nav emailalert searchbtn searchbox tablepage yinyongbenwen piczone journalimg searchdiv qikanlogo popupnotification paper
2024 04 v.39 305-324
逻辑动态系统的最优控制研究进展
基金项目(Foundation): 国家自然科学基金资助项目(62473239); 山东省优质研究生课程资助项目(SDYKC2022052); 山东师范大学校级本科教改资助项目(2021BJ052)
邮箱(Email):
DOI:
中文作者单位:

山东师范大学数学与统计学院;

摘要(Abstract):

近年来,国内外学者对逻辑动态系统的分析与控制进行了大量研究。本文通过梳理已有相关文献,主要介绍关于逻辑网络最优控制问题的一些研究结果,包括最优控制问题的研究背景、基于矩阵半张量积方法解决逻辑网络最优控制问题的方法、逻辑网络最优控制问题的重要研究工作等,并在此基础上进行研究展望,为逻辑动态系统最优控制理论的后续研究提供参考。

关键词(KeyWords): 逻辑动态系统;最优控制;动态规划;矩阵半张量积
参考文献

[ 1 ] 贺建勋,连瑞兴.实用最优控制理论[M].厦门:厦门大学出版社,1989.

[ 2 ] 邓子辰.最优控制理论的发展及现状[J].大自然探索,1994,13(2):32-36.

[ 3 ] 刘骏跃.最优控制理论的现状与发展[J].机电工程,2000,17(5):4-6.

[ 4 ] 钱伟懿,徐恭贤,宫召华.最优控制理论及其应用[M].大连:大连理工大学出版社,2010.

[ 5 ] Wu Y,Cheng D,Ghosh B K,et al.Recent advances in optimization and game theoretic control for networked systems[J].Asian Journal of Control,2019,21(6):2493-2512.

[ 6 ] Newman M E J.Resource letter CS-1:Complex systems[J].American Journal of Physics,2011,79(8):800-810.

[ 7 ] Kaufiman S A.Metabolic stability and epigenesis in randomly constructed genetic nets[J].Journal of Theoretical Biology,1968,22(3):437-467.

[ 8 ] Boccaletti S,Latora V,Moreno Y,et al.Complex networks:Structure and dynamics[J].Physics Reports,2006,424(4-5):175-308.

[ 9 ] Taoma K,Tyson J J,Laomettachit T,et al.Stochastic Boolean model of normal and aberrant cell cycles in budding yeast[J].NPJ Systems Biology and Applications,2024,10(1):1-12.

[ 10 ] Veliz-Cuba A,Stigler B.Boolean models can explain bistability in the lac operon[J].Journal of Computational Biology,2011,18(6):783-794.

[ 11 ] Kauffman S A.The origins of order:Self-organization and selection in evolution[M].New York:Oxford University Press,1993.

[ 12 ] Cheng D,He F,Qi H,et al.Modeling,analysis and control of networked evolutionary games[J].IEEE Transactions on Automatic Control,2015,60(9):2402-2415.

[ 13 ] Li C,Xing Y,He F,et al.A strategic learning algorithm for state-based games[J].Automatica,2020,113:108615.

[ 14 ] Li C,He F,Qi H,et al.Potential games design using local information[C]// Proceedings of the 57th IEEE Conference on Decision and Control.Miami,USA,2018:1911-1916.

[ 15 ] Li C,Li A,Wu Y,et al.Logical dynamic games:models,equilibria,and potentials[J].IEEE Transactions on Automatic Control,2024,29(11):7584-7599.

[ 16 ] Zheng Y,Li C,Feng J.Modeling and dynamics of networked evolutionary game with switched time delay[J].IEEE Transactions on Control of Network Systems,2021,8(4):1778-1787.

[ 17 ] Lu J,Li M,Liu Y,et al.Nonsingularity of Grain-like cascade FSRs via semi-tensor product[J].Science China Information Sciences,2018,61:1-12.

[ 18 ] Xu X,Hong Y.Matrix expression and reachability analysis of finite automata[J].Journal of Control Theory and Applications,2012,10(2):210-215.

[ 19 ] Zhang K,Zhang L.Observability of Boolean control networks:A unified approach based on finite automata[J].IEEE Transactions on Automatic Control,2015,61(9):2733-2738.

[ 20 ] Zhang K,Zhang L,Xie L.Finite automata approach to observability of switched Boolean control networks[J].Nonlinear Analysis:Hybrid Systems,2016,19:186-197.

