Practical Fixed-Time Bipartite Consensus of Nonlinear Incommensurate Fractional-Order Multiagent Systems in Directed Signed Networks

Gong, Ping; Han, Qing‐Long

doi:10.1137/19m1282970

Cited by 23 publications

(9 citation statements)

References 30 publications

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“…In a given time interval, the tracking error between every follower and the leader is expected to converge to zero in Problem 1 whereas a closed set in Problem 2. On the one hand, remarkably, the significance of practical prescribed-time consensus can be understood by analogy with the practical finite-time consensus 27 and practical fixed-time consensus, [28][29][30] which also require that the tracking error converges to a closed set centered on zero. As mentioned in Reference 25, the practical consensus is more practical and general than the accurate consensus when taking unknown parameters and external disturbances into account.…”

Section: Assumption 2 |Umentioning

confidence: 99%

“…More specially,

{\mu}_2(t)\to \infty

{\mathscr{H}}_i{o}_2\to 0

t={t}_2+{T}_2

. Referred from References 30 and 40, the dynamic damped reciprocal technology is useful to avoid such singularity phenomenon by utilizing

\frac{1}{\rho}\to \frac{\rho }{\rho^2+{\varepsilon}^2}

\varepsilon \to 0

. Based on the dynamic damped reciprocal method, a distributed observer is provided as

\begin{matrix} alignleft \\ align-1 {\dot{ℓ}}_{i, k} & align-2 = - φ_{k} (t) [\sum_{j = 1}^{N} a_{i j} (ℓ_{i, k} - ℓ_{j, k}) + b_{i} (ℓ_{i, k} - x_{0, k})] + ℓ_{i, k + 1}, k = 1, 2, \dots, n - 1, \\ align-1 {\dot{ℓ}}_{i, n} & align-2 = - φ_{n} (t) ξ \end{matrix}

…”

Section: Leader‐following Mass With Nonzero Leader's Input and Mismat...mentioning

confidence: 99%

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Observer‐based prescribed‐time consensus control for heterogeneous multi‐agent systems under directed graphs

Zeng

Duan

2022

Intl J Robust & Nonlinear

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This work studies the prescribed‐time robust consensus tracking problem of heterogeneous multi‐agent systems over directed graphs. Aiming at multi‐agent systems with a static leader and only matched disturbances, a distributed observer‐based consensus algorithm is developed, to ensure that the tracking errors converge to zero accurately in prescribed time. For the case of multi‐agent systems with a dynamic leader and mismatched/matched disturbances, an adaptive strategy based on a distributed observer and a disturbance observer is designed by the dynamic damping reciprocal technology. Such strategy can avoid the numerical singularity, adapt to the situation that the upper bounds of the disturbances are unknown, and assure that the tracking errors converge to an adjustable neighborhood of zero within prescribed time. Finally, simulations are given to verify the effectiveness of the proposed control strategies.

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Section: Assumption 2 |Umentioning

confidence: 99%

“…More specially,

{\mu}_2(t)\to \infty

{\mathscr{H}}_i{o}_2\to 0

t={t}_2+{T}_2

. Referred from References 30 and 40, the dynamic damped reciprocal technology is useful to avoid such singularity phenomenon by utilizing

\frac{1}{\rho}\to \frac{\rho }{\rho^2+{\varepsilon}^2}

\varepsilon \to 0

. Based on the dynamic damped reciprocal method, a distributed observer is provided as

\begin{matrix} alignleft \\ align-1 {\dot{ℓ}}_{i, k} & align-2 = - φ_{k} (t) [\sum_{j = 1}^{N} a_{i j} (ℓ_{i, k} - ℓ_{j, k}) + b_{i} (ℓ_{i, k} - x_{0, k})] + ℓ_{i, k + 1}, k = 1, 2, \dots, n - 1, \\ align-1 {\dot{ℓ}}_{i, n} & align-2 = - φ_{n} (t) ξ \end{matrix}

…”

Section: Leader‐following Mass With Nonzero Leader's Input and Mismat...mentioning

confidence: 99%

Observer‐based prescribed‐time consensus control for heterogeneous multi‐agent systems under directed graphs

Zeng

Duan

2022

Intl J Robust & Nonlinear

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“…For signed graph with directed spanning tree, Reference 24 shown that agents in general do not enjoy bipartite consensus, but the interval bipartite consensus. Further extension and generalization can be subsequently found in finite‐time convergence, 25 time‐delay bipartite consensus, 26 impulsive consensus, 27 fractional‐order multi‐agent systems, 28 and stochastic approximation, 29 etc.…”

Section: Introductionmentioning

confidence: 99%

Consensus for cooperative–competitive network systems: An impulsive perspective

Zhang

Liu

Lou

et al. 2023

Intl J Robust & Nonlinear

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Usually, hypotheses involving cooperative interactions and continuous interplay among interacting agents may result in somewhat conservatism, drastically hurdling potential about interpretations of prevalent aggregation phenomena arising in both nature and practical application. Of interest uncovered in this article is the cooperative-competitive consensus problems for multi-agent systems by leverage of impulsive-based control perspective. We first discuss the possibility of quantifying interaction relation of the agents and the description of cooperative-competitive phenomena that capture massive interest recently.Specifically, the former is done by algebraic graph theory, following the same research avenue as the convention; while the cooperative-competitive information is described by some nonzero scaling parameter. We shall pursue the tie that enables to anchor the consensus of participating agents, without depending on the signed graph theory. Subsequently, a manner relying on the local information is carried out to induce the consensus error to circumvent the global information. Then, consensus condition, in connection with the features of both continuous and impulsivebased dynamics, is obtained, as well as several typical circumstances are also elaborated. Both the proposed consensus algorithms and the derived results are underpinned via a numerical study eventually.

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“…Adaptive control strategy is applied to the consensus of incommensurate order multi-agent systems in Gong's excellent works. 18,19 It is worth noting that the above results are concerned with leader-following consensus; furthermore, adaptive methods have been used. A question naturally arises: are there consensus behaviors in an incommensurate order network, which is described as follows…”

Section: Introductionmentioning

confidence: 99%

On leaderless consensus of incommensurate order multi-agent systems

Wang,

Zhang,

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article concerns the leaderless consensus problem of incommensurate-order multi-agent systems. First, a detailed analysis of the consensus between two agents with incommensurate order is shown. From this, one can conclude that consensus behavior exists in such cases. Furthermore, the initial value of the agent with a lower order will decide the consensus state. Second, a general incommensurate order multi-agent system is investigated under the directed ring topology, and the results imply that the consensus behavior also exists in such a topology. At the same time, the initial values of the agent with minimum order will determine the consensus state. Finally, some numerical examples are given to show the effectiveness of the aforementioned theoretical results. In addition, several attempts are given just by simulations when the topology is undirected and connected, and some discussions are conducted in the end.

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Practical Fixed-Time Bipartite Consensus of Nonlinear Incommensurate Fractional-Order Multiagent Systems in Directed Signed Networks

Cited by 23 publications

References 30 publications

Observer‐based prescribed‐time consensus control for heterogeneous multi‐agent systems under directed graphs

Observer‐based prescribed‐time consensus control for heterogeneous multi‐agent systems under directed graphs

Consensus for cooperative–competitive network systems: An impulsive perspective

On leaderless consensus of incommensurate order multi-agent systems

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