Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems
01 Sep 2017-Iet Control Theory and Applications (The Institution of Engineering and Technology)-Vol. 11, Iss: 13, pp 2040-2047
TL;DR: The main concern of this study is to present a comprehensive introduction to logical networks and some other applications under the framework of STP of matrices.
Abstract: This study presents a detailed survey on recent development of logical networks and its applications, including the background of logical networks, the theory of a new matrix product called semi-tensor product (STP) of matrices, some fundamental works on logical networks, and some current research works. Particularly, some fundamental works on logical networks are presented for the past years, including controllability, stability and stabilisation, synchronisation, disturbance decoupling and so on. Due to the great potential of STP in dealing with logical networks, a surge of attraction from overseas is paid on the study of STP and its applications. Currently, some new research areas are widely studied including pinning control, function perturbations, system decomposition, trajectory control, output tracking issues, symbolic dynamics and so on. The main concern of this study is to present a comprehensive introduction to logical networks and some other applications under the framework of STP of matrices.
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TL;DR: A novel policy iteration algorithm, which can find the optimal state feedback controller in finite iteration steps, is proposed by resorting to Laurent series expression for the average infinite horizon problem of BCNs.
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TL;DR: A comprehensive survey on the applications of STP method in engineering, including gene regulation, power system, wireless communication, smart grid, information security, combustion engine and vehicle control, are presented.
Abstract: Semi-tensor product (STP) of matrices has attracted more and more attention from both control theory and engineering in the last two decades. This paper presents a comprehensive survey on the applications of STP method in engineering. Firstly, some preliminary results on STP method are recalled. Secondly, some applications of STP method in engineering, including gene regulation, power system, wireless communication, smart grid, information security, combustion engine and vehicle control, are reviewed. Finally, some potential applications of STP method are predicted.
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TL;DR: In this article, the authors summarize and explain the concepts for Boolean network modeling and present application examples and guidelines to work with and analyze Boolean network models, which can be applied to unravel the mechanisms regulating the properties of the system or to identify promising intervention targets.
Abstract: Boolean network models are one of the simplest models to study complex dynamic behavior in biological systems. They can be applied to unravel the mechanisms regulating the properties of the system or to identify promising intervention targets. Since its introduction by Stuart Kauffman in 1969 for describing gene regulatory networks, various biologically based networks and tools for their analysis were developed. Here, we summarize and explain the concepts for Boolean network modeling. We also present application examples and guidelines to work with and analyze Boolean network models.
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Cites background from "Survey on semi-tensor product metho..."
...However, as for other BN approaches, the exponential time complexity limits semi-tensor-product approaches to focus on networks with a relatively small number of components [89]....
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References
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TL;DR: Probabilistic Boolean Networks (PBN) are introduced that share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty.
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TL;DR: Under this framework, a Boolean network equation is converted into an equivalent algebraic form as a conventional discrete-time linear system, and a matrix expression of logic is proposed, where a logical variable is expressed as a vector, a logical function is express as a multiple linear mapping.
Abstract: A new matrix product, called semi-tensor product of matrices, is reviewed Using it, a matrix expression of logic is proposed, where a logical variable is expressed as a vector, a logical function is expressed as a multiple linear mapping Under this framework, a Boolean network equation is converted into an equivalent algebraic form as a conventional discrete-time linear system Analyzing the transition matrix of the linear system, formulas are obtained to show a) the number of fixed points; b) the numbers of cycles of different lengths; c) transient period, for all points to enter the set of attractors; and d) basin of each attractor The corresponding algorithms are developed and used to some examples
589 citations
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