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H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach
Bomo S. Wibowo1,2, *, Bambang Riyanto Trilaksono1 & Arief Syaichu-Rohman1
1School of Electrical Engineering and Informatics, Bandung Institute of Technology,
Jalan Ganesa No.10, Bandung 40132, Indonesia
2Dept. of Electrical Engineering, University of Tanjungpura,
Jalan Jendral Ahmad Yani, Pontianak 78124, Indonesia
*Email: bomowibowo@students.itb.ac.id
Abstract. This paper proposes the control design ofa nonlinear polynomial fuzzy system with H∞ performance objective using a sum of squares (SOS) approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the H∞ performance objective. The design condition is represented in terms of an SOS that can be numerically solved via the SOSTOOLS. A simulation study is presented to show the effectiveness of the SOS-based H∞ control designfor nonlinear polynomial fuzzy systems.
Keywords: H∞; nonlinear; polynomial fuzzy controller; polynomial fuzzy system; polynomial Lyapunov function; SOSTOOLS; sum of squares.
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