Output tracking of delayed logical control networks with multi-constraint

ZHENG Ya-ting; FENG Jun-e

doi:10.1631/FITEE.1900376

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Output tracking of delayed logical control networks with multi-constraint

Special Issue on Complex Systems and Networks with Their Applications | Updated：2022-05-19

- Output tracking of delayed logical control networks with multi-constraint
- 多重受限时滞逻辑控制网络的输出跟踪
- Frontiers of Information Technology & Electronic Engineering Vol. 21, Issue 2, Pages: 316-323(2020)
- Affiliations：
  
  School of Mathematics, Shandong University, Jinan 250100, China
- Author bio：
  
  [ "FENG Jun-e,E-mail:fengjune@sdu.edu.cn" ]
- Funds：
- DOI：10.1631/FITEE.1900376
  CLC： O231
- Received：29 July 2019，
  
  Revised：2019-12-19，
  
  Published：2020-02
- Accepted：
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ZHENG Ya-ting, FENG Jun-e. Output tracking of delayed logical control networks with multi-constraint[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 316-323.
DOI：

ZHENG Ya-ting, FENG Jun-e. Output tracking of delayed logical control networks with multi-constraint[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 316-323. DOI： 10.1631/FITEE.1900376.

摘要

本文深入研究具有状态和控制受限的时滞逻辑控制网络的输出跟踪问题。与其他类型时滞相比，状态依赖型时滞数值的更新依赖当前的状态值和一个伪逻辑函数。多重受限意味着状态的取值局限在一个给定的非空集合以及控制器的设计有条件限定。采用矩阵半张量积方法将动态方程转化为代数形式，进而构造一个等价扩维系统。基于该扩维系统，输出跟踪问题被转化为集合镇定问题。利用变换的状态转移矩阵，可得到该系统实现输出跟踪的充分必要条件，通过数学软件容易验证此条件。此外，设计了状态反馈控制器使时滞逻辑控制网络的输出能跟踪参考信号。最后，通过一个例子验证本文的理论结果。

Abstract

In this study

the output tracking of delayed logical control networks (DLCNs) with state and control constraints is further investigated. Compared with other delays

state-dependent delay updates its value depending on the current state values and a pseudo-logical function. Multiple constraints mean that state values are constrained in a nonempty set and the design of the controller is conditioned. Using the semi-tensor product of matrices

dynamical equations of DLCNs are converted into an algebraic description

and an equivalent augmented system is constructed. Based on the augmented system

the output tracking problem is transformed into a set stabilization problem. A deformation of the state transition matrix is computed

and a necessary and sufficient condition is derived for the output tracking of a DLCN with multi-constraint. This condition is easily verified by mathematical software. In addition

the admissible state-feedback controller is designed to enable the outputs of the DLCN to track the reference signal. Finally

theoretical results are illustrated by an example.

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Keywords

references

T Akutsu , , , M Hayashida , , , WK Ching , , , 等 . . Control of Boolean networks: hardness results and algorithms for tree structured networks . . J Theor Biol , , 2007 . . 244 ( ( 4 ): ): 670 - - 679 . . DOI: 10.1016/j.jtbi.2006.09.023 http://doi.org/10.1016/j.jtbi.2006.09.023 . .

F Ay , , , F Xu , , , T Kahveci . . Scalable steady state analysis of Boolean biological regulatory networks . . PLoS ONE , , 2009 . . 4 ( ( 12 ): ): e7992 DOI: 10.1371/journal.pone.0007992 http://doi.org/10.1371/journal.pone.0007992 . .

N Bof , , , E Fornasini , , , ME Valcher . . Output feedback stabilization of Boolean control networks . . Automatica , , 2015 . . 57 21 - - 28 . . DOI: 10.1016/j.automatica.2015.03.032 http://doi.org/10.1016/j.automatica.2015.03.032 . .

