Design of Polynomial Fuzzy Observer-Controller with Membership Functions using Unmeasurable Premise Variables for Nonlinear Systems

TY - JOUR

T1 - Design of Polynomial Fuzzy Observer-Controller with Membership Functions using Unmeasurable Premise Variables for Nonlinear Systems

AU - Liu, Chuang

AU - Lam, H.K.

AU - Ban, Xiaojun

AU - Zhao, Xudong

PY - 2016/4/2

Y1 - 2016/4/2

N2 - In this paper, the stability of polynomial fuzzy-model-based (PFMB) observer-control system is investigated via Lyapunov stability theory. The polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states. Then the estimated system states are used for the state-feedback control of nonlinear systems. Although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy-model-based (FMB) control strategy, it leads to non-convex stability conditions. Therefore, the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares (SOS) with less manually designed parameters. In addition, the membership functions of the polynomial observer-controller are optimized by the improved gradient descent method, which outperforms the widely applied parallel distributed compensation (PDC) approach according to a general performance index. Simulation examples are provided to verify the proposed design and optimization scheme.

AB - In this paper, the stability of polynomial fuzzy-model-based (PFMB) observer-control system is investigated via Lyapunov stability theory. The polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states. Then the estimated system states are used for the state-feedback control of nonlinear systems. Although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy-model-based (FMB) control strategy, it leads to non-convex stability conditions. Therefore, the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares (SOS) with less manually designed parameters. In addition, the membership functions of the polynomial observer-controller are optimized by the improved gradient descent method, which outperforms the widely applied parallel distributed compensation (PDC) approach according to a general performance index. Simulation examples are provided to verify the proposed design and optimization scheme.

KW - Polynomial fuzzy observer-controller

KW - Optimized membership functions

KW - Unmeasurable premise variables

KW - Nonlinear system

KW - Sum of squares (SOS)

KW - Gradient descent

U2 - 10.1016/j.ins.2016.03.038

DO - 10.1016/j.ins.2016.03.038

M3 - Article

SN - 0020-0255

JO - INFORMATION SCIENCES

JF - INFORMATION SCIENCES

ER -