Modeling and solution based on stochastic games for development of COA under uncertainty
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摘要
Developing a course of action(COA) is a key step in military planning. In most extant studies on the COA development,only the unilateral actions of friendly forces are considered. Based on stochastic games, we propose models that could deal with the complexities and uncertainties of wars. By analyzing the equilibrium state of both opponent sides, outcomes preferable to one side could be achieved by adopting the methods obtained from the proposed models. This research could help decision makers take the right COA in a state of uncertainty.
Developing a course of action(COA) is a key step in military planning. In most extant studies on the COA development,only the unilateral actions of friendly forces are considered. Based on stochastic games, we propose models that could deal with the complexities and uncertainties of wars. By analyzing the equilibrium state of both opponent sides, outcomes preferable to one side could be achieved by adopting the methods obtained from the proposed models. This research could help decision makers take the right COA in a state of uncertainty.
Developing a course of action(COA) is a key step in military planning. In most extant studies on the COA development,only the unilateral actions of friendly forces are considered. Based on stochastic games, we propose models that could deal with the complexities and uncertainties of wars. By analyzing the equilibrium state of both opponent sides, outcomes preferable to one side could be achieved by adopting the methods obtained from the proposed models. This research could help decision makers take the right COA in a state of uncertainty.
引文
[1]GUI J,ZHOU K.Flexible adjustments between energy and capacity for topology control in heterogeneous wireless multihop networks.Journal of Network and Systems Management,2016,24(4):789-812.
[2]WU Z Z,ZHUANG Y.Linear-quadratic partially observed forward-backward stochastic differential games and its application in finance.Applied Mathematics&Computation,2018,321:577-592.
[3]ZHANG W,WANG B,CHEN D.Continuous-time constrained stochastic games with average criteria.Operations Research Letters,2017,46(1):109-115.
[4]S`EVE C,LEBLANC S,DURAND M,et al.Course-of-action theory in table tennis:a qualitative analysis of the knowledge used by three elite players during matches.Revue Europeenne de Psychologie Appliquee,2017,55(3):145-155.
[5]ZILIOTTO B.Tauberian theorems for general iterations of operators:applications to zero-sum stochastic games.Games&Economic Behavior,2018:1-18.
[6]ALLAMIGEON X,GAUBERT S,SKOMRA M.Solving generic nonarchimedean semidefinite programs using stochastic game algorithms.Journal of Symbolic Computation,2018,85:25-54.
[7]ALTMAN E,PELLEGRINI F D.Dynamic games in novel networks:guest editors’forewords.Dynamic Games&Applications,2016,6(4):427-428.
[8]BAGH A.Existence of equilibria in constrained discontinuous games.International Journal of Game Theory,2016,45(4):769-793.
[9]BENSOUSSAN A,DELARUE F.Editorial:first issue on mean field games.Applied Mathematics&Optimization,2016,74(3):455-457.
[10]BERTRAND P,MUHAREMOVIC T,JIANG J.Random access design for high doppler in wireless networks.U.S.Patent8,199,706.2012-6-12.
[11]SHEN J,FENG D.A game-theoretic method for cross-layer stochastic resilient control design in CPS.International Journal of Systems Science,2018,49(4):677-691.
[12]SUN J,YONG J.Linear quadratic stochastic two-person nonzero-sum differential games:open-loop and closed-loop Nash equilibria m.Stochastic Processes&Their Applications,2019,129(2):381-418.
[13]LAMPRECHT A L,TURNER K J.Scientific workflows.International Journal on Software Tools for Technology Transfer,2016,261(2):1357-1398.
[14]LUIRO H,PARVIAINEN M.Regularity for nonlinear stochastic games.Annales de Linstitut Henri Poincar′e C Analyse Non Lin′eaire,2018,42(5):2161-2196.
[15]LV J,RONG J.Virtualisation security risk assessment for enterprise cloud services based on stochastic game nets model.IET Information Security,2018,12(1):7-14.
[16]WAGENHALS L W,LEVIS A H.Course of action development and evaluation.Fairfax,Virginia,US:System Architectures Laboratory of George Mason University,2000.
