Predefined-time consensus using a time base generator (TBG)

Predefined-time convergence means that a system is driven to the origin of its state space in a desired settling time that can be set as an explicit parameter of the controller and it is achieved independently of the initial conditions. In this paper, we propose distributed control protocols that enforce predefined-time convergence in the consensus problem for first order systems. The proposed control method is based on the so-called time base generator (TBGs), which are time-dependent functions used to build time-varying control laws. Our method can be applied to any first-order linearizable nonlinear system. In particular, a robust nonlinear control protocol is proposed to deal with perturbed systems. Stability of the closed-loop protocols is proved for connected undirected communication topologies of the network system and for directed topologies having a spanning tree. The performance of the proposed consensus protocols are evaluated and compared in simulation with finite and fixed-time controllers and other previous scheme that also reaches consensus at a preset time. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.