Multiplicative Sampled-Data Control for Interval Type-2 Fuzzy Interconnected PDE Systems Under Memory Event-Triggered Scheme

This paper investigates the multiplicative sampled-data control for the interconnected non-linear partial differential equation (PDE) systems with parameter uncertainties. First, an interval type-2 (IT2) Takagi–Sugeno fuzzy model is employed to reconstruct the studied system. In contrast to type-1 fuzzy sets, IT2 fuzzy sets can handle parameter uncertainties that type-1 fuzzy sets cannot handle, and they can characterize parameter uncertainties by utilizing upper and lower membership functions. Next, based on the IT2 fuzzy model, a sampled-data IT2 fuzzy controller containing multiplicative control gain uncertainties is designed to reduce the control cost, where a Bernoulli distribution is adopted to depict the stochastically occurring multiplicative gain uncertainties. Moreover, to conserve communication resources, a memory event-triggered strategy (METS) is employed to decrease the amount of useless data transmitted in the network channel. In contrast to the event-triggered strategy (ETS), the METS triggers these data with a small relative error between the current data and the latest published data, thereby achieving better control. Finally, an example is given to demonstrate the validity of the proposed methodology.