Abstract
Boolean multiplex (multilevel) networks (BMNs) are currently receiving considerable attention as theoretical arguments for modeling of biological systems and system level analysis. Studying control-related problems in BMNs may not only provide new views into the intrinsic control in complex biological systems, but also enable us to develop a method for manipulating biological systems using exogenous inputs. In this article, the observability of the Boolean multiplex control networks (BMCNs) are studied. First, the dynamical model and structure of BMCNs with control inputs and outputs are constructed. By using of Semi-Tensor Product (STP) approach, the logical dynamics of BMCNs is converted into an equivalent algebraic representation. Then, the observability of the BMCNs with two different kinds of control inputs is investigated by giving necessary and sufficient conditions. Finally, examples are given to illustrate the efficiency of the obtained theoretical results.
Highlights
Boolean multiplex networks (BMNs) are currently receiving considerable attention as theoretical arguments for modeling of biological systems and system level analysis
By using of Semi-Tensor Product (STP) approach, the logical dynamics of Boolean multiplex control networks (BMCNs) is converted into an equivalent algebraic representation
We consider the observability of BMCNs, following the standard formulation of the observability problem in systems theory, namely, we assume that the Boolean Networks (BNs) structure is known and that the goal is to infer the initial condition based on an output sequence
Summary
Yuhu Wu1, Jingxue Xu1, Xi-Ming Sun1,2 & Wei Wang received: 01 December 2016 accepted: 17 March 2017 Published: 28 April 2017. The observability of the Boolean multiplex control networks (BMCNs) are studied. J. et al studied controllability problem for multi-level Boolean control networks47 When it comes to the observability problem of BMCNs, to our best knowledge, there have been even no results, because there are many differences between BMNs and single-layer BNs. Even for the degenerated BMNs, their observability are different from the single-layer BNs’, for example the BCNs studied by Cheng, D. et al. and Li, F. et al.. We consider the observability of BMCNs, following the standard formulation of the observability problem in systems theory, namely, we assume that the BN structure is known and that the goal is to infer the initial condition based on an output sequence.
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