Fuzzy Model and Particle Swarm Optimization for Nonlinear Identification of a Chua´s Oscillator

The identification of a nonlinear system with chaotic behavior denoted Chua´s oscillator by using fuzzy models intertwined with particle swarm optimization (PSO) method is presented. This hybrid approach is applied to experimental data generated by an inductorless Chua´s circuit that consists of an electronic chaotic oscillator. Chua´s circuit has been used as a test platform by various scientific and engineering communities related to the study of chaos due its great potencial in technological applications, for instance, telecommunications, cryptography and physics. Fuzzy set theory has been evolved as a powerful modeling tool that can cope with uncertainties and nonlinearities in modeling and identification procedures. The identification of a optimized fuzzy model Takagi-Sugeno (T-S) fuzzy model involves two primary tasks: parameter tuning and structure optimization. The premise part of production rules is optimized here by using the particle swarm optimization method. In turn, least mean squares technique is applied to the consequent part of a T-S fuzzy model. Results indicate PSO method and Least Mean Square technique succeeded in constructing a T-S fuzzy model when dealing with chaotic dynamics obtained through experimental data supplied by inductorless Chua´s electronic circuit.