A Novel H∞ Control for T–S Fuzzy Systems With Membership Functions Online Optimization Learning

This article investigatesthe optimization <tex-math notation="LaTeX">H∞</tex-math> nonparallel distribution compensation (non-PDC) control issue for nonlinear systems under Takagi–Sugeno (T–S) fuzzy framework. First, sufficient conditions of designing fuzzy non-PDC controller to assure asymptotic stability while maintaining <tex-math notation="LaTeX">H∞</tex-math> performance for studied systems are presented. Afterward, in the case of guaranteeing performance requirements, based on the feasible region of controller membership functions, a novel membership functions online learning algorithm utilizing gradient decent strategy is first proposed to adjust controller membership functions in real time to achieve a superior <tex-math notation="LaTeX">H∞</tex-math> performance. Compared with conventional non-PDC fuzzy control scheme, the actual response of interference attenuation performance can be decreased efficaciously. In the light of Lyapunov stability theory, sufficient condition is derived to ensure the error convergence of cost function. At last, two illustrative examples are provided to demonstrate the effectiveness and usefulness of the proposed online learning algorithm.