Modeling and analysis of networked finite state machine subject to random communication losses

Weiwei Han; Zhipeng Zhang; Chengyi Xia; Weiwei Han; Zhipeng Zhang; Chengyi Xia

doi:10.3934/mmc.2023005

Mathematical Modelling and Control

2023, Volume 3, Issue 1: 50-60. doi: 10.3934/mmc.2023005

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Modeling and analysis of networked finite state machine subject to random communication losses

1.
Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin, 300384, China
2.
School of Artificial Intelligence, Tiangong University, Tianjin, 300387, China

Received: 11 September 2022 Revised: 07 January 2023 Accepted: 26 January 2023 Published: 15 February 2023

In networked control systems, channel packet loss is inevitable due to the restricted bandwidth, especially in control (from supervisory controller to some remote actuators), which will lead to the occurrence of failure control. In this paper, the controllability of networked finite state machine (NFSM) is investigated within the framework of matrix semi-tensor product (STP), where random channel packet losses are considered. Firstly, to capture the transition dynamics under random packet losses in the control channel, we introduce a stochastic variable to estimate the state evolution, and the variable is assumed to obey the Bernoulli binary distribution. Meanwhile, the NFSM with random channel packet losses can be expressed as a probabilistic logic representation. Subsequently, by means of the delicate operation of matrix STP, some concise validation conditions for the controllability with a probability of one ($ w.p. $ 1), are derived for NFSM based on the probabilistic logic representation. Finally, a typical computing instance is used to demonstrate the validity of the proposed method. The conclusions are conducive to study the security issues of the system involving opacity, fault detection, controller design and so on.
- semi-tensor product,
- networked system,
- finite state machine,
- controllability,
- channel packet losses
Citation: Weiwei Han, Zhipeng Zhang, Chengyi Xia. Modeling and analysis of networked finite state machine subject to random communication losses[J]. Mathematical Modelling and Control, 2023, 3(1): 50-60. doi: 10.3934/mmc.2023005

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Abstract

In networked control systems, channel packet loss is inevitable due to the restricted bandwidth, especially in control (from supervisory controller to some remote actuators), which will lead to the occurrence of failure control. In this paper, the controllability of networked finite state machine (NFSM) is investigated within the framework of matrix semi-tensor product (STP), where random channel packet losses are considered. Firstly, to capture the transition dynamics under random packet losses in the control channel, we introduce a stochastic variable to estimate the state evolution, and the variable is assumed to obey the Bernoulli binary distribution. Meanwhile, the NFSM with random channel packet losses can be expressed as a probabilistic logic representation. Subsequently, by means of the delicate operation of matrix STP, some concise validation conditions for the controllability with a probability of one ($ w.p. $ 1), are derived for NFSM based on the probabilistic logic representation. Finally, a typical computing instance is used to demonstrate the validity of the proposed method. The conclusions are conducive to study the security issues of the system involving opacity, fault detection, controller design and so on.

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