An optimal harvesting problem for linear age-dependent population dynamics is investigated.By Mazur's Theorem,the existence of solutions of the optimal control problem (OH) is demonstrated.The first order necessar...An optimal harvesting problem for linear age-dependent population dynamics is investigated.By Mazur's Theorem,the existence of solutions of the optimal control problem (OH) is demonstrated.The first order necessary conditions of optimality for problem (OH) is obtained by the conception of normal cone. Finally,under suitable assumptions,the uniqueness of solutions of the optimal control problem (OH) is given.The results extend some known criteria.展开更多
This work is concerned with a kind of optimal control problem for a size-structured biological population model.Well-posedness of the state system and an adjoint system are proved by means of Banach＇s fixed point the...This work is concerned with a kind of optimal control problem for a size-structured biological population model.Well-posedness of the state system and an adjoint system are proved by means of Banach＇s fixed point theorem.Existence and uniqueness of optimal control are shown by functional analytical approach.Optimality conditions describing the optimal strategy are established via tangent and normal cones technique.The results are of the first ones for this novel structure.展开更多
This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among...This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among the adjoint processes, the generalized Hamiltonian function and the value function are given. A portfolio optimization problem under model uncertainty in the financial market is discussed to show the applications of our result.展开更多
Loss of Control (LOC) is the primary factor responsible for the majority of fatal air accidents during past decade. LOC is characterized by the pilot’s inability to control the aircraft and is typically associated wi...Loss of Control (LOC) is the primary factor responsible for the majority of fatal air accidents during past decade. LOC is characterized by the pilot’s inability to control the aircraft and is typically associated with unpredictable behavior, potentially leading to loss of the aircraft and life. In this work, the minimum time dynamic optimization problem to LOC is treated using Pontryagin’s Maximum Principle (PMP). The resulting two point boundary value problem is solved using stochastic shooting point methods via a differential evolution scheme (DE). The minimum time until LOC metric is computed for corresponding spatial control limits. Simulations are performed using a linearized longitudinal aircraft model to illustrate the concept.展开更多
In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strate...In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur’s theorem and optimality condition is derived by means of normal cone.展开更多
We consider optimal birth control for the McKendrick equation of population dyna-mics.It consists of optimizing a system described by a first order partial differential equationwith nonlo-cal bilinear boundary control...We consider optimal birth control for the McKendrick equation of population dyna-mics.It consists of optimizing a system described by a first order partial differential equationwith nonlo-cal bilinear boundary control.Approximate minimum principles are obtained usingEkeland’s vari ational principle.展开更多
基金Supported by the National Natural Science Foundation of China( 1 9971 0 66)
文摘An optimal harvesting problem for linear age-dependent population dynamics is investigated.By Mazur's Theorem,the existence of solutions of the optimal control problem (OH) is demonstrated.The first order necessary conditions of optimality for problem (OH) is obtained by the conception of normal cone. Finally,under suitable assumptions,the uniqueness of solutions of the optimal control problem (OH) is given.The results extend some known criteria.
基金Supported by the ZPNSFC (LY12A01023)the National Natural Science Foundation of China (11271104,11061017)
文摘This work is concerned with a kind of optimal control problem for a size-structured biological population model.Well-posedness of the state system and an adjoint system are proved by means of Banach＇s fixed point theorem.Existence and uniqueness of optimal control are shown by functional analytical approach.Optimality conditions describing the optimal strategy are established via tangent and normal cones technique.The results are of the first ones for this novel structure.
文摘This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among the adjoint processes, the generalized Hamiltonian function and the value function are given. A portfolio optimization problem under model uncertainty in the financial market is discussed to show the applications of our result.
文摘Loss of Control (LOC) is the primary factor responsible for the majority of fatal air accidents during past decade. LOC is characterized by the pilot’s inability to control the aircraft and is typically associated with unpredictable behavior, potentially leading to loss of the aircraft and life. In this work, the minimum time dynamic optimization problem to LOC is treated using Pontryagin’s Maximum Principle (PMP). The resulting two point boundary value problem is solved using stochastic shooting point methods via a differential evolution scheme (DE). The minimum time until LOC metric is computed for corresponding spatial control limits. Simulations are performed using a linearized longitudinal aircraft model to illustrate the concept.
基金supported by the National Natural Science Foundation of China(11061017)the Natural Science Foundation of Gansu Province(1010RJZA075)
文摘In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur’s theorem and optimality condition is derived by means of normal cone.
基金The work is supported by‘Qing Lan’Talent Engineering Funds(QL-05-1SA) by Lanzhou Jiaotong Universitythe National Natural Science Foundation of China under Grant No.604730304.
文摘在这篇论文，我们为一个年龄依赖者调查最佳的政策 n 维的比赛系统，它被富饶控制。由使用 Dubovitskii-Milyutin 的一般理论，最大的原则与免费终端状态为这些问题被获得，无限的地平线，；分别地指向集合。
基金This work was supported in part by a grant from the International Development Research Centre Ottawa,Canada
文摘We consider optimal birth control for the McKendrick equation of population dyna-mics.It consists of optimizing a system described by a first order partial differential equationwith nonlo-cal bilinear boundary control.Approximate minimum principles are obtained usingEkeland’s vari ational principle.