[17]TIAN Z,LI J X.Approach for course of actions determination in influence nets based on greedy algorithm.Command Control&Simulation,2013,(3):14-17.(in Chinese)
[18]WANG Y,WANG L.Forward backward stochastic differential games for optimal investment and dividend problem of an insurer under model uncertainty.Applied Mathematical Modelling,2018,58:254-269.
[19]WAN L,LI W,HUANG A.The modeling frame and generation flow of combat course of action.Proc.of the 5th International Conference on Frontiers of Manufacturing Science and Measuring Technology,2017:1621-1627.
[20]DU Z J,CHEN C,JIANG X.Modeling and solution of course of action based on influence net and sequential game.Systems Engineering-Theory&Practice,2013,33(1):215-222.(in Chinese)
[21]SUMILE M S.Collaborative modeling&tailored simulation for course of action validation.Proc.of the Military Modeling&Simulation Symposium,2013:No.1.
[22]LEI T,ZHU C,ZHANG W.Dynamic Bayes network based target-attacking course of action generation.Proc.of the IEEEInternational Conference on Signal Processing,Communication and Computing,2013:1-5.
[23]HAIDER S,LEVIS A H.Modeling time-varying uncertain situations using dynamic influence nets.International Journal of Approximate Reasoning,2008,49(2):488-502.
[24]ZAIDI A K,LEVIS A H,PAPANTONI-KAZAKOS P.On extending temporal models in timed influence networks.Fairfax,Virginia,US:System Architectures Laboratory of George Mason University,2009.
[25]HAIDER S,LEVIS A H.Finding effective courses of action using particle swarm optimization.Proc.of the Evolutionary Computation,2008:1135-1140.
[26]RAFI M F,ZAIDI A K,LEVIS A H,et al.Optimization of actions in activation timed influence nets.Informatica,2009,33(3):285-296.
[27]ZAIDI A K,MANSOOR F,PAPANTONI-KAZAKOS T P.Theory of influence networks.Journal of Intelligent&Robotic Systems,2010,60(3-4):457-491.
[28]TANG P,WANG H,QI C.Anytime heuristic search in temporal HTN planning for developing incident action plans.Artificial Intelligence Communications,2012,25(4):321-342.
[29]POUSI J.Decision analytical approach to effects-based operations.Helsinki,Finland:Helsinki University of Technology,2009.
[30]YAMAN D.A fuzzy cognitive map approach for effect-based operations:an illustrative case.Information Sciences,2009,179(4):382-403.
[31]CHEN C,KONG D F,DU Z J,et al.Modeling and solution of COA development based on timed influence net and game theory.Applied Mathematical Modelling,2014,38(21-22):5269-5278.
[32]WEI L,SARWAT A,SAAD W,et al.Stochastic games for power grid protection against coordinated cyber-physical attacks.IEEE Trans.on Smart Grid,2018,9(2):684-694.
[33]FENG X.Stochastic differential games with competing Brownian particles and related Isaacs’equations.Optimal Control Applications&Methods,2018,39(2):519-536.
[34]WANG Y,WANG L.Forward-backward stochastic differential games for optimal investment and dividend problem of an insurer under model uncertainty.Applied Mathematical Modelling,2018,58:254-269.
[35]SHEN J,FENG D.A game-theoretic method for cross-layer stochastic resilient control design in CPS.International Journal of Systems Science,2018,49(4):677-691.
[36]CHEN Z,LIU J,LI G,et al.Composite time-consistent multiperiod risk measure and its application in optimal portfolio selection.TOP,2016,24(3):515-540.
[37]LV J,RONG J.Virtualization security risk assessment for enterprise cloud services based on stochastic game nets model.IET Information Security,2018,12(1):7-14.
[38]HE L,CHEN Y,ZHAO H,et al.Game-based analysis of energy-water nexus for identifying environmental impacts during Shale gas operations under stochastic input.Science of the Total Environment,2018,627:1585-1601.
[39]JIANG H,SHANBHAG U V,MEYN S P.Distributed computation of equilibria in misspecified convex stochastic Nash games.IEEE Trans.on Automatic Control,2018,63(2):360-371.
