Modelling complex dynamical systems with a new fuzzy inference system for differential equations: the case of robotic dynamic systems

Abstract

We describe a new method for modelling complex dynamical systems based on the use of a new fuzzy inference system for differential equations. It is well known that formulating a unique and sufficiently accurate mathematical model for a complex dynamical system may be very difficult or even impossible in some cases. For this reason, it may be more efficient to formulate a set of mathematical models that approximate the local behavior of the dynamical system for different parameter regions. We formulate a set of fuzzy if-then rules relating these regions to their corresponding mathematical models. We assume, without loss of generality that the models can be expressed as nonlinear differential equations. We have developed a fuzzy inference system that enables fuzzy reasoning with multiple differential equations. The new fuzzy system can be considered as a generalization of Sugeno's inference procedure. We illustrate our new method with the case of modelling robotic dynamic systems.