Paper Info
Title
Static Output Feedback Fault Tolerant Control and Relaxed Stability Analysis of Positive Polynomial Fuzzy Systems
Abstract
The increased demand for safety in control systems has motivated the research for fault-tolerant controllers (FTCs). This article presents the static output feedback FTC design and relaxed stability analysis for positive nonlinear systems on account of polynomial fuzzy models. A polynomial copositive Lyapunov function candidate is proposed for the stability analysis of positive polynomial fuzzy-model-based (PPFMB) control systems for the first time. This method develops the decision variable on the polynomial copositive Lyapunov function candidate to be a polynomial vector and also makes it independent of the form of the positive polynomial fuzzy model. Thus, it can be applied to a more extensive range of PPFMB control systems and potentially generates more relaxed stability analysis results. To achieve the stability analysis and control synthesis, the following challenges are overcome: 1) approximate the nonconvex terms in stability and positivity conditions into convex ones through the idea of matrix decomposition; 2) eliminate the nonconvex conditions resulting from the derivative of the polynomial Lyapunov function by employing an sum-of-squares (SOS) optimization method; 3) relax the results of stability analysis and control design by introducing the advanced membership-function-dependent technique to develop both the stability conditions and the positivity conditions. The relaxed conditions are obtained on the basis of SOS form so that the MATLAB third-party toolbox, SOSTOOLS, can be used to find feasible solutions. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed method.
Year
DOI
Venue
2022
10.1109/TFUZZ.2021.3134100
IEEE Transactions on Fuzzy Systems
Keywords
DocType
Volume
Fault-tolerant controller (FTC),membership functions,positive polynomial fuzzy-model-based (PPFMB) control systems,static output feedback,sum of squares (SOS)
Journal
30
Issue
ISSN
Citations 
9
1063-6706
0
PageRank 
References 
Authors
0.34
22
4
Name
Order
Citations
PageRank
Aiwen Meng100.34
H. K. Lam23618193.15
Ziguang Wang300.34
Fucai Liu411.36