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Robust Minimum Variance Lower Bound Estimation by Uncertainty Modeling Using Interval Type‐2 Fuzzy set
Author(s) -
Alipouri Yousef,
Poshtan Javad
Publication year - 2017
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1307
Subject(s) - parametric statistics , interval (graph theory) , variance (accounting) , mathematics , fuzzy set , interval estimation , upper and lower bounds , fuzzy logic , set (abstract data type) , mathematical optimization , control theory (sociology) , type (biology) , computer science , statistics , control (management) , artificial intelligence , confidence interval , mathematical analysis , ecology , accounting , combinatorics , business , biology , programming language
The Minimum Variance Lower Bound (MVLB) represents the best achievable controller capability in a variance sense. Estimation of the MVLB for nonlinear systems confronts some difficulties. If one simply ignores these nonlinearities, there is the danger of over‐estimating the performance of the control loop in rejecting uncertainties. Assuming that almost all models have uncertainties, in this paper, the MVLB has been estimated considering three types of uncertainties: structural, parametric, and algorithmic. To achieve accurate estimation of the MVLB an interval type‐2 fuzzy set has been utilized. This paper utilizes a strategy for modeling of symmetric interval type‐2 fuzzy sets using their uncertainty degrees. Then, based on this uncertainty measure, one method to construct interval type‐2 fuzzy set models using the uncertain interval data is introduced. Finally, simulation studies demonstrate the effectiveness of the proposed control scheme.