[40]LIANG S,YI P,HONG Y.Distributed Nash equilibrium seeking for aggregative games with coupled constraints.Automatica A Journal of IFAC the International Federation of Automatic Control,2017,85:179-185.
[41]ITO Y,MIYAUCHI A,ODA H.Active surveillance as the initial course of action in low-risk papillary microcarcinoma.MANCINO A T,LAWRENCE T K ed.Management of differentiated thyroid cancer.New York:Springer International Publishing,2017.
[42]DARIO P,BASILIO G,FRANCESCA P,et al.Nash and wardrop equilibria in aggregative games with coupling constraints.IEEE Trans.on Automatic Control,2018:64(4):1374-1388.
[2]WU Z Z,ZHUANG Y.Linear-quadratic partially observed forward-backward stochastic differential games and its application in finance.Applied Mathematics&Computation,2018,321:577-592.
[3]ZHANG W,WANG B,CHEN D.Continuous-time constrained stochastic games with average criteria.Operations Research Letters,2017,46(1):109-115.
[4]S`EVE C,LEBLANC S,DURAND M,et al.Course-of-action theory in table tennis:a qualitative analysis of the knowledge used by three elite players during matches.Revue Europeenne de Psychologie Appliquee,2017,55(3):145-155.
[5]ZILIOTTO B.Tauberian theorems for general iterations of operators:applications to zero-sum stochastic games.Games&Economic Behavior,2018:1-18.
[6]ALLAMIGEON X,GAUBERT S,SKOMRA M.Solving generic nonarchimedean semidefinite programs using stochastic game algorithms.Journal of Symbolic Computation,2018,85:25-54.
[7]ALTMAN E,PELLEGRINI F D.Dynamic games in novel networks:guest editors’forewords.Dynamic Games&Applications,2016,6(4):427-428.
[8]BAGH A.Existence of equilibria in constrained discontinuous games.International Journal of Game Theory,2016,45(4):769-793.
[9]BENSOUSSAN A,DELARUE F.Editorial:first issue on mean field games.Applied Mathematics&Optimization,2016,74(3):455-457.
[10]BERTRAND P,MUHAREMOVIC T,JIANG J.Random access design for high doppler in wireless networks.U.S.Patent8,199,706.2012-6-12.
[11]SHEN J,FENG D.A game-theoretic method for cross-layer stochastic resilient control design in CPS.International Journal of Systems Science,2018,49(4):677-691.
[12]SUN J,YONG J.Linear quadratic stochastic two-person nonzero-sum differential games:open-loop and closed-loop Nash equilibria m.Stochastic Processes&Their Applications,2019,129(2):381-418.
[13]LAMPRECHT A L,TURNER K J.Scientific workflows.International Journal on Software Tools for Technology Transfer,2016,261(2):1357-1398.
[14]LUIRO H,PARVIAINEN M.Regularity for nonlinear stochastic games.Annales de Linstitut Henri Poincar′e C Analyse Non Lin′eaire,2018,42(5):2161-2196.
[15]LV J,RONG J.Virtualisation security risk assessment for enterprise cloud services based on stochastic game nets model.IET Information Security,2018,12(1):7-14.
[16]WAGENHALS L W,LEVIS A H.Course of action development and evaluation.Fairfax,Virginia,US:System Architectures Laboratory of George Mason University,2000.
[17]TIAN Z,LI J X.Approach for course of actions determination in influence nets based on greedy algorithm.Command Control&Simulation,2013,(3):14-17.(in Chinese)
[18]WANG Y,WANG L.Forward backward stochastic differential games for optimal investment and dividend problem of an insurer under model uncertainty.Applied Mathematical Modelling,2018,58:254-269.
[19]WAN L,LI W,HUANG A.The modeling frame and generation flow of combat course of action.Proc.of the 5th International Conference on Frontiers of Manufacturing Science and Measuring Technology,2017:1621-1627.