[ 21 ] Lujan J M,Bermúdez V,Guardiola C,et al.A methodology for combustion detection in diesel engines through in-cylinder pressure derivative signal[J].Mechanical Systems and Signal Processing,2010,24(7):2261-2275.

[ 22 ] Bertsekas D P.Dynamicprogramming and stochastic control[M].New York:Academic Press,1976.

[ 23 ] Mu Y,Guo L.Optimization and identification in a non-equilibrium dynamic game[C]// Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference.Shanghai,China,2009:5750-5755.

[ 24 ] Wang L,Liu Y,Wu Z,et al.Strategy optimization for static games based on STP method[J].Applied Mathematics and Computation,2018,316:390-399.

[ 25 ] 程代展,赵寅,徐听听.演化博弈与逻辑动态系统的优化控制[J].系统科学与数学,2012,32(10):1226-1238.

[ 26 ] Piccione M,Rubinstein A.Finite automata play a repeated extensive game[J].Journal of Economic Theory,1993,61(1):160-168.

[ 27 ] Alexander J M K.Random Boolean networks and evolutionary game theory[J].Philosophy of Science,2003,70(5):1289-1304.

[ 28 ] Zhao Y,Li Z,Cheng D.Optimal control of logical control networks[J].IEEE Transactions on Automatic Control,2010,56(8):1766-1776.

[ 29 ] Ching W K,Zhang S Q,Jiao Y,et al.Optimal control policy for probabilistic Boolean networks with hard constraints[J].IET Systems Biology,2009,3(2):90-99.

[ 30 ] Cheng D,Qi H,Zhao Y.An introduction to semi-tensor product of matrices and its applications[M].Singapore:World Scientific,2012.

[ 31 ] Liu Q.Optimal finite horizon control in gene regulatory networks[J].The European Physical Journal B,2013,86(6):1-5.

[ 32 ] Yang C,Wai-Ki C,Nam-Kiu T,et al.On finite-horizon control of genetic regulatory networks with multiple hard-constraints[J].BMC Systems Biology,2010,4(S2):1-7.

[ 33 ] Fornasini E,Valcher M E.Optimal control of Boolean control networks[J].IEEE Transactions on Automatic Control,2013,59(5):1258-1270.

[ 34 ] Wu Y,Kumar M,Shen T.A stochastic logical system approach to model and optimal control of cyclic variation of residual gas fraction in combustion engines[J].Applied Thermal Engineering,2016,93:251-259.

[ 35 ] Li Z,Cheng D.Algebraic approach to dynamics of multivalued networks[J].International Journal of Bifurcation and Chaos,2010,20(3):561-582.

[ 36 ] 程代展,齐洪胜,赵寅.布尔网络的分析与控制—矩阵半张量积方法[J].自动化学报,2011,37(5):529-540.

[ 37 ] Cheng D,Qi H,Li Z,et al.Stability and stabilization of Boolean networks[J].International Journal of Robust and Nonlinear Control,2011,21(2):134-156.

[ 38 ] Zhong J,Ho D W C,Lu J,et al.Global robust stability and stabilization of Boolean network with disturbances[J].Automatica,2017,84:142-148.

[ 39 ] Cheng D,Li C,He F.Observability of Boolean networks via set controllability approach[J].Systems & Control Letters,2018,115:22-25.

[ 40 ] Zhang K,Johansson K H.Efficient verification of observability and reconstructibility for large Boolean control networks with special structures[J].IEEE Transactions on Automatic Control,2020,65(12):5144-5158.

[ 41 ] Cheng D,Li C,Zhang X,et al.Controllability of Boolean networks via mixed controls[J].IEEE Control Systems Letters,2018,2(2):254-259.

[ 42 ] Li F,Sun J.Controllability of probabilistic Boolean control networks[J].Automatica,2011,47(12):2765-2771.

[ 43 ] Wang Y,Li C,Feng J.Distributed pinning controllers design for set stabilization of k-valued logical control networks[J].Mathematical Modelling and Control,2023,3(1):61-72.

[ 44 ] Li C,Zhang X,Feng J,et al.Transition analysis of stochastic logical control networks[J].IEEE Transactions on Automatic Control,2023,69(2):1226-1233.

[ 45 ] Cheng D,Xu X.Bi-decomposition of multi-valued logical functions and its applications[J].Automatica,2013,49(7):1979-1985.

[ 46 ] Fornasini E,Valcher M E.Observability,reconstructibility and state observers of Boolean control networks[J].IEEE Transactions on Automatic Control,2012,58(6):1390-1401.