C Chaouiya , , , A Naldi , , , D Thieffry . . Logical modelling of gene regulatory networks with GINsim. In: van Helden J, Toussaint A, Thieffry D (Eds.), Bacterial Molecular Networks . . Springer, New York , , 2012 . . 463 - - 479 . . DOI: 10.1007/978-1-61779-361-5_23 http://doi.org/10.1007/978-1-61779-361-5_23 . .

D Cheng , , , H Qi , , , Y Zhao . . An Introduction to Semi-tensor Product of Matrices and its Applications . . World Scientific, Singapore , , 2012 . . .

TH Chueh , , , HHS Lu . . Inference of biological pathway from gene expression profiles by time delay Boolean networks . . PLoS ONE , , 2012 . . 7 ( ( 8 ): ): e42095 DOI: 10.1371/journal.pone.0042095 http://doi.org/10.1371/journal.pone.0042095 . .

HB Fan , , , JE Feng , , , M Meng , , , 等 . . General decomposition of fuzzy relations: semi-tensor product approach . . Fuzzy Set Syst , , 2018 . . p.1 - - 16 . . DOI: 10.1016/j.fss.2018.12.012 http://doi.org/10.1016/j.fss.2018.12.012 . .

E Fornasini , , , ME Valcher . . Observability, reconstructibility and state observers of Boolean control networks . . IEEE Trans Autom Contr , , 2013 . . 58 ( ( 6 ): ): 1390 - - 1401 . . DOI: 10.1109/TAC.2012.2231592 http://doi.org/10.1109/TAC.2012.2231592 . .

E Fornasini , , , ME Valcher . . Optimal control of Boolean control networks . . IEEE Trans Autom Contr , , 2014 . . 59 ( ( 5 ): ): 1258 - - 1270 . . DOI: 10.1109/TAC.2013.2294821 http://doi.org/10.1109/TAC.2013.2294821 . .

YQ Guo , , , RP Zhou , , , YH Wu , , , 等 . . Stability and set stability in distribution of probabilistic Boolean networks . . IEEE Trans Autom Contr , , 2019 . . 64 ( ( 2 ): ): 736 - - 742 . . DOI: 10.1109/TAC.2018.2833170 http://doi.org/10.1109/TAC.2018.2833170 . .

S Haider , , , R Pal . . Boolean network inference from time series data incorporating prior biological knowledge . . BMC Genom , , 2012 . . 13 S9 DOI: 10.1186/1471-2164-13-S6-S9 http://doi.org/10.1186/1471-2164-13-S6-S9 . .

S Kauffman . . Metabolic stability and epigenesis in randomly constructed genetic nets . . J Theor Biol , , 1969 . . 22 ( ( 3 ): ): 437 - - 467 . . DOI: 10.1016/0022-5193(69)90015-0 http://doi.org/10.1016/0022-5193(69)90015-0 . .

D Laschov , , , M Margaliot . . Controllability of Boolean control networks via the Perro--Frobenius theory . . Automatica , , 2012 . . 48 ( ( 6 ): ): 1218 - - 1223 . . DOI: 10.1016/j.automatica.2012.03.022 http://doi.org/10.1016/j.automatica.2012.03.022 . .

D Laschov , , , M Margaliot . . Minimum-time control of Boolean networks . . SIAM J Contr Optim , , 2013 . . 51 ( ( 4 ): ): 2869 - - 2892 . . DOI: 10.1137/110844660 http://doi.org/10.1137/110844660 . .

BW Li , , , JG Lou , , , Y Liu , , , 等 . . Robust invariant set analysis of Boolean networks . . Complexity , , 2019 . . 2019 2731395 DOI: 10.1155/2019/2731395 http://doi.org/10.1155/2019/2731395 . .

FF Li . . Stability of Boolean networks with delays using pinning control . . IEEE Trans Contr Netw Syst , , 2018 . . 5 ( ( 1 ): ): 179 - - 185 . . DOI: 10.1109/TCNS.2016.2585861 http://doi.org/10.1109/TCNS.2016.2585861 . .

