Distributed optimization for consensus performance of delayed fractional-order double-integrator multi-agent systems

Li, Jun; Zhou, Nan; Qin, Kaiyu; Chen, Badong; Wu, Yonghong; Choi, Kup‐Sze

doi:10.1016/j.neucom.2022.12.005

Cited by 6 publications

(1 citation statement)

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“…Further for the multi-agent systems of fractional order, the authors showed that by appropriate choice of the intensity of delayed state fractional order derivative, the robustness against communication time delay can be improved. In [37], Liu et al introduced a delay in the fractional derivative to reduce the effect of nonuniform time delays on the consensus of double-integrator multi-agent system of fractional order.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions, Convergence and Global stability of delayed differential system with delay in the state variable of the Caputo derivative

Kumar,

Sharma,

Singh

2023

Preprint

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The aim of this paper is to investigate the numerical solutions of delayed fractional differential equations (FDEs). A constant time delay is taken in the Caputo derivative of the state variable and also in the state variable. To obtain solutions, we extend the block boundary value method (BBVM) and show the convergence of the resulting scheme. Further, it is found that the order of convergence is $\min\{m,q-\delta+1\}$, where $m$ and $q$ are the order and block-size of the BBVM, respectively, and $\delta$ lies in between $0$ and $1$. In our methodology, we approximate the fractional-ordered derivative by a combination of the $m^{\text{th}}$-order BBVM and a $q^{\text{th}}$-order Lagrange interpolating polynomial. Lastly, we analyze the global stability of the numerical scheme and with the aid of some numerical examples, its computational effectiveness is proved. In examples, we analyse some fractional order delay differential systems and present a comparison of solutions for different fractional order derivatives. Furthermore, it is demonstrated that the global errors diminish as the order of the fractional derivative decreases, and this fact is supported by the theoretical order of convergence. MSC Classification: 34K37 , 34D23 , 65L20

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Section: Introductionmentioning

confidence: 99%