Fixed-time Consensus Algorithm for Multi-agent Systems with Integrator Dynamics

Abstract

The paper addresses the problem of exact average-consensus reaching in a prescribed time. The communication topology is assumed to be defined by a weighted undirected graph and the agents are represented by integrators. A nonlinear control protocol, which ensures a finite-time convergence, is proposed. With the designed protocol, any prescribed convergence time can be guaranteed regardless of the initial conditions.

Non‐singular fixed‐time terminal sliding mode control of non‐linear systems

“…However, a small β < 1 in Yang's controller (refer to (23) of [15]) leads to very large control effort. In addition, the form of (13) is more concise.…”

Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics

“…Definition 2: [18] The origin of the system (1) is said to be globally fixed-time stable if it is globally uniformly finite-time stable and the settling time function T is globally bounded, i.e., there exists a finite constant Tmax ∈ R+ such that T ≤ Tmax and x(t) = 0 for all t ≥ T and x0 ∈ R n . Lemma 1: [18], [19] If there exists a continuous radially unbounded and positive definite function V (x) such thaṫ…”

“…To be specific, for any given desired To, ε will be specified by (19) accordingly if the order of the multi-agent system is fixed, but the observer parameters (16)-(18) will be then tuned according to the prescribed ε, the network topology and the number of agents in a group. In other words, (19) provides an explicit algorithm for adjusting the observer parameters to predefine the settling time estimate.…”

“…The fixed-time stability exhibits an elegant property in some applications, like hybrid systems design. The first attempt in fixed-time consensus for integrator-type multi-agents can be found in [19], [20]. Then, the fixed-time consensus design framework is generalized in [21] for the first-order integrator multi-agent systems subject to external disturbances.…”

A class of robust consensus algorithms with predefined‐time convergence under switching topologies

“…The first one is based on the fixed‐time stability theory of autonomous systems proposed in the work of Andrieu et al and Polyakov . Based on this class of systems, fixed‐time consensus algorithms have been proposed either based on the homogeneity theory developed in the work of Andrieu et al as in the work of Gómez‐Gutiérrez et al, the settling‐time estimation provided in the work of Polyakov, as in the works of Zuo et al and Hong et al, or the subclass of fixed‐time stable systems, with an upper bound of the settling time that is less conservative than the one in the work of Polyakov, presented in the work of Parsegov et al, as in other works . However, despite the advantages in terms of settling‐time estimation, this approach does not enable to easily arbitrarily preassign the settling time.…”