On predefined-time consensus protocols for dynamic networks

Abstract

This paper presents new classes of consensus protocols with fixed-time convergence, which enable the definition of an upper bound for consensus state as a parameter of the consensus protocol, ensuring its independence from the initial condition of the nodes. We demonstrate that our methodology subsumes current classes of fixed-time consensus protocols that are based on homogeneous in the bi-limit vector fields. Moreover, the proposed framework enables for the development of independent consensus protocols that are not needed to be homogeneous in the bi-limit. This proposal offers extra degrees of freedom to implement consensus algorithms with enhanced convergence features, such as reducing the gap between the real convergence moment and the upper bound chosen by the user. We present two classes of fixed-time consensus protocols for dynamic networks, consisting of nodes with first-order dynamics, and provide sufficient conditions to set the upper bound for convergence a priori as a consensus protocol parameter. The first protocol converges to the average value of the initial condition of the nodes, even when switching among dynamic networks. Unlike the first protocol, which requires, at each instant, an evaluation of the non-linear predefined time-consensus function, hereinafter introduced, per neighbor, the second protocol requires only a single evaluation and ensures a predefined time-consensus for static topologies and fixed-time convergence for dynamic networks. Predefined-time convergence is proved using Lyapunov analysis, and simulations are carried out to illustrate the performance of the suggested techniques. The exposed results have been applied to the design of predefined time-convergence formation control protocols to exemplify their main features.For agents with first-order dynamics, a consensus protocol with asymptotic convergence to the average value of the initial conditions of the node has been proposed in [1]. Using the stability results of the switching systems [10] it can be shown that such protocols reach a consensus even on dynamic networks by arbitrarily switching between highly connected graphs [1,11]. Consensus protocols with enhanced convergence properties have been suggested based on finite-time [12,13], and fixed-time [14,15] stability theory.In [16][17][18][19][20][21] continuous and discontinuous protocols with finite-time convergence were proposed. However, the convergence-time is an unbounded function of the initial conditions. A remarkable extension of the previous methods is the fixed-time convergent consensus. In this case, there exists a bound for the convergence time that is independent of the initial conditions [14,22]. Therefore, for the design of high-performance consensus protocols, the fixed-time convergence is a desirable property. Several consensus protocol have been proposed based on the fixed-time stability results from [14,15], see e.g., [23][24][25][26][27][28][29]. However, these consensus protocols have been justified only for static networks. Another fixed-time con...

Predefined-time stability for a class of dynamical systems and its application on the consensus control for nonlinear multi-agent systems

“…Therefore, the problem of predefined-time consensus for multi-agent systems is becoming one of the research focuses in engineering control field currently. For example, the predefined-time average consensus and formation were investigated for the first-order linear multi-agent systems in [29]. The authors studied the predefined-time tracking control for second-order multi-agent systems by the sliding mode protocol in [30].…”