation and Optimization Toolbox for constraint resolution.