[ 47 ] Li R,Chu T.Complete synchronization of Boolean networks[J].IEEE Transactions on Neural Networks and Learning Systems,2012,23(5):840-846.

[ 48 ] Zhang H,Wang X,Lin X.Synchronization of Boolean networks with different update schemes[J].IEEE Transactions on Computational Biology and Bioinformatics,2014,11(5):965-972.

[ 49 ] Zhang Z,Leifeld T,Zhang P.Finite horizon tracking control of Boolean control networks[J].IEEE Transactions on Automatic Control,2017,63(6):1798-1805.

[ 50 ] Zhang Q,Feng J,Jiao T.Finite horizon tracking control of probabilistic Boolean control networks[J].Journal of the Franklin Institute,2021,358(18):9909-9928.

[ 51 ] Li F,Sun J.Controllability of Boolean control networks with time delays in states[J].Automatica,2011,47(3):603-607.

[ 52 ] Yang M,Li R,Chu T.Controller design for disturbance decoupling of Boolean control networks[J].Automatica,2013,49(1):273-277.

[ 53 ] Ding X,Li H,Lu J,et al.Optimal strategy estimation of random evolutionary Boolean games[J].IEEE Transactions on Cybernetics,2021,52(8):7899-7905.

[ 54 ] Li Y,Li H,Zhao G.Optimal state estimation for finite-field networks with stochastic disturbances[J].Neurocomputing,2020,414:238-244.

[ 55 ] 程代展,夏元清,马宏宾,闫莉萍.矩阵代数、控制与博弈[M].北京:北京理工大学出版社,2016.

[ 56 ] Shmulevich I,Dougherty E R,Zhang W.Gene perturbation and intervention in probabilistic Boolean networks[J].Bioinformatics,2002,18(10):1319-1331.

[ 57 ] Shmulevich I,Dougherty E R,Zhang W.Control of stationary behavior in probabilistic Boolean networks by means of structural intervention[J].Journal of Biological Systems,2002,10(4):431-445.

[ 58 ] Datta A,Choudhary A,Bittner M L,et al.External control in Markovian genetic regulatory networks[J].Machine Learning,2003,52:169-191.

[ 59 ] Liu Q,Guo X,Zhou T.Optimal control for probabilistic Boolean networks[J].IET Systems Biology,2010,4(2):99-107.

[ 60 ] Pal R,Datta A,Bittner M L,et al.Intervention in context-sensitive probabilistic Boolean networks[J].Bioinformatics,2005,21(7):1211-1218.

[ 61 ] Pal R,Datta A,Dougherty E R.Optimal infinite-horizon control for probabilistic Boolean networks[J].IEEE Transactions on Signal Processing,2006,54(6):2375-2387.

[ 62 ] Bertsekas D.Dynamic programming and optimal control:Volume I[M].Belmont:Athena Scientific,2000.

[ 63 ] Akutsu T,Hayashida M,Ching W K,et al.Control of Boolean networks:Hardness results and algorithms for tree structured networks[J].Journal of Theoretical Biology,2007,244(4):670-679.

[ 64 ] Laschov D,Margaliot M.A maximum principle for single-input Boolean control networks[J].IEEE Transactions on Automatic Control,2010,56(4):913-917.

[ 65 ] Laschov D,Margaliot M.A Pontryagin maximum principle for multi-input Boolean control networks[C]// Recent Advances in Dynamics and Control of Neural Networks.Cambridge:Cambridge Scientific Publishers,2011:1-21.

[ 66 ] Li F,Lu X.Minimum energy control and optimal-satisfactory control of Boolean control network[J].Physics Letters A,2013,377(43):3112-3118.

[ 67 ] Laschov D,Margaliot M.Minimum-time control of Boolean networks[J].SIAM Journal on Control and Optimization,2013,51(4):2869-2892.

[ 68 ] Li H,Wang Y.Controllability analysis and control design for switched Boolean networks with state and input constraints[J].SIAM Journal on Control and Optimization,2015,53(5):2955-2979.

[ 69 ] Laschov D,Margaliot M,Even G.Observability of Boolean networks:A graph-theoretic approach[J].Automatica,2013,49(8):2351-2362.

[ 70 ] Zhao Y,Li Z,Cheng D.Optimal control of logical control networks[J].IEEE Transactions on Automatic Control,2010,56(8):1766-1776.

[ 71 ] Zhao Y.A Floyd-like algorithm for optimization of mix-valued logical control networks[C]// Proceedings of the 30th Chinese Control Conference.Yantai,China,2011:1972-1977.

