Adaptive fuzzy identification of nonlinear dynamical systems based on quantum mechanics

Importation of methods from statistical physics into machine learning has led to rapid advancement in algorithms for efficient learning of good representations for complex problems. This paper presents a systematic approach to constructing a self-organizing fuzzy identifier. The proposed identifier is built on a fuzzy system consisting of a quantum clustering network and radial basis function network. We develop the corresponding self-organizing algorithms. Quantum clustering network, a new fuzzy clustering neural network model, combines the idea of quantum mechanics and the structure of Kohonen clustering network. The strategy proposed in our approach for the update rules of Kohonen clustering network is derived from the fixed-point iteration for the solution of nonlinear equations. The model eliminates the sensitivity to the choice of the initial configuration and yields a dynamic fuzzy clustering solution. Quantum clustering network is used for the generation of fuzzy rules as well as the construction of radial basis function network for fuzzy inference. Furthermore, the complex dynamical behavior in the proposed quantum learning systems is investigated. The concept of self-organization in complex dynamical systems and the role of quantum mechanics are presented. It provides us with efficient tools to get better insight into learning dynamics. Simulation results show that the proposed method can provide the fuzzy models with satisfactory accuracy.