Consensus problems in networks of agents with double-integrator dynamics and time-varying delays

Abstract

In this article, we consider consensus problems in networks of agents with double-integrator dynamics and non-uniform time-varying delays. The agent dynamics is adopted as a typical point mass model based on Newton's law. Without assuming that the weighting factors in the information update schemes are non-negative, we propose two protocols such that both the state and the velocity of agents achieve consensus. An equivalent reduced-order system is introduced to analyse the convergence of the protocols. Some necessary and (or) sufficient conditions for consensus are established in terms of linear matrix inequalities. Simulation results are provided that demonstrate the effectiveness of our theoretical results.

Neural‐network‐based adaptive leader‐following consensus control for second‐order non‐linear multi‐agent systems

“…Owing to the complexity of the non-linearity, the existing linear consensus methods, such as [12][13][14][15][16][17], cannot be directly applied to non-linear systems. In recent years, several scholars have addressed the non-linear consensus problem [18][19][20][21].…”

“…So the second-order agreement is more challenging, and can be more widely applied to real systems. In recent decades, many eminent research results about linear second-order consensus control have been published [12][13][14][15][16][17], where [12,13] for leaderless consensus and [14-17] for leader-following consensus.In reality, most multi-agent system dynamics contain the intrinsic non-linearity. Owing to the complexity of the non-linearity, the existing linear consensus methods, such as [12][13][14][15][16][17], cannot be directly applied to non-linear systems.…”

Consensus Analysis of Heterogeneous Multi-Agent Systems with Time-Varying Delay

“…Let the Lyapunov functionals defined by (12) and (13) be the common Lyapunov functional for the switched System (21), respectively. Then, similar to the analysis in Theorem 1 and Corollary 1, we get the following consensus results for the case of switching topology.…”

“…[1][2][3][4][5]. Consensus seeking has been analyzed mainly for first-order multi-agent systems modeled by a single integrator [6][7][8][9][10][11] and second-order multi-agent systems modeled by double integrators [12][13][14], respectively.…”

Fuzzy distributed cooperative tracking for a swarm of unmanned aerial vehicles with heterogeneous goals

“…For example, consensus was examined for multi-agent systems with general linear dynamics in Li et al (2007), Seo et al (2009). In Ren and Beard (2008), Sun and Long (2009) consensus problems for agents with single/double or higher integrator dynamics were studied. In Fax and Murray (2004), the authors focused on the stabilisation of a network of identical agents with linear dynamics whilst in Cai et al (2011) the authors suggested necessary and sufficient conditions for swarm stability of high-order linear time-invariant (LTI) multi-agent systems.…”