[ 72 ] Li F,Lu X,Yu Z.Optimal control algorithms for switched Boolean network[J].Journal of the Franklin Institute,2014,351(6):3490-3501.

[ 73 ] Cui X,Feng J E,Wang S.Optimal control problem of Boolean control networks:A graph-theoretical approach[C]// 2018 Chinese Control and Decision Conference (CCDC).Shenyang,China,2018:4511-4516.

[ 74 ] Bondy J A,Murty U S R.Graph theory with applications[M].London:Macmillan,1976.

[ 75 ] Gao S,Sun C,Xiang C,et al.Finite-horizon optimal control of Boolean control networks:A unified graph-theoretical approach[J].IEEE Transactions on Neural Networks and Learning Systems,2020,33(1):157-171.

[ 76 ] Toyoda M,Wu Y.Mayer-type optimal control of probabilistic Boolean control network with uncertain selection probabilities[J].IEEE Transactions on Cybernetics,2019,51(6):3079-3092.

[ 77 ] Wu Y,Shen T.An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems[J].Systems & Control Letters,2015,82:108-114.

[ 78 ] Wu Y,Shen T.Policy iteration algorithm for optimal control of stochastic logical dynamical systems[J].IEEE Transactions on Neural Networks and Learning Systems,2017,29(5):2031-2036.

[ 79 ] Wu Y,Shen T.Policy iteration approach to control residual gas fraction in IC engines under the framework of stochastic logical dynamics[J].IEEE Transactions on Control Systems Technology,2016,25(3):1100-1107.

[ 80 ] Wu Y,Sun X M,Zhao X,et al.Optimal control of Boolean control networks with average cost:A policy iteration approach[J].Automatica,2019,100:378-387.

[ 81 ] Wu Y,Shen T.A finite convergence criterion for the discounted optimal control of stochastic logical networks[J].IEEE Transactions on Automatic Control,2017,63(1):262-268.

[ 82 ] Wu Y,Guo Y,Toyoda M.Policy iteration approach to the infinite horizon average optimal control of probabilistic Boolean networks[J].IEEE Transactions on Neural Networks and Learning Systems,2020,32(7):2910-2924.

[ 83 ] Zhu Q,Liu Y,Lu J,et al.On the optimal control of Boolean control networks[J].SIAM Journal on Control and Optimization,2018,56(2):1321-1341.

[ 84 ] Gao S,Sun C,Xiang C,et al.Infinite-horizon optimal control of switched Boolean control networks with average cost:An efficient graph-theoretical approach[J].IEEE Transactions on Cybernetics,2020,52(4):2314-2328.

[ 85 ] Cheng D,Zhao Y,Xu T.Receding horizon based feedback optimization for mix-valued logical networks[J].IEEE Transactions on Automatic Control,2015,60(12):3362-3366.

[ 86 ] Zhao Y,Qi H,Cheng D.Input-state incidence matrix of Boolean control networks and its applications[J].Systems & Control Letters,2010,59(12):767-774.

[ 87 ] Gibbons R.A Primer in Game Theory[M].London:Prentice Hall,1992.

[ 88 ] Kwon W H,Han S H.Receding horizon control:Model predictive control for state models[M].London:Springer,2005.

[ 89 ] Kwan C,Lewis F L.Robust backstepping control of nonlinear systems using neural networks[J].IEEE Transactions on Systems,Man,and Cybernetics-Part A:Systems and Humans,2000,30(6):753-766.

[ 90 ] Cheng D,Zhao Y,Xu T.Receding horizon based feedback optimization for mix-valued logical networks[J].IEEE Transactions on Automatic Control,2015,60(12):3362-3366.

[ 91 ] Xu T,Cheng D.Receding horizon-based feedback optimization for mix-valued logical networks:The imperfect information case[C]// Proceedings of the 32nd Chinese Control Conference.Xi′an,China,2013:2147-2152.

[ 92 ] Papagiannis G,Moschoyiannis S.Deep reinforcement learning for control of probabilistic Boolean networks[C]// Proceedings of the Ninth International Conference on Complex Networks.Madrid,Spain,2020:361-371.

[ 93 ] Acernese A,Yerudkar A,Glielmo L,et al.Double deep-Q learning-based output tracking of probabilistic Boolean control networks[J].IEEE Access,2020,8:199254-199265.

[ 94 ] Acernese A,Yerudkar A,Glielmo L,et al.Reinforcement learning approach to feedback stabilization problem of probabilistic Boolean control networks[J].IEEE Control Systems Letters,2020,5(1):337-342.

