Adaptive fuzzy connectivity-preserving consensus protocols for stochastic strict-feedback nonlinear MASs subject to unmeasured periodic disturbances

Abstract

Two adaptive fuzzy connectivity-preserving consensus control schemes, in continuous and event-triggered manners, are proposed for stochastic strict-feedback nonlinear multi-agent systems subject to unmeasured periodic disturbances. Differently from the existing works on connectivity-preserving consensus where the deterministic dynamics are investigated, stochastic multi-agent systems are considered. An error transformation is incorporated to preserve the initial interaction pattern determined by initial positions and communication ranges of the agents. Moreover, the stochastic system model suffers from unmeasured periodic disturbances in a nonlinear manner. By associating Fourier series expansion with fuzzy logic system, a novel function approximator is constructed to describe the packaged disturbance-dependent nonlinear functions. Meanwhile, a nonlinear filter is designed to avert the ”explosion of complexity” problem in conventional backstepping recursive design procedure. In addition, the proposed continuous controller is developed to event-triggered one. Then, it is proved that the consensus is achieved and the initial connectivity of communication graph is preserved in the sense of probability. In simulations, two examples are provided to substantiate the effectiveness of the proposed consensus protocols.