Novel Fuzzy Modeling and Synchronization of Chaotic Systems With Multinonlinear Terms by Advanced Ge-Li Fuzzy Model
提出一种改进的葛-李模糊模型，可处理任意复杂非线性项，仅需m×2条模糊规则和两个线性子系统即可建模，并实现结构完全不同系统的模糊同步，用Mathieu-Van der Pol系统和量子细胞神经网络系统验证了有效性。
Ge and Li proposed an alternative strategy to model and synchronize two totally different nonlinear systems in the end of 2011, which provided a new version for fuzzy modeling and has been applied to several fields to simplify their modeling works and solve the mismatch problems [1]-[17]. However, the proposed model limits the number of nonlinear terms in each equation so that this model could not be used in all kinds of nonlinear dynamic systems. As a result, in this paper, a more efficient and comprehensive advanced-Ge-Li fuzzy model is given to further release the limitation and improve the effectiveness of the original one. The novel fuzzy model can be applied to all kinds of complex nonlinear systems--this is the universal strategy and only m x 2 fuzzy rules as well as two linear subsystems are needed to simulate nonlinear behaviors (m is the number of states in a nonlinear dynamic system), whatever the nonlinear terms are copious or complicated. Further, the fuzzy synchronization of two nonlinear dynamic systems with totally distinct structures can be achieved via only two sets of control gains designed through the novel fuzzy model as well as its corresponding fuzzy synchronization scheme. Two complicated dynamic systems are designed to be the illustrations, Mathieu-Van der pol system with uncertainties and Quantum-cellular neural networks nano system with uncertainties, to show the effectiveness and feasibility of the novel fuzzy model.