Yong J [Acta Math. Appl. Sin. Engl. Ser. 28(2012), 1–30] [Math. Control Relat. Fields1(2011), 83–118] studied a standard linear quadratic time-inconsistent optimal control problem via a cooperative and non-cooperati...Yong J [Acta Math. Appl. Sin. Engl. Ser. 28(2012), 1–30] [Math. Control Relat. Fields1(2011), 83–118] studied a standard linear quadratic time-inconsistent optimal control problem via a cooperative and non-cooperative approach, respectively. The authors extend his results to a singular case. To handle the singularity, the authors prove the solvability of a generalized Riccati equation,and introduce a notion of MP-convergence of matrix. It is shown that the authors can obtain a family of parameter equilibrium controls in both cases. Another interesting outcome is that a new type of parameter forward-backward Volterra integral equations is derived.展开更多
基金supported by the Natural Science Foundation of China under Grant No.11971334.
文摘Yong J [Acta Math. Appl. Sin. Engl. Ser. 28(2012), 1–30] [Math. Control Relat. Fields1(2011), 83–118] studied a standard linear quadratic time-inconsistent optimal control problem via a cooperative and non-cooperative approach, respectively. The authors extend his results to a singular case. To handle the singularity, the authors prove the solvability of a generalized Riccati equation,and introduce a notion of MP-convergence of matrix. It is shown that the authors can obtain a family of parameter equilibrium controls in both cases. Another interesting outcome is that a new type of parameter forward-backward Volterra integral equations is derived.
