A Novel Approach to T-S Fuzzy Modeling of Nonlinear Dynamic Systems with Uncertainties using Symbolic Interval-Valued Outputs
Salman Zaidi, Andreas Kroll · IFAC-PapersOnLine · 2015
A novel approach to Takagi-Sugeno (T-S) fuzzy modeling of a class of nonlinear dynamic systems having variability in their outputs for the Nonlinear Output Error (NOE) case is addressed in this article. Multiple input-output datasets were obtained by repeating the identification experiment. The variability in the output time series is captured by defining the envelops of response at each time instant. These envelops actually provide the confidence interval based upper and lower bounds of the output time series using the extended Chebyshev’s Inequality. Different from the previous approach, in which two independent T-S fuzzy models were used for identifying each bound, a single T-S fuzzy model is identified in this work, which resulted in interval parameters for the antecedent and consequent variables. This is accomplished by first transforming the bounds into the symbolic interval-valued data and then using this data for identification. In order to get the expected value of the response, the estimated lower and upper bound time series of the identified T-S fuzzy model were averaged out at each time instant, as permitted by the extended Chebyshev’s Inequality. The proposed approach is demonstrated on an industrial diesel-engine electro-mechanical throttle valve.