Novel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients

Ruoyu Wei; Jinde Cao; Jurgen Kurths; Ruoyu Wei; Jinde Cao; Jurgen Kurths

doi:10.3934/math.2020199

AIMS Mathematics

2020, Volume 5, Issue 4: 3089-3110. doi: 10.3934/math.2020199

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Research article

Novel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients

1.
School of Mathematics, Southeast University, Nanjing 210096, China
2.
Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany

Received: 16 January 2020 Accepted: 18 March 2020 Published: 23 March 2020
MSC : 92B20

In this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixedtime control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results.
- quaternion,
- time-varying coefficients,
- bidirectional associative memory neural networks (BAMNNs),
- adaptive control,
- fixed-time stabilization
Citation: Ruoyu Wei, Jinde Cao, Jurgen Kurths. Novel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients[J]. AIMS Mathematics, 2020, 5(4): 3089-3110. doi: 10.3934/math.2020199

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Abstract

In this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixedtime control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

References

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