Uncertain saddle point equilibrium differential games with non-anticipating strategies
Tài liệu tham khảo
Behn, 1968, On a class of linear stochastic differential games, IEEE Trans. Automat. Contr., 13, 227, 10.1109/TAC.1968.1098898
Berkovitz, 1985, The existence of value and saddle point in games of fixed duration, SIAM J. Control Optim., 23, 172, 10.1137/0323015
Buckdahn, 2008, Stochastic differential games and viscosity solutions of Hamilton–Jacobi–Bellman–Isaacs equations, SIAM J. Control Optim., 47, 444, 10.1137/060671954
Chen, 2016, Indefinite LQ optimal control with equality constraint for discrete-time uncertain systems, Jpn. J. Ind. Appl. Math., 33, 361, 10.1007/s13160-016-0217-9
Conway, 1964, Hamilton’s theory and generalized solutions of the Hamilton–Jacobi equation, J. Math. Mech., 13, 939
Crandall, 1983, Viscosity solutions of Hamilton–Jacobi equations, Trans. Am. Math. Soc., 277, 1, 10.1090/S0002-9947-1983-0690039-8
Elliott, 1976, The existence of value in stochastic differential games, SIAM J. Control Optim., 14, 85, 10.1137/0314006
Elliott, 1972, The existence of value in differential games, Mem. Am. Math. Soc., 126, 1
Evans, 1980, On solving certain nonlinear partial differential equations by accretive operator methods, Israel J. Math., 36, 225, 10.1007/BF02762047
Evans, 1984, Differential games and representation formulas for solutions of Hamilton–Jacobi–Isaacs equations, Indiana U. Math. J., 33, 773, 10.1512/iumj.1984.33.33040
Fleming, 1969, The cauchy problem for a nonlinear first order partial differential equation, J. Differ. Equ., 5, 515, 10.1016/0022-0396(69)90091-6
Friedman, 1971
Gao, 2017, Uncertain Shapley value of coalitional game with application to supply chain alliance, Appl. Soft Comput., 10.1016/j.asoc.2016.06.018
Hamadene, 1995, Zero-sum stochastic differential games and backward equations, Sys. Control Lett., 24, 259, 10.1016/0167-6911(94)00011-J
Isaacs, 1975
Ishii, 1984, Uniqueness of unbounded viscosity solutions of Hamilton–Jacobi equations, Indiana U. Math. J., 33, 721, 10.1512/iumj.1984.33.33038
Ji, 2015, Multi-dimensional uncertain differential equation: existence and uniqueness of solution, Fuzzy Optim. Decis. Mak., 14, 477, 10.1007/s10700-015-9210-z
Lions, 1985, Differential games, optimal control and directional derivatives of viscosity solutions of Bellman’s and Isaacs’ equations, SIAM J. Control Optim., 23, 566, 10.1137/0323036
Liu, 2007
Liu, 2008, Fuzzy process, hybrid process and uncertain process, J. Uncertain Syst., 2, 3
Liu, 2009, Some research problems in uncertainty theory, J. Uncertain Syst., 3, 3
Liu, 2010
Liu, 2015
von Neumann, 1944
Pontryagin, 1966, On the theory of differential games, Russ. Math. Surv., 21, 193, 10.1070/RM1966v021n04ABEH004171
Sheng, 2013, Optimistic value model of uncertain optimal control, Int. J. Uncertain. Fuzziness Knowl. Based Syst., 21, 75, 10.1142/S0218488513400060
Shu, 2017, Stability and optimal control for uncertain continuous-time singular systems, Eur. J. Control, 34, 16, 10.1016/j.ejcon.2016.12.003
Sun, 2016, Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon, ESAIM Contr. Optim. Calculus, 22, 743, 10.1051/cocv/2015024
Sun, 2017, Bang–bang property for an uncertain saddle point problem, J. Intell. Manuf., 28, 605, 10.1007/s10845-014-1003-7
Yan, 2017, A linear–quadratic control problem of uncertain discrete-time switched systems, J. Ind. Manag. Optim., 13, 267, 10.3934/jimo.2016016
Yang, 2016, Linear–quadratic uncertain differential game with application to resource extraction problem, IEEE T. Fuzzy Syst., 24, 819, 10.1109/TFUZZ.2015.2486809
Yang, 2017, Bayesian equilibria for uncertain bimatrix game with asymmetric information, J. Intell. Manuf., 28, 515, 10.1007/s10845-014-1010-8
Yao, 2013, Some stability theorems of uncertain differential equation, Fuzzy Optim. Decis. Mak., 12, 3, 10.1007/s10700-012-9139-4
Zhang, 2016, Valuation of interest rate ceiling and floor in uncertain financial market, Fuzzy Optim. Decis. Mak., 15, 139, 10.1007/s10700-015-9223-7
Zhu, 2010, Uncertain optimal control with application to a portfolio selection model, Cybernet. Syst., 41, 535, 10.1080/01969722.2010.511552