Abstract
This work focuses on the fixed-time leader-following flocking for multi-agent systems. Different from the previous continuous inherent dynamic f(x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ,v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ,t) for agent i, a new nonlinear discontinuous one is firstly proposed in this paper. Employing non-smooth techniques, graph theory and fixed-time stability theory, the fixed-time leader-following flocking is achieved. Moreover, an upper bound of the settling time is independent of initial states. In addition, two illustrative examples are given to verify the effectiveness of the theoretical results.
Highlights
The study of cooperative control of autonomous agents has recently attracted significant interest, due to it is a basic research of multi-agent systems and it has potential applications, such as formation flying of unmanned aerial vehicles [3], distributed sensor networks [17] and cooperation of multi-robot teams [2]
The main contributions in the present work are summarized as follows: 1) An inherent dynamics which is the first time we proposed here is discontinuous and it is quite different from a Lipschitz-type function [22], [39], [40]
2) Unlike the results in [16], [35], where the flocking is achieved in a finite-time depending on initial states of the systems, we investigate the fixed-time leader-following flocking and estimate the upper bound of the settling time which is independence of initial states by the new protocol
Summary
The study of cooperative control of autonomous agents has recently attracted significant interest, due to it is a basic research of multi-agent systems and it has potential applications, such as formation flying of unmanned aerial vehicles (short for UAVs) [3], distributed sensor networks [17] and cooperation of multi-robot teams [2]. Ning et al [4], [5] considered the finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics. Z. Xu et al.: Fixed-Time Leader-Following Flocking for Nonlinear Second-Order Multi-Agent Systems flocking problem for a discontinuous Cucker-Smale type model under a long-range interaction. (I).Can the flocking occur in the leader-following multi-agent systems with discontinuous inherent dynamics in a fixed-time?. 2) Unlike the results in [16], [35], where the flocking is achieved in a finite-time depending on initial states of the systems, we investigate the fixed-time leader-following flocking and estimate the upper bound of the settling time which is independence of initial states by the new protocol.
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