H Li , , , Y Zheng , , , F Alsaadi . . Algebraic formulation and topological structure of Boolean networks with state-dependent delay . . J Comput Appl Math , , 2019a . . 350 87 - - 97 . . DOI: 10.1016/j.cam.2018.10.003 http://doi.org/10.1016/j.cam.2018.10.003 . .

H Li , , , X Xu , , , X Ding . . Finite-time stability analysis of stochastic switched Boolean networks with impulsive effect . . Appl Math Comput , , 2019b . . 347 557 - - 565 . . DOI: 10.1016/j.amc.2018.11.018 http://doi.org/10.1016/j.amc.2018.11.018 . .

HT Li , , , YZ Wang , , , LH Xie . . Output tracking control of Boolean control networks via state feedback: constant reference signal case . . Automatica , , 2015 . . 59 54 - - 59 . . DOI: 10.1016/j.automatica.2015.06.004 http://doi.org/10.1016/j.automatica.2015.06.004 . .

XD Li , , , HT Li , , , GD Zhao . . Function perturbation impact on feedback stabilization of Boolean control networks . . IEEE Trans Neur Netw Learn Syst , , 2019 . . 30 ( ( 8 ): ): 2548 - - 2554 . . DOI: 10.1109/TNNLS.2018.2881168 http://doi.org/10.1109/TNNLS.2018.2881168 . .

YY Li , , , BW Li , , , Y Liu , , , 等 . . Set stability and set stabilization of switched Boolean networks with state-based switching . . IEEE Access , , 2018 . . 6 35624 - - 35630 . . DOI: 10.1109/ACCESS.2018.2851391 http://doi.org/10.1109/ACCESS.2018.2851391 . .

YY Li , , , RJ Liu , , , JG Lou , , , 等 . . Output tracking of Boolean control networks driven by constant reference signal . . IEEE Access , , 2019 . . 7 112572 - - 112577 . . DOI: 10.1109/ACCESS.2019.2934740 http://doi.org/10.1109/ACCESS.2019.2934740 . .

ZQ Li , , , DZ Cheng . . Algebraic approach to dynamics of multivalued networks . . Int J Bifurc Chaos , , 2010 . . 20 ( ( 3 ): ): 561 - - 582 . . DOI: 10.1142/S0218127410025892 http://doi.org/10.1142/S0218127410025892 . .

Y Liu , , , BW Li , , , JQ Lu , , , 等 . . Pinning control for the disturbance decoupling problem of Boolean networks . . IEEE Trans Autom Contr , , 2017 . . 62 ( ( 12 ): ): 6595 - - 6601 . . DOI: 10.1109/TAC.2017.2715181 http://doi.org/10.1109/TAC.2017.2715181 . .

JQ Lu , , , J Zhong , , , DWC Ho , , , 等 . . On controllability of delayed Boolean control networks . . SIAM J Contr Optim , , 2016 . . 54 ( ( 2 ): ): 475 - - 494 . . DOI: 10.1137/140991820 http://doi.org/10.1137/140991820 . .

JQ Lu , , , LJ Sun , , , Y Liu , , , 等 . . Stabilization of Boolean control networks under aperiodic sampled-data control . . SIAM J Contr Optim , , 2018a . . 56 ( ( 6 ): ): 4385 - - 4404 . . DOI: 10.1137/18M1169308 http://doi.org/10.1137/18M1169308 . .

JQ Lu , , , ML Li , , , TW Huang , , , 等 . . The transformation between the Galois NLFSRs and the Fibonacci NLFSRs via semi-tensor product of matrices . . Automatica , , 2018b . . 96 393 - - 397 . . DOI: 10.1016/j.automatica.2018.07.011 http://doi.org/10.1016/j.automatica.2018.07.011 . .

M Meng , , , J Lam , , , JE Feng , , , 等 . . Stability and stabilization of Boolean networks with stochastic delays . . IEEE Trans Autom Contr , , 2019 . . 64 ( ( 2 ): ): 790 - - 796 . . DOI: 10.1109/TAC.2018.2835366 http://doi.org/10.1109/TAC.2018.2835366 . .

