Modelling Complex Dynamical Systems with a Fuzzy Inference System for Differential Equations

Abstract

We describe in this chapter a new method for modelling complex dynamical systems based on the use of a new fuzzy inference system for multiple differential equations. It is well known that formulating a unique and sufficiently accurate mathematical model for a complex dynamical system (over a whole region of discourse) may be very difficult or even impossible in some cases (Castillo and Melin, 1996). 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 can then formulate a set of fuzzy if-then rules relating these regions to their corresponding mathematical models. We can assume, without loss of generality that the models can be expressed as non-linear differential equations (Castillo and Melin, 1997). 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, in which we are now using differential equations as consequents of the fuzzy rules instead of simple polynomials like in Sugeno’s original method. We illustrate our new method for modelling with two cases: robotic dynamic systems, and aircraft systems. These two applications are complex enough to illustrate the power of our method for modelling.KeywordsFuzzy RuleRobotic SystemFuzzy Inference SystemRobotic ManipulatorInertia MomentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.