Robust Output-Feedback $\mathcal {H}_{\infty }$ Online Optimization Control for T–S Fuzzy Systems via Differential Evolution Algorithm
Zhenxing Zhang, Jiuxiang Dong
Abstract
This article is concerned with robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance online optimization problem for a group of Takagi–Sugeno (T–S) fuzzy systems in the framework of differential evolution (DE) algorithm. First, by virtue of nonparallel distribution compensation (non-PDC) technique, sufficient conditions that can stabilize the fuzzy systems and guarantee the desired <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance are derived. Whereafter, in the premise of ensuring the stability of systems, based on the allowable intervals of controller membership functions (MFs), a new MFs online optimization strategy utilizing DE technique is first proposed to seek the optimal values in real time so as to acquire a better <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance. In contrast with the conventional control where the controller MFs are built based on experts' subjective knowledge or intuition, by this advanced optimal control method, not only is the influence of MFs modeling errors robustly tolerated, but also the practical disturbance resistance capability can be efficaciously enhanced. Additionally, the proposed MFs online optimization scheme is also able to sustain the desired <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance when the interference channels suffer from modeling errors. Lastly, simulation examples are presented to ascertain the effectiveness and superiorities of the proposed theoretical results.