Consensus of nonlinear multi‐agent systems via distributed hybrid controls

Abstract

AbstractThe consensus problem of nonlinear multi‐agent systems with nonuniform time‐varying connection topologies via two novel distributed hybrid control protocols is discussed. By using the degrees of freedom brought by coupling weights, impulsive control with impulse time windows integrates intermittent control and impulsive control into a unified control framework and is more suitable for the situations where only the time intervals in which impulses occur are known but the exact instants of impulses cannot be identified. Compared with intermittent control, the intermittent impulsive control (IIC) reduces the amount of data transmission and improves the security of the system. The introduction of the rest windows makes the IIC break the limit of the upper bound of impulsive intervals of general impulsive control, and the system is easier to maintain according to plan. Control‐time‐dependent Lyapunov function based methods are developed to overcome the difficulty of stability analysis of the error systems caused by continuous switching of multiple dynamic subsystems. Two consensus criteria are presented and the corresponding controller design schemes are proposed. The results can uniformly deal with the positive and negative effects of impulses, and do not require at least one subsystem of the error system to be stable. Three examples are given to demonstrate the effectiveness of the derived theoretical results.