Updated Formulas for Semi-tensor Product of Matrices
详细信息 查看官网全文
- 英文论文题名：Updated Formulas for Semi-tensor Product of Matrices
- 论文作者：Yaqi Hao ; Xiao Zhang ; Daizhan Cheng
- 英文论文作者：Yaqi Hao ; Xiao Zhang ; Daizhan Cheng ; School of Control Science and Engineering ; Shandong University ; Academy of Mathematics and Systems Science ; Chinese Academy of Sciences
- 年：2017
- 作者机构：School of Control Science and Engineering,Shandong University;Academy of Mathematics and Systems Science,Chinese Academy of Sciences;
- 英文论文关键词：Semi-tensor product of matrices ; Semi-tensor addition ; Logical system ; Algebraic state space representation ; Symmetric game
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O151.21
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：7
- 文件大小：219k
- 原文格式：D
- 会议级别：全国
摘要
Some main formulas about semi-tensor product(STP) of matrices are presented in their mostly updated forms. The formulas consist of(i) fundamental formulas about STP;(ii) swap and permutation related formulas;(iii) formulas for the application of STP to logical systems;(iv) the relationship of STP with Kronecker products;(v) formulas for the application of STP to game theory. The paper provides a convenient tool for investigating and applying STP.
Some main formulas about semi-tensor product(STP) of matrices are presented in their mostly updated forms. The formulas consist of(i) fundamental formulas about STP;(ii) swap and permutation related formulas;(iii) formulas for the application of STP to logical systems;(iv) the relationship of STP with Kronecker products;(v) formulas for the application of STP to game theory. The paper provides a convenient tool for investigating and applying STP.
Some main formulas about semi-tensor product(STP) of matrices are presented in their mostly updated forms. The formulas consist of(i) fundamental formulas about STP;(ii) swap and permutation related formulas;(iii) formulas for the application of STP to logical systems;(iv) the relationship of STP with Kronecker products;(v) formulas for the application of STP to game theory. The paper provides a convenient tool for investigating and applying STP.
引文
[1]R.Branzei,D.Dimitrov,S.Tijs,Models in Cooperative Game Theory,Springer-Verlag,Berlin,2005.
[2]D.Cheng,Semi-tensor product of matrices and its application to Morgan’s problem,Science in China,Series F:Information Science,44(3):195–212,2001.
[3]D.Cheng,J.Ma,Q.Lu,S.Mei,Quadratic form of stable submanifold for power systems,Int.J.Rob.Nonlin.Contr.,14:773–788,2004.
[4]D.Cheng,H.Qi,Semi-tensor Product of Matrices-Theory and Applications.Beijing:Science Press,2007(Second Ed,2011).(in Chinese)
[5]D.Cheng,H.Qi,Z.Li,Analysis and Control of Boolean Networks:A Semi-tensor Product Approach.London:Springer,2011.
[6]D.Cheng,H.Qi,Y.Zhao,An Introduction to Semi-tensor Product of Matrices and Its Applications.Singapore:World Scientific,2012.
[7]D.Cheng,J.Feng,H.Lv,Solving fuzzy relational equations via semi-tensor product,IEEE Trans.Fuzzy Systems,20(2):390–396,2012.
[8]D.Cheng,X.Xu,Bi-decomposition of multi-valued logical functions and its applications,Automatica,49(7):1979–1985,2013.
[9]D.Cheng,On finite potential games,Automatica,50(7):1793–1801,2014.
[10]D.Cheng,T.Liu,Y.Wang,Matrix approach to game theory,J.Sys.Sci.Math,34(11):1291–1305,2014(in Chinese).
[11]D.Cheng,F.He,H.Qi,T.Xu,Modeling,analysis and control of networked evolutionary games.IEEE Trans.Aut.Contr.,60(9):2402–2415,2015.
[12]D.Cheng,On equivalence of matrices,ar Xiv preprint ar Xiv:1605.09523,2016.
[13]D.Cheng,T.Liu,Linear representation of symmetric games,preprint.
[14]J.Feng,H.Lv,D.Cheng,Multiple fuzzy relation and its application to coupled fuzzy control,Asian J.Contr.,15(5):1313–1324,2013.
[15]E.Fornasini,M.E.Valcher,Observability,reconstructibility and state observers of Boolean control networks,IEEE Trans.Aut.Contr.,58(6):1390–1401,2013.
[16]B.Gao,L.Li,H.peng,et al,Principle for performing attractor transits with single control in Boolean networks,Physical Review E,88(6):062706,2013.
[17]P.Guo,Y.Wang,H.Li,Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method,Automatica,49(11):3384–3389,2013.
[18]G.Hochma,M.Margaliot,E.Fornasini,Symbolic dynamics of Boolean control networks,Automatica,49(8):2525–2530,2013.
[19]R.A.Horn,C.R.Johnson,Topics in Matrix Analysis.Cambridge:Cambridge Univ.Press,1991.
[20]D.Laschov,M.Margaliot,Minimum-time control of Boolean networks,SIAM J.Contr.Opt.,51(4):2869–2892,2013.
[21]R.Li,T.Chu,Synchronization in an array of coupled Boolean networks,Physics Letters A,376(45):3071–3075,2012.
