Predefined-Time Consensus of Nonlinear First-Order Systems Using a Time Base Generator

Abstract

This paper proposes a couple of consensus algorithms for multiagent systems in which agents have first-order nonlinear dynamics, reaching the consensus state at a predefined time independently of the initial conditions. The proposed consensus protocols are based on the so-called time base generators (TBGs), which are time-dependent functions used to build time-varying control laws. Predefined-time convergence to the consensus is proved for connected undirected communication topologies and directed topologies having a spanning tree. Furthermore, one of the proposed protocols is based on the super-twisting controller, providing robustness against disturbances while maintaining the predefined-time convergence property. The performance of the proposed methods is illustrated in simulations, and it is compared with finite-time, fixed-time, and predefined-time consensus protocols. It is shown that the proposed TBG protocols represent an advantage not only in the possibility to define a settling time but also in providing smoother and smaller control actions than existing finite-time, fixed-time, and predefined-time consensus.