Probabilistic message passing control and FPD based decentralised control for stochastic complex systems

Yuyang Zhou; Randa Herzallah; Yuyang Zhou; Randa Herzallah

doi:10.3934/ElectrEng.2020.2.216

AIMS Electronics and Electrical Engineering

2020, Volume 4, Issue 2: 216-233. doi: 10.3934/ElectrEng.2020.2.216

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Research article Special Issues

Probabilistic message passing control and FPD based decentralised control for stochastic complex systems

Yuyang Zhou ^,,
Randa Herzallah

The Systems Analytics Research Institute, Aston University, Aston Triangle, Birmingham B4 7ET, UK

Received: 07 April 2020 Accepted: 28 May 2020 Published: 10 June 2020

This paper offers a novel decentralised control strategy for a class of linear stochastic largescale complex systems. The proposed control strategy is developed to address the main challenges in controlling complex systems such as high dimensionality, stochasticity, uncertainties, and unknown system parameters. To overcome a wide range of domain of complex systems, the proposed strategy decomposes the complex system into several subsystems and controls the system in a decentralised manner. The global control objective is achieved by individually controlling all the local subsystems and then exchanging information between subsystems about their state values.
This paper mainly focuses on the probabilistic communication between subsystems, therefore the detailed process of message-passing probabilistic framework is provided. For each subsystem, the regulation problem is considered, and fully probabilistic design (FPD) is applied to take the stochastic nature of complex systems into consideration. Also, since the governing equations of the system dynamics are assumed to be unknown, linear optimisation methods are employed to estimate the parameters of the subsystems. To demonstrate the effectiveness of the proposed control framework, a numerical example is given.
- stochastic system control,
- decentralised control,
- fully probabilistic design,
- message passing,
- complex network control
Citation: Yuyang Zhou, Randa Herzallah. Probabilistic message passing control and FPD based decentralised control for stochastic complex systems[J]. AIMS Electronics and Electrical Engineering, 2020, 4(2): 216-233. doi: 10.3934/ElectrEng.2020.2.216

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Abstract

This paper offers a novel decentralised control strategy for a class of linear stochastic largescale complex systems. The proposed control strategy is developed to address the main challenges in controlling complex systems such as high dimensionality, stochasticity, uncertainties, and unknown system parameters. To overcome a wide range of domain of complex systems, the proposed strategy decomposes the complex system into several subsystems and controls the system in a decentralised manner. The global control objective is achieved by individually controlling all the local subsystems and then exchanging information between subsystems about their state values.
This paper mainly focuses on the probabilistic communication between subsystems, therefore the detailed process of message-passing probabilistic framework is provided. For each subsystem, the regulation problem is considered, and fully probabilistic design (FPD) is applied to take the stochastic nature of complex systems into consideration. Also, since the governing equations of the system dynamics are assumed to be unknown, linear optimisation methods are employed to estimate the parameters of the subsystems. To demonstrate the effectiveness of the proposed control framework, a numerical example is given.

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