Decentralized observer-based event-triggered control for an interconnected fractional-order system with stochastic Cyber-attacks

Zhaohui Chen; Jie Tan; Yong He; Zhong Cao; Zhaohui Chen; Jie Tan; Yong He; Zhong Cao

doi:10.3934/math.2024091

AIMS Mathematics

2024, Volume 9, Issue 1: 1861-1876. doi: 10.3934/math.2024091

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Research article

Decentralized observer-based event-triggered control for an interconnected fractional-order system with stochastic Cyber-attacks

1.
School of Mathematics, Physics and Data Science, Chongqing University of Science and Technology, Chongqing 401331, China
2.
School of electronics and communication Engineering, Guangzhou University, Guangzhou 510006, China

Received: 12 October 2023 Revised: 27 November 2023 Accepted: 06 December 2023 Published: 15 December 2023
MSC : 93A14, 93B50, 93D99

The problem of decentralized observer-based event-triggered stabilization for an interconnected fractional-order system subject to stochastic cyber-attacks is studied. To address this issue, the decentralized event-triggered mechanism is proposed for the interconnected fractional-order system, where the event-triggered schemes are designed based on the states of fractional-order observers, and the stochastic attacks are considered both on control inputs and observer outputs. By combining decentralized observers and decentralized event-triggered controllers, we aim to achieve decentralized control with reduced amplifying error and use local signals to improve overall system performance. By utilizing the diffusive representation of the fractional-order system, the interconnected fractional-order system is transformed into an equivalent integer-order one to simplify the analysis and control design. Employing the Lyapunov indirect approach, a sufficient condition is obtained to guarantee the stochastic asymptotically stability of the augmented system. Additionally, by the singular value decomposition technique, the approach of simultaneously computing the decentralized observer gains and controller gains is presented. Finally, a simulation example is provided to validate the theoretical findings.
- interconnected fractional-order system,
- event-triggered control,
- observer,
- stochastic cyber-attack,
- Lyapunov indirect approach
Citation: Zhaohui Chen, Jie Tan, Yong He, Zhong Cao. Decentralized observer-based event-triggered control for an interconnected fractional-order system with stochastic Cyber-attacks[J]. AIMS Mathematics, 2024, 9(1): 1861-1876. doi: 10.3934/math.2024091

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Abstract

The problem of decentralized observer-based event-triggered stabilization for an interconnected fractional-order system subject to stochastic cyber-attacks is studied. To address this issue, the decentralized event-triggered mechanism is proposed for the interconnected fractional-order system, where the event-triggered schemes are designed based on the states of fractional-order observers, and the stochastic attacks are considered both on control inputs and observer outputs. By combining decentralized observers and decentralized event-triggered controllers, we aim to achieve decentralized control with reduced amplifying error and use local signals to improve overall system performance. By utilizing the diffusive representation of the fractional-order system, the interconnected fractional-order system is transformed into an equivalent integer-order one to simplify the analysis and control design. Employing the Lyapunov indirect approach, a sufficient condition is obtained to guarantee the stochastic asymptotically stability of the augmented system. Additionally, by the singular value decomposition technique, the approach of simultaneously computing the decentralized observer gains and controller gains is presented. Finally, a simulation example is provided to validate the theoretical findings.

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