Observability of switched Boolean control networks using algebraic forms

Yvjing Yang; Yang Liu; Jungang Lou; Zhen Wang

doi:10.3934/dcdss.2020373

Article Contents

2021, Volume 14, Issue 4: 1519-1533. Doi: 10.3934/dcdss.2020373

This issue Previous Article Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning Next Article Fully distributed consensus for higher-order nonlinear multi-agent systems with unmatched disturbances

Observability of switched Boolean control networks using algebraic forms

1.
College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
2.
School of Information Engineering, Huzhou University, Huzhou, China
3.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China

^* Corresponding author: Zhen Wang
^* Corresponding author: Zhen Wang

Received: October 2019

Revised: February 2020

Early access: May 2020

Published: April 2021

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Abstract

This paper addresses the observability of a switched Boolean control network (SBCN) using semi-tensor product (STP) of matrices. First, the observability of the SBCN is determined under desirable switching signals and arbitrary switching signals by encoding the switching signal as a boolean input. Then an algorithm is designed for determining the observability. Furthermore, feedback control laws are obtained to guarantee the observability of SBCNs. Examples and corresponding state trajectory graphs are given to illustrate the effectiveness of the given results.

Keywords:

Mathematics Subject Classification: Primary: 93B07; Secondary: 93C30.

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Figure 1. The state trajectory graph of $ \delta_{64}^{2} $, $ \delta_{64}^{20} $, $ \delta_{64}^{38} $, $ \delta_{64}^{56} $, where $ \delta_{64}^0 $ is a virtual state, number $ i $ in each cycle denote state $ \delta_{64}^i $, number $ j $ beside each edge stand for wight $ \delta_8^j $, and $ c\in\Lambda_0 $

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Figure 2. The state trajectory graph of $ \delta_{64}^{6} $, $ \delta_{64}^{15} $, $ \delta_{64}^{29} $, $ \delta_{64}^{23} $, $ \delta_{64}^{11} $, where number $ s $ in each cycle denote state $ \delta_{64}^s $, weight $ (i,j) $ beside each edge stands for weight $ (\delta_2^i, j) $, $ \delta_2^i $ refers to input, and $ j $ means the $ jth $ subsystem

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