[20]DU Z J,CHEN C,JIANG X.Modeling and solution of course of action based on influence net and sequential game.Systems Engineering-Theory&Practice,2013,33(1):215-222.(in Chinese)
[21]SUMILE M S.Collaborative modeling&tailored simulation for course of action validation.Proc.of the Military Modeling&Simulation Symposium,2013:No.1.
[22]LEI T,ZHU C,ZHANG W.Dynamic Bayes network based target-attacking course of action generation.Proc.of the IEEEInternational Conference on Signal Processing,Communication and Computing,2013:1-5.
[23]HAIDER S,LEVIS A H.Modeling time-varying uncertain situations using dynamic influence nets.International Journal of Approximate Reasoning,2008,49(2):488-502.
[24]ZAIDI A K,LEVIS A H,PAPANTONI-KAZAKOS P.On extending temporal models in timed influence networks.Fairfax,Virginia,US:System Architectures Laboratory of George Mason University,2009.
[25]HAIDER S,LEVIS A H.Finding effective courses of action using particle swarm optimization.Proc.of the Evolutionary Computation,2008:1135-1140.
[26]RAFI M F,ZAIDI A K,LEVIS A H,et al.Optimization of actions in activation timed influence nets.Informatica,2009,33(3):285-296.
[27]ZAIDI A K,MANSOOR F,PAPANTONI-KAZAKOS T P.Theory of influence networks.Journal of Intelligent&Robotic Systems,2010,60(3-4):457-491.
[28]TANG P,WANG H,QI C.Anytime heuristic search in temporal HTN planning for developing incident action plans.Artificial Intelligence Communications,2012,25(4):321-342.
[29]POUSI J.Decision analytical approach to effects-based operations.Helsinki,Finland:Helsinki University of Technology,2009.
[30]YAMAN D.A fuzzy cognitive map approach for effect-based operations:an illustrative case.Information Sciences,2009,179(4):382-403.
[31]CHEN C,KONG D F,DU Z J,et al.Modeling and solution of COA development based on timed influence net and game theory.Applied Mathematical Modelling,2014,38(21-22):5269-5278.
[32]WEI L,SARWAT A,SAAD W,et al.Stochastic games for power grid protection against coordinated cyber-physical attacks.IEEE Trans.on Smart Grid,2018,9(2):684-694.
[33]FENG X.Stochastic differential games with competing Brownian particles and related Isaacs’equations.Optimal Control Applications&Methods,2018,39(2):519-536.
[34]WANG Y,WANG L.Forward-backward stochastic differential games for optimal investment and dividend problem of an insurer under model uncertainty.Applied Mathematical Modelling,2018,58:254-269.
[35]SHEN J,FENG D.A game-theoretic method for cross-layer stochastic resilient control design in CPS.International Journal of Systems Science,2018,49(4):677-691.
[36]CHEN Z,LIU J,LI G,et al.Composite time-consistent multiperiod risk measure and its application in optimal portfolio selection.TOP,2016,24(3):515-540.
[37]LV J,RONG J.Virtualization security risk assessment for enterprise cloud services based on stochastic game nets model.IET Information Security,2018,12(1):7-14.
[38]HE L,CHEN Y,ZHAO H,et al.Game-based analysis of energy-water nexus for identifying environmental impacts during Shale gas operations under stochastic input.Science of the Total Environment,2018,627:1585-1601.
[39]JIANG H,SHANBHAG U V,MEYN S P.Distributed computation of equilibria in misspecified convex stochastic Nash games.IEEE Trans.on Automatic Control,2018,63(2):360-371.
[40]LIANG S,YI P,HONG Y.Distributed Nash equilibrium seeking for aggregative games with coupled constraints.Automatica A Journal of IFAC the International Federation of Automatic Control,2017,85:179-185.
[41]ITO Y,MIYAUCHI A,ODA H.Active surveillance as the initial course of action in low-risk papillary microcarcinoma.MANCINO A T,LAWRENCE T K ed.Management of differentiated thyroid cancer.New York:Springer International Publishing,2017.
[42]DARIO P,BASILIO G,FRANCESCA P,et al.Nash and wardrop equilibria in aggregative games with coupling constraints.IEEE Trans.on Automatic Control,2018:64(4):1374-1388.