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
A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibri...A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game （but essentially cooperative in some sense） is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.展开更多
This paper introduces non-local equilibrium model of the transpiratin cooling control with moving boundary. We regard the velocity of the coolant as the controlled of system, and prove that the solutio to the transpir...This paper introduces non-local equilibrium model of the transpiratin cooling control with moving boundary. We regard the velocity of the coolant as the controlled of system, and prove that the solutio to the transpiration coolig control problem exists uniquely under the fair assumption with non-ablation. Moreover, continuous dependence of solution on the controller is presented.展开更多
This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov chain.Open-loop equilibrium control is studied in this paper whose ...This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov chain.Open-loop equilibrium control is studied in this paper whose existence is characterized via Markov-chain-modulated forward-backward stochastic difference equations and generalized Riccati-like equations with jumps.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.
文摘A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game （but essentially cooperative in some sense） is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.
文摘This paper introduces non-local equilibrium model of the transpiratin cooling control with moving boundary. We regard the velocity of the coolant as the controlled of system, and prove that the solutio to the transpiration coolig control problem exists uniquely under the fair assumption with non-ablation. Moreover, continuous dependence of solution on the controller is presented.
基金the National Key R&D Program of China under Grant No.2018YFA0703800the National Natural Science Foundation of China under Grant Nos.61773222,61877057 and 61973172。
文摘This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov chain.Open-loop equilibrium control is studied in this paper whose existence is characterized via Markov-chain-modulated forward-backward stochastic difference equations and generalized Riccati-like equations with jumps.
