Fuzzy Logic for Non-Smooth Dynamical Systems

Bridging the two seemingly unrelated concepts, fuzzy logic and nonlinear piecewise-smooth dynamical systems theory is chiefly motivated by the concept of soft computing (SC), initiated by Lotfi A. Zadeh, the founder of fuzzy set theory. The principal components of SC, as defined in his initiative for soft computing1, are fuzzy logic (FL), neural network theory (NN) and probabilistic reasoning (PR), with the latter subsuming parts of belief networks, genetic algorithms, chaos theory and learning theory. SC is essentially distant from traditional, immutable (hard) computing and is much more aligned to the main ideas of Kansei Engineering in that the imprecision, uncertainty and partial truth reflecting the working of the human mind are incorporated into the computing process to form a new paradigm to tackle highly complex, nonlinear systems. The aim of this chapter is to combine FL from general Soft Computing theory and piece-wise smooth dynamical systems from ABStRACt