A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,...A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).展开更多
With advantages of strong drive capability,nested-loop secondary linear machine(NLS-LM)has great potentiality in linear metro.For its secondary structure with multiple loops,it is difficult to calculate the electromag...With advantages of strong drive capability,nested-loop secondary linear machine(NLS-LM)has great potentiality in linear metro.For its secondary structure with multiple loops,it is difficult to calculate the electromagnetic thrust of NLS-LM reasonably.Hence,in this paper,one thrust calculation method is proposed considering variable loop inductance and transient loop current.Firstly,to establish the secondary winding function,the modeling domain is confined to a limited range,and the equivalent loop span is employed by analyzing the coupling relationship between primary and secondary.Then,in order to obtain the secondary flux density,the transient secondary current is solved based on the loop impedance and induced voltage.Finally,the electromagnetic thrust can be calculated reasonably by the given primary current sheet and the calculated secondary flux density.Comprehensive simulations and experiments have demonstrated the effectiveness of the proposed method.展开更多
This paper deals with the problem of position and attitude tracking control for a rigid spacecraft.A fully actuated system(FAS)model for the six degree-of-freedom(6DOF)spacecraft motion is derived first from the state...This paper deals with the problem of position and attitude tracking control for a rigid spacecraft.A fully actuated system(FAS)model for the six degree-of-freedom(6DOF)spacecraft motion is derived first from the state-space model by variable elimination.Considering the uncertainties from external disturbance,unknown motion information,and uncertain inertia properties,an extended state observer(ESO)is designed to estimate the total disturbance.Then,a tracking controller based on FAS approach is designed,and this makes the closed-loop system a constant linear one with an arbitrarily assignable eigenstructure.The solution to the parameter matrices of the observer and controller is given subsequently.It is proved via the Lyapunov stability theory that the observer errors and tracking errors both converge into the neighborhood of the origin.Finally,numerical simulation demonstrates the effectiveness of the proposed controller.展开更多
An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional.The coefficients and the weighting matrices in the cost functional are all assumed to be ...An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional.The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.Closedloop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in applications.In this paper,the existence of an optimal closed-loop strategy for the system(also called the closedloop solvability of the problem)is characterized by the existence of a regular solution to the coupled two(generalized)Riccati equations,together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.12025105, 11971334 and 11931011)the Chang Jiang Scholars Program and the Science Development Project of Sichuan University (Grant Nos. 2020SCUNL101 and 2020SCUNL201)。
文摘A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).
基金supported in part by the National Natural Science Foundation of China under Grants 52277050the Shenzhen International Collaboration under Grant GJHZ20210705142539007。
文摘With advantages of strong drive capability,nested-loop secondary linear machine(NLS-LM)has great potentiality in linear metro.For its secondary structure with multiple loops,it is difficult to calculate the electromagnetic thrust of NLS-LM reasonably.Hence,in this paper,one thrust calculation method is proposed considering variable loop inductance and transient loop current.Firstly,to establish the secondary winding function,the modeling domain is confined to a limited range,and the equivalent loop span is employed by analyzing the coupling relationship between primary and secondary.Then,in order to obtain the secondary flux density,the transient secondary current is solved based on the loop impedance and induced voltage.Finally,the electromagnetic thrust can be calculated reasonably by the given primary current sheet and the calculated secondary flux density.Comprehensive simulations and experiments have demonstrated the effectiveness of the proposed method.
基金This research was partially supported by the Science Center Program of the National Natural Science Foundation of China under Grant No.62188101the Major Program of the National Natural Science Foundation of China under Grant Nos.61690210 and 61690212the National Natural Science Foundation of China under Grant Nos.62103164 and 61703437.
文摘This paper deals with the problem of position and attitude tracking control for a rigid spacecraft.A fully actuated system(FAS)model for the six degree-of-freedom(6DOF)spacecraft motion is derived first from the state-space model by variable elimination.Considering the uncertainties from external disturbance,unknown motion information,and uncertain inertia properties,an extended state observer(ESO)is designed to estimate the total disturbance.Then,a tracking controller based on FAS approach is designed,and this makes the closed-loop system a constant linear one with an arbitrarily assignable eigenstructure.The solution to the parameter matrices of the observer and controller is given subsequently.It is proved via the Lyapunov stability theory that the observer errors and tracking errors both converge into the neighborhood of the origin.Finally,numerical simulation demonstrates the effectiveness of the proposed controller.
基金supported by Hong Kong RGC under grants 519913,15209614 and 15224215Jingrui Sun was partially supported by the National Natural Science Foundation of China(11401556)+1 种基金the Fundamental Research Funds for the Central Universities(WK 2040000012)Jiongmin Yong was partially supported by NSF DMS-1406776.
文摘An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional.The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.Closedloop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in applications.In this paper,the existence of an optimal closed-loop strategy for the system(also called the closedloop solvability of the problem)is characterized by the existence of a regular solution to the coupled two(generalized)Riccati equations,together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.
