Uncertainty Nonlinear Systems Modeling with Fuzzy Equations

Many uncertain nonlinear systems can be modeled by linear-in-parameter models. The uncertainties can be regarded as parameter changes, which can be described as fuzzy numbers. These models are fuzzy equations. They are alternative models for uncertain nonlinear systems. The modeling of the uncertain nonlinear systems is to find the coefficients of the fuzzy equation. Since the coefficients are in form of fuzzy numbers, they cannot be determined by the normal methods. In this paper, we transform the fuzzy equation into a neural network. Then we modify the gradient descent method for fuzzy numbers updating, and propose a back-propagation learning rule for fuzzy equations. The novel modeling method is validated with two benchmark examples.