Multilayer Fuzzy Supremum Approximation to Discrete-Time Synchronization

Spatiality and temporality represent key features of the real world. A critical hurdle in the application of fuzzy logic systems lies in their limited capability to directly approximate the variables across spatial and temporal scales. This article investigates the fuzzy approximation problem of uncertain nonlinear spatiotemporal systems. A novel multilayer fuzzy supremum approximation (MFSA) is designed to map a spatiotemporal function to a state-based iterative supremum function by separating the time-varying parameters, which can be further approximated using the proposed fuzzy upremum approximation algorithm. It is indicated that MFSA is an effective approximation method for spatiotemporal functions as compared to the references. Subsequently, MFSA is developed into the leader-following synchronization problem of discrete-time multiagent systems. The MFSA-based observer and synchronization control schemes are designed by removing the assumption that either the leader's control input or the bound of the leader's control input is a known prior to each follower. The uniformly ultimate boundedness of the observer estimation errors and synchronization errors are achieved. The corresponding simulations indicate the efficacy of our approach.