System modeling and synchronization of nonlinear chaotic systems with uncertainty and disturbance by innovative fuzzy modeling strategy

In this paper, an application of the innovative fuzzy model [1] is applied to simulate and synchronize two classical Sprott chaotic systems with unknown noise and disturbance. In traditional Takagi-Sugeno fuzzy (T-S fuzzy) model, there will be 2^N linear subsystems (according to 2^N fuzzy rules) and m × 2^N equations in the T-S fuzzy system, where N is the number of minimum nonlinear terms and m is the order of the system. Through the new fuzzy model, a complicated nonlinear system is linearized to a simple form - linear coupling of only two linear subsystems and the numbers of fuzzy rules can be reduced from 2^N to 2 × N. The fuzzy equations become much simpler. There are two Sprott systems in numerical simulations to show the effectiveness and feasibility of new model.