LJ Sun , , , JQ Lu , , , WK Ching . . Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable . . Front Inform Technol Electron Eng , , 2020 . . 21 ( ( 2 ): ): 260 - - 267 . . DOI: 10.1631/FITEE.1900312 http://doi.org/10.1631/FITEE.1900312 . .

LY Tong , , , Y Liu , , , YY Li , , , 等 . . Robust control invariance of probabilistic Boolean control networks via event-triggered control . . IEEE Access , , 2018 . . 6 37767 - - 37774 . . DOI: 10.1109/ACCESS.2018.2828128 http://doi.org/10.1109/ACCESS.2018.2828128 . .

A Veliz-Cuba , , , B Stigler . . Boolean models can explain bistability in the lac operon . . J Comput Biol , , 2011 . . 18 ( ( 6 ): ): 783 - - 794 . . DOI: 10.1089/cmb.2011.0031 http://doi.org/10.1089/cmb.2011.0031 . .

B Wang , , , JE Feng , , , M Meng . . Model matching of switched asynchronous sequential machines via matrix approach . . Int J Contr , , 2019 . . 92 ( ( 10 ): ): 2430 - - 2440 . . DOI: 10.1080/00207179.2018.1441552 http://doi.org/10.1080/00207179.2018.1441552 . .

YH Wu , , , XM Sun , , , XD Zhao , , , 等 . . Optimal control of Boolean control networks with average cost: a policy iteration approach . . Automatica , , 2019 . . 100 378 - - 387 . . DOI: 10.1016/j.automatica.2018.11.036 http://doi.org/10.1016/j.automatica.2018.11.036 . .

YY Yu , , , JE Feng , , , JF Pan . . Block decoupling of Boolean control networks . . IEEE Trans Autom Contr , , 2019a . . 64 ( ( 8 ): ): 3129 - - 3140 . . DOI: 10.1109/TAC.2018.2880411 http://doi.org/10.1109/TAC.2018.2880411 . .

YY Yu , , , B Wang , , , JE Feng . . Input observability of Boolean control networks . . Neurocomputing , , 2019b . . 333 22 - - 28 . . DOI: 10.1016/j.neucom.2018.12.014 http://doi.org/10.1016/j.neucom.2018.12.014 . .

J Zhong , , , DWC Ho , , , JQ Lu , , , 等 . . Pinning controllers for activation output tracking of Boolean network under one-bit perturbation . . IEEE Trans Cybern , , 2019 . . 49 ( ( 9 ): ): 3398 - - 3408 . . DOI: 10.1109/TCYB.2018.2842819 http://doi.org/10.1109/TCYB.2018.2842819 . .

QX Zhu , , , Y Liu , , , J Lu , , , 等 . . Further results on the controllability of Boolean control networks . . IEEE Trans Autom Contr , , 2019 . . 64 ( ( 1 ): ): 440 - - 442 . . DOI: 10.1109/TAC.2018.2830642 http://doi.org/10.1109/TAC.2018.2830642 . .

SY Zhu , , , JG Lou , , , Y Liu , , , 等 . . Event-triggered control for the stabilization of probabilistic Boolean control networks . . Complexity , , 2018 . . 2018 9259348 DOI: 10.1155/2018/9259348 http://doi.org/10.1155/2018/9259348 . .

SY Zhu , , , JQ Lu , , , Y Liu . . Asymptotical stability of probabilistic Boolean networks with state delays . . IEEE Trans Autom Contr , in press , , 2019a . . DOI: 10.1109/TAC.2019.2934532 http://doi.org/10.1109/TAC.2019.2934532 . .

SY Zhu , , , JQ Lu , , , Y Liu , , , 等 . . Output tracking of probabilistic Boolean networks by output feedback control . . Inform Sci , , 2019b . . 483 96 - - 105 . . DOI: 10.1016/j.ins.2018.12.087 http://doi.org/10.1016/j.ins.2018.12.087 . .

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