A Comprehensive Fuzzy Uncertainty Analysis of a Controlled Nonlinear System With Unstable Internal Dynamics

Abstract

Fuzzy uncertainty analyses disclose a deeper insight and provide a better understanding of complex systems with highly interdependent parameters. In contrast to probability theory, fuzzy arithmetic is concerned with epistemic uncertainties, which originate from a lack of knowledge or from idealizing assumptions in the modeling process. Direct fuzzy arithmetic can be used to illustrate how parameter uncertainties propagate through a system. In contrast, inverse fuzzy arithmetic can be used to identify admissible parameter uncertainties that obey defined error bounds. In addition, fuzzy arithmetic is capable of providing global sensitivity analyses. Therefore, an improved formulation for inverse analyses as well as a new concept for the computation of global sensitivities is presented. These tools are used here to assess the model-based feed-forward control of a nonlinear system with unstable internal dynamics.