[ 95 ] Bajaria P,Yerudkar A,Del Vecchio C.Random forest Q-learning for feedback stabilization of probabilistic Boolean control networks[C]// 2021 IEEE International Conference on Systems,Man,and Cybernetics (SMC).Melbourne,Austrilia,2021:1539-1544.

[ 96 ] Ng M K,Zhang S Q,Ching W K,et al.A control model for Markovian genetic regulatory networks[C]// IEEE International Conference on Granular Computing.Beijing,China,2005:36-48.

[ 97 ] Faryabi B,Datta A,Dougherty E R.On approximate stochastic control in genetic regulatory networks[J].IET Systems Biology,2007,1(6):361-368.

[ 98 ] Chen P C Y,Chen J W.A Markovian approach to the control of genetic regulatory networks[J].Biosystems,2007,90(2):535-545.

[ 99 ] Van Giang T,Hiraishi K.On attractor detection and optimal control of deterministic generalized asynchronous random Boolean networks[J].IEEE Transactions on Computational Biology and Bioinformatics,2020,19(3):1794-1806.

[100] Kharade S,Sutavani S,Wagh S,et al.Optimal control of probabilistic Boolean control networks:A scalable infinite horizon approach[J].International Journal of Robust and Nonlinear Control,2023,33(9):4945-4966.

[101] Ni J,Li F,Wu Z G.Deep reinforcement learning based optimal infinite-horizon control of probabilistic boolean control networks[EB/OL].(2023-04-07)[2024-08-21].https://arxiv.org/abs/2304.03489.

[102] Chen H,Wu B,Lu J.A minimum-time control for Boolean control networks with impulsive disturbances[J].Applied Mathematics and Computation,2016,273:477-483.

[103] Tan S,Zhou R,Wang Y,et al.Optimal control of Boolean control networks with state-triggered impulses[J].Expert Systems with Applications,2024,252:124014.

[104] Wang Y,Feng J,Meng M.Topological structure and optimal control of singular mix-valued logical networks[J].Control Theory and Technology,2015,13(4):321-332.

[105] Meng M,Feng J.Optimal control problem of singular Boolean control networks[J].International Journal of Control,Automation and Systems,2015,13:266-273.

[106] Wang Y,Guo P.Optimal control of singular Boolean control networks via Ledley solution method[J].Journal of the Franklin Institute,2021,358(12):6161-6173.

[107] Liu Q,Guo X,Zhou T.Optimal control for generalized asynchronous probabilistic Boolean networks[J].Current Bioinformatics,2012,7(1):56-62.

[108] Kobayashi K,Hiraishi K.Optimal control of Boolean biological networks modeled by Petri nets[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2013,96(2):532-539.

[109] Alkhudhayr H,Steggles J.A compositional framework for Boolean networks[J].Biosystems,2019,186:103960.

[110] Li H,Pang X.Stability analysis of large-scale Boolean networks via compositional method[J].Automatica,2024,159:111397.

[111] Zhao Y,Kim J,Filippone M.Aggregation algorithm towards large-scale Boolean network analysis[J].IEEE Transactions on Automatic Control,2013,58(8):1976-1985.

[112] Li H,Wang S,Li W.Aggregationmethod to strategy consensus of large-size networked evolutionary matrix games[J].IEEE Transactions on Automatic Control,2023.

[113] Han M,Liu Y,Tu Y.Controllability of Boolean control networks with time delays both in states and inputs[J].Neurocomputing,2014,129:467-475.

[114] Lu J,Zhong J,Ho D W C,et al.On controllability of delayed Boolean control networks[J].SIAM Journal on Control and Optimization,2016,54(2):475-494.

[115] Li H,Yang X.Robust optimal control of logical control networks with function perturbation[J].Automatica,2023,152:110970.

[116] Gao S,Xiang C,Sun C,et al.Efficient Boolean modeling of gene regulatory networks via random forest based feature selection and best-fit extension[C]// 2018 IEEE 14th International Conference on Control and Automation (ICCA).Anchorage,USA,2018:1076-1081.

基本信息:

DOI:

中图分类号:O232

引用信息:

[1]贾雪,李海涛.逻辑动态系统的最优控制研究进展[J].山东师范大学学报(自然科学版),2024,39(04):305-324.

基金信息:

国家自然科学基金资助项目(62473239); 山东省优质研究生课程资助项目(SDYKC2022052); 山东师范大学校级本科教改资助项目(2021BJ052)

检 索 高级检索

引用

GB/T 7714-2015 格式引文
MLA格式引文
APA格式引文