The basic objective of system modeling is to establish an input-output representative mapping that can satisfactorily describe the system behaviors, by using the available input-output data based upon physical or empirical knowledge about the structure of the unknown system.
Conventional system modeling techniques suggest constructing a model described by a set of differential or difference equations. This approach is effective only when the underlying system is mathematically well-defined and precisely expressible. They often fail to handle uncertain, vague or ill-defined physical systems, and yet most real-world problems do not obey such precise, idealized, and subjective mathematical rules. According to the incompatibility principle (Zadeh, 1973), as the complexity of a system increases, human’s ability to make precise and significant statements about its behaviors decreases, until a threshold is reached beyond which precision and significance become impossible. Under this principle, Zadeh (1973) proposed a modeling method of human thinking with fuzzy numbers rather than crisp numbers, which had eventually led to the development of various fuzzy modeling techniques later on.
Key Terms in this Chapter
Fuzzy System: A system formulated and described by fuzzy set-based real-valued functions.
Fuzzy Rule: A logical rule established based on fuzzy logic.
Structure Identification: Find a mathematical representation of the unknown system’s structure.
Genetic Algorithm: An optimization scheme based on biological genetic evolutionary principles.
Parameter Identification: Find appropriate parameter values in a mathematical model.
Least-Squares Algorithm: An optimization scheme that minimizes the square of the sum of the approximation errors.
System Modeling: A mathematical formulation of an unknown physical system or process.