Membership-Function-Dependent Fuzzy Control of Reaction-Diffusion Memristive Neural Networks With a Finite Number of Actuators and Sensors

This paper investigates the fuzzy control design problem for reaction-diffusion memristive (MNNs). Initially, by introducing the logical switched functions, the original reaction-diffusion MNN is transformed into another model form. Subsequently, a Takagi-Sugeno (T-S) fuzzy PDE model is devoted to accurately representing the reaction-diffusion MNN. Then, via the obtained T-S fuzzy model, under the hypothesis that the actuators and sensors are collocated while the spatial domain is separated into several subdomains, a Lyapunov-based membership-function-dependent fuzzy control design employing a finite number of actuators and sensors is developed in terms of linear matrix inequalities, such that the closed-loop reaction-diffusion MNN is exponentially stable. In final, numerical simulations illustrate the effectiveness of the proposed fuzzy control design method.