Constrained Proportional Integral Tracking Control for Takagi-Sugeno Fuzzy Model

Abstract

Similarly to previous PDF tracking problems, after using B-spline approximation theory for the output PDFs, the SDC problem can be transformed into a tracking problem for weighting dynamics. A T-S fuzzy model, as a model identifier, is first utilized to identify the nonlinear dynamics that cannot be modeled exactly, which represents a significant extension to the previous results. A robust tracking problem is studied for a T-S fuzzy weight system which models non-zero equilibriums, time delays, partial state constraints and exogenous disturbances. Meanwhile, a PI controller can be obtained through solving improved LMIs such that stability, tracking performances, robustness and state constraints can be guaranteed simultaneously. Furthermore, the peak-to-peak measure is applied to optimize the tracking performance, which generalizes the corresponding result for linear systems with zero equilibrium.