Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the...Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment.This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process.By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls.Meanwhile, we also analyze the structure of optimal controls carefully.Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent.Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent.In addition, this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses, and makes analyses and discussions of the model have the exactitude of mathematical sense.展开更多
We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another ...We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion.We derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case.展开更多
To deal with over-shooting and gouging in high speed machining, a novel approach for velocity smooth link is proposed. Considering discrete tool path, cubic spline curve fitting is used to find dangerous points, and a...To deal with over-shooting and gouging in high speed machining, a novel approach for velocity smooth link is proposed. Considering discrete tool path, cubic spline curve fitting is used to find dangerous points, and according to spatial geometric properties of tool path and the kinematics theory, maximum optimal velocities at dangerous points are obtained. Based on method of velocity control characteristics stored in control system, a fast algorithm for velocity smooth link is analyzed and formulated. On-line implementation results show that the proposed approach makes velocity changing more smoothly compared with traditional velocity control methods and improves productivity greatly.展开更多
In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are o...In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.展开更多
We investigate the close-range relative motion and control of a spacecraft approaching a tumbling target. Unlike the traditional rigid-body dynamics with translation and rotation about the center of mass（CM）, the ki...We investigate the close-range relative motion and control of a spacecraft approaching a tumbling target. Unlike the traditional rigid-body dynamics with translation and rotation about the center of mass（CM）, the kinematic coupling between translation and rotation is taken into consideration to directly describe the motion of the spacecraft＇s sensors or devices which are not coincident with the CM. Thus, a kinematically coupled 6 degrees-of-freedom（DOF） relative motion model for the instrument（feature point） is set up. To make the chaser spacecraft＇s feature point track the target＇s, an optimal tracking problem is defined and a control law with a feedback-feedforward structure is designed. With quasi-linearization of the nonlinear dynamical system, the feedforward term is computed from a specified constraint about the dynamical system and the reference model, and the feedback action is derived starting from the state-dependent Ricca equation（SDRE）. The proposed controller is compared with an existing suboptimal tracking controller, and numerical simulations are presented to illustrate the effectiveness and superiority of the proposed method.展开更多
针对具有冗余机械臂的自由漂浮空间机器人(Free Floating Space Robot,FFSR)点到点避免奇异性规划和控制问题,提出了一种冗余FFSR的点到点避免奇异控制方法。首先,该方法基于离散状态依赖李卡提方程(DSDRE)控制器设计方法,利用FFSR的动...针对具有冗余机械臂的自由漂浮空间机器人(Free Floating Space Robot,FFSR)点到点避免奇异性规划和控制问题,提出了一种冗余FFSR的点到点避免奇异控制方法。首先,该方法基于离散状态依赖李卡提方程(DSDRE)控制器设计方法,利用FFSR的动力学和运动学方程实现了FFSR系统方程的伪线性重构;然后,基于伪线性重构系统及DSDRE状态调节器设计方法实现了FFSR的关节角速度和末端位姿的同时跟踪控制;其次,根据跟踪控制器对FFSR广义雅克比矩阵(GJM)行满秩的设计要求,定义FFSR的奇异性判别依据,构造了避奇异约束函数;再次,由于冗余FFSR系统具有多逆运动学解特点,考虑关节角及关节角速度约束,结合避奇异约束函数设计了FFSR的期望轨迹在线规划器,进一步将设计的跟踪控制器与规划器相结合提出了冗余FFSR末端点到点避奇异运动控制方法。最后,为验证所提方法的有效性同时考虑简化计算,采用平面4连杆FFSR模型进行数值仿真,仿真结果表明所提点到点避奇异运动控制方法能够有效实现冗余FFSR系统的点到点避奇异运动。展开更多
基金Supported by the National Natural Science Foundation of China (Grant No 19671004)
文摘Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment.This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process.By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls.Meanwhile, we also analyze the structure of optimal controls carefully.Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent.Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent.In addition, this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses, and makes analyses and discussions of the model have the exactitude of mathematical sense.
基金supported by National Natural Science Foundation of China(Grant No11301560)
文摘We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion.We derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case.
基金This project is supported by National Hi-tech Research and Development Program of China (863 Program, No. 2002AA421150)Specialized Re-search Fund for Doctor Program of Higher Education of China (No. 20030335091).
文摘To deal with over-shooting and gouging in high speed machining, a novel approach for velocity smooth link is proposed. Considering discrete tool path, cubic spline curve fitting is used to find dangerous points, and according to spatial geometric properties of tool path and the kinematics theory, maximum optimal velocities at dangerous points are obtained. Based on method of velocity control characteristics stored in control system, a fast algorithm for velocity smooth link is analyzed and formulated. On-line implementation results show that the proposed approach makes velocity changing more smoothly compared with traditional velocity control methods and improves productivity greatly.
基金the National Natural Science Foundation of China(No.10571092)
文摘In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.
基金Project supported by the Major Program of the National Natural Science Foundation of China(Grant Nos.61690210 and 61690213)
文摘We investigate the close-range relative motion and control of a spacecraft approaching a tumbling target. Unlike the traditional rigid-body dynamics with translation and rotation about the center of mass（CM）, the kinematic coupling between translation and rotation is taken into consideration to directly describe the motion of the spacecraft＇s sensors or devices which are not coincident with the CM. Thus, a kinematically coupled 6 degrees-of-freedom（DOF） relative motion model for the instrument（feature point） is set up. To make the chaser spacecraft＇s feature point track the target＇s, an optimal tracking problem is defined and a control law with a feedback-feedforward structure is designed. With quasi-linearization of the nonlinear dynamical system, the feedforward term is computed from a specified constraint about the dynamical system and the reference model, and the feedback action is derived starting from the state-dependent Ricca equation（SDRE）. The proposed controller is compared with an existing suboptimal tracking controller, and numerical simulations are presented to illustrate the effectiveness and superiority of the proposed method.
文摘针对具有冗余机械臂的自由漂浮空间机器人(Free Floating Space Robot,FFSR)点到点避免奇异性规划和控制问题,提出了一种冗余FFSR的点到点避免奇异控制方法。首先,该方法基于离散状态依赖李卡提方程(DSDRE)控制器设计方法,利用FFSR的动力学和运动学方程实现了FFSR系统方程的伪线性重构;然后,基于伪线性重构系统及DSDRE状态调节器设计方法实现了FFSR的关节角速度和末端位姿的同时跟踪控制;其次,根据跟踪控制器对FFSR广义雅克比矩阵(GJM)行满秩的设计要求,定义FFSR的奇异性判别依据,构造了避奇异约束函数;再次,由于冗余FFSR系统具有多逆运动学解特点,考虑关节角及关节角速度约束,结合避奇异约束函数设计了FFSR的期望轨迹在线规划器,进一步将设计的跟踪控制器与规划器相结合提出了冗余FFSR末端点到点避奇异运动控制方法。最后,为验证所提方法的有效性同时考虑简化计算,采用平面4连杆FFSR模型进行数值仿真,仿真结果表明所提点到点避奇异运动控制方法能够有效实现冗余FFSR系统的点到点避奇异运动。
