Application of a new theory of fuzzy chaos for the simulation and control of nonlinear dynamical systems

Authors:
Oscar Castillo;Patricia Melin
Affiliations:
Computer Science Department, Tijuana Institute of Technology, P.O. Box 4207, Chula Vista CA;Computer Science Department, Tijuana Institute of Technology, P.O. Box 4207, Chula Vista CA
Venue:
Systems Analysis Modelling Simulation
Year:
2003

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Abstract

We describe in this article a new theory of chaos using fuzzy logic techniques. Chaotic behavior in nonlinear dynamical systems is very difficult to detect and control. Part of the problem is that mathematical results for chaos are difficult to use in many cases, and even if one could use them there is an underlying uncertainty in the accuracy of the numerical simulations of the dynamical systems. For this reason, we can model the uncertainty of detecting the range of values where chaos occurs, using fuzzy sets theory. Using fuzzy sets, we can build a new theory of Fuzzy Chaos, where we can use fuzzy set to describe the behaviors of a system. We illustrate our approach with two cases: Chua's circuit and Duffing's oscillator.