[22]H.Li,Y.Wang,Boolean derivative calculation with application to fault detection of combinational cirts via the semi-tensor product method,Automatica,48(4):688–693,2012.
[23]X.Liu,Y.Xu,An inquiry method of transit network based on semi-tensor product,J.Agency of Complex Syst.Complexity Sci.,10(1):38–44,2013.
[24]X.Liu,J.Zhu,On potential equations of finite games,Automatica,68:245–253,2016.
[25]T.Liu,J.Wang,D.Cheng,Game theoretic control of multiagent systems,ar Xir preprinter,ar Xiv:1608.00192,2016.
[26]J.Lu,J.Zhong,D.W.C.Ho,Y.Tang,J.Cao,On controlllability of delayed Boolean control networks,SIAM J.Cont.Opt.,54(2):475–494,2016.
[27]S.Mei,F.Liu,A.Xie,Transient Analysis of Power Systems-A Semi-tensor Product Approach.Beijing:Tsinghua Univ.Press,2010.(in Chinese)
[28]C.R.Rao,Estimation of heteroscedastic variances in linear models,J.Amer Statist Assoc,65:161–172,1970.
[29]Y.Wang,C.Zhang,Z.Liu,A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems,Automatica,48(7):1227–1236,2012.
[30]Y.Wang,T.Liu,D.Cheng,Some notes on semi-tensor product of matrices and swap matrix,J.Sys.Sci.&Math.Scis.,36(9):1367–1375,2016(in Chinese).
[31]Y.Wu,T.Shen,An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamic systems,Sys.Contr.Lett.,82:108–144,2015.
[32]X.Xu,Y.Hong,Matrix expression to model matching of asynchronous sequential machines,IEEE Trans.Aut.Contr.,58(11):2974–2979,2013.
[33]A.Xue,F.Wu,Q.Lu,S.Mei,Power system dynamic security region and its approximations,IEEE Trans.Circ.Sys.I,53(12):2849–2859,2006.
[34]Y.Yan,Z.Chen,Z.Liu,Semi-tensor product approach to controllability and stabilizability of finite automata,J.Syst.Engn.Electron.,26(1):134–141,2015.
[35]Y.Zhao,J.Kim,M.Filippone,Aggregation algorithm towards large-scale Boolean netwok analysis,IEEE Trans.Aut.Contr.,58(8):1976–1985,2013.
[36]L.Zhan,J.Feng,Mix-valued logic-based formation control,Int.J.Contr.,86(6):1191–1199,2013.
[37]K.Zhang,On Some Control-theoretic and Dynamical Problems of Logical Dynamical Systems,Ph D dissertation.Harbin:Harbin Engineering University,2012(in Chinese).
[38]D.Zhao,H.Peng,L.Li,et al.Novel way to research nonlinear feedback shift register,Science China F,Information Sciences,57(9):1–14,2014.
[39]X.Zhang,Matrix Analysis and Applications.Beijing:Tsinghua Univ.Press,Springer,2004(in Chinese).
[40]K.Zhang,L.Zhang,L.Xie,Invertibility and nonsingularity of Boolean control networks,Automatica,60(c):155–164,2015.
[41]J.Zhong and D.Lin,A new linearization method for nonlinear feedback shift registers,Journal of Computer and System Sciences,81:783–796,2015.
[42]J.Zhong,J.Lu,L.Li,J.Cao,Finding graph minimum stable set and core via semi-tensor product approach,Neurocomputing,174:588–596,2016.
[43]Y.Zou,J.Zhu,Kalman decomposition for Boolean control networks,Automatica,54:64–71,2015.
[2]D.Cheng,Semi-tensor product of matrices and its application to Morgan’s problem,Science in China,Series F:Information Science,44(3):195–212,2001.
[3]D.Cheng,J.Ma,Q.Lu,S.Mei,Quadratic form of stable submanifold for power systems,Int.J.Rob.Nonlin.Contr.,14:773–788,2004.
[4]D.Cheng,H.Qi,Semi-tensor Product of Matrices-Theory and Applications.Beijing:Science Press,2007(Second Ed,2011).(in Chinese)
[5]D.Cheng,H.Qi,Z.Li,Analysis and Control of Boolean Networks:A Semi-tensor Product Approach.London:Springer,2011.
[6]D.Cheng,H.Qi,Y.Zhao,An Introduction to Semi-tensor Product of Matrices and Its Applications.Singapore:World Scientific,2012.
[7]D.Cheng,J.Feng,H.Lv,Solving fuzzy relational equations via semi-tensor product,IEEE Trans.Fuzzy Systems,20(2):390–396,2012.
[8]D.Cheng,X.Xu,Bi-decomposition of multi-valued logical functions and its applications,Automatica,49(7):1979–1985,2013.
[9]D.Cheng,On finite potential games,Automatica,50(7):1793–1801,2014.
[10]D.Cheng,T.Liu,Y.Wang,Matrix approach to game theory,J.Sys.Sci.Math,34(11):1291–1305,2014(in Chinese).
