Fuzzy adaptive control of two totally different chaotic systems with complicated structures by novel pragmatically adaptive control strategy

In this paper, a set of novel fuzzy adaptive control strategy is proposed to control two totally different nonlinear systems with complicated structure and different numbers of nonlinear terms. This novel adaptive control strategy is composed of three main points—(1) novel fuzzy model, proposed via Li and Ge (IEEE Trans Syst Man Cybern Part B Cybern 41(4):1015–1026, 2011), provides a set of simple and effective modeling strategy to reduce the total numbers of fuzzy rules through modeling process, and only two linear subsystems are needed; (2) novel control Lyapunov function is set as an exponential form of error states and tries to speed up the variance of states in this article; and (3) pragmatical asymptotically stability theorem: this theorem can be applied to proof that the error of parameters can achieve the original point strictly. Mathieu–Van der Pol system and quantum cellular neural networks nanosystem are used for illustrations in numerical simulation results to show the effectiveness and feasibility of the new fuzzy adaptive approach. Traditional fuzzy modeling and adaptive control method are given for further comparison.