[11]D.Cheng,F.He,H.Qi,T.Xu,Modeling,analysis and control of networked evolutionary games.IEEE Trans.Aut.Contr.,60(9):2402–2415,2015.
[12]D.Cheng,On equivalence of matrices,ar Xiv preprint ar Xiv:1605.09523,2016.
[13]D.Cheng,T.Liu,Linear representation of symmetric games,preprint.
[14]J.Feng,H.Lv,D.Cheng,Multiple fuzzy relation and its application to coupled fuzzy control,Asian J.Contr.,15(5):1313–1324,2013.
[15]E.Fornasini,M.E.Valcher,Observability,reconstructibility and state observers of Boolean control networks,IEEE Trans.Aut.Contr.,58(6):1390–1401,2013.
[16]B.Gao,L.Li,H.peng,et al,Principle for performing attractor transits with single control in Boolean networks,Physical Review E,88(6):062706,2013.
[17]P.Guo,Y.Wang,H.Li,Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method,Automatica,49(11):3384–3389,2013.
[18]G.Hochma,M.Margaliot,E.Fornasini,Symbolic dynamics of Boolean control networks,Automatica,49(8):2525–2530,2013.
[19]R.A.Horn,C.R.Johnson,Topics in Matrix Analysis.Cambridge:Cambridge Univ.Press,1991.
[20]D.Laschov,M.Margaliot,Minimum-time control of Boolean networks,SIAM J.Contr.Opt.,51(4):2869–2892,2013.
[21]R.Li,T.Chu,Synchronization in an array of coupled Boolean networks,Physics Letters A,376(45):3071–3075,2012.
[22]H.Li,Y.Wang,Boolean derivative calculation with application to fault detection of combinational cirts via the semi-tensor product method,Automatica,48(4):688–693,2012.
[23]X.Liu,Y.Xu,An inquiry method of transit network based on semi-tensor product,J.Agency of Complex Syst.Complexity Sci.,10(1):38–44,2013.
[24]X.Liu,J.Zhu,On potential equations of finite games,Automatica,68:245–253,2016.
[25]T.Liu,J.Wang,D.Cheng,Game theoretic control of multiagent systems,ar Xir preprinter,ar Xiv:1608.00192,2016.
[26]J.Lu,J.Zhong,D.W.C.Ho,Y.Tang,J.Cao,On controlllability of delayed Boolean control networks,SIAM J.Cont.Opt.,54(2):475–494,2016.
[27]S.Mei,F.Liu,A.Xie,Transient Analysis of Power Systems-A Semi-tensor Product Approach.Beijing:Tsinghua Univ.Press,2010.(in Chinese)
[28]C.R.Rao,Estimation of heteroscedastic variances in linear models,J.Amer Statist Assoc,65:161–172,1970.
[29]Y.Wang,C.Zhang,Z.Liu,A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems,Automatica,48(7):1227–1236,2012.
[30]Y.Wang,T.Liu,D.Cheng,Some notes on semi-tensor product of matrices and swap matrix,J.Sys.Sci.&Math.Scis.,36(9):1367–1375,2016(in Chinese).
[31]Y.Wu,T.Shen,An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamic systems,Sys.Contr.Lett.,82:108–144,2015.
[32]X.Xu,Y.Hong,Matrix expression to model matching of asynchronous sequential machines,IEEE Trans.Aut.Contr.,58(11):2974–2979,2013.
[33]A.Xue,F.Wu,Q.Lu,S.Mei,Power system dynamic security region and its approximations,IEEE Trans.Circ.Sys.I,53(12):2849–2859,2006.
[34]Y.Yan,Z.Chen,Z.Liu,Semi-tensor product approach to controllability and stabilizability of finite automata,J.Syst.Engn.Electron.,26(1):134–141,2015.
[35]Y.Zhao,J.Kim,M.Filippone,Aggregation algorithm towards large-scale Boolean netwok analysis,IEEE Trans.Aut.Contr.,58(8):1976–1985,2013.
[36]L.Zhan,J.Feng,Mix-valued logic-based formation control,Int.J.Contr.,86(6):1191–1199,2013.
[37]K.Zhang,On Some Control-theoretic and Dynamical Problems of Logical Dynamical Systems,Ph D dissertation.Harbin:Harbin Engineering University,2012(in Chinese).
[38]D.Zhao,H.Peng,L.Li,et al.Novel way to research nonlinear feedback shift register,Science China F,Information Sciences,57(9):1–14,2014.
[39]X.Zhang,Matrix Analysis and Applications.Beijing:Tsinghua Univ.Press,Springer,2004(in Chinese).
[40]K.Zhang,L.Zhang,L.Xie,Invertibility and nonsingularity of Boolean control networks,Automatica,60(c):155–164,2015.
[41]J.Zhong and D.Lin,A new linearization method for nonlinear feedback shift registers,Journal of Computer and System Sciences,81:783–796,2015.
[42]J.Zhong,J.Lu,L.Li,J.Cao,Finding graph minimum stable set and core via semi-tensor product approach,Neurocomputing,174:588–596,2016.
[43]Y.Zou,J.Zhu,Kalman decomposition for Boolean control networks,Automatica,54:64–71,2015.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |