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1.
A stochastic maximum principle for the risk-sensitive optimal control problem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.  相似文献   

2.
本文研究具有终端约束的最优控制问题.利用构造罚函数的方法将其转化为无约束的近似问题,从而证明最优控制的存在性及其所满足的最大值原理.  相似文献   

3.
A maximum principle is proved for semilinear stochastic evolution systems. The main contribution of this work is that in our problem, the infinitesimal generator of the semigroup of the systems need not to be elliptic. This generalizes a result of A. Bensoussan in 1983.  相似文献   

4.
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.  相似文献   

5.
1IntroductionItiswellkllownthatDuboviskij-Milujintheorembeef.1providesanapproachtoderivingPontryagin'smedmumprincipleforOPtalcontrolproblemswith"dxedphase-controlconstraints.Totreatphase-controlconstraintsofequalitytype,oneimmediatelyencountersaproblem:isthesumOfw*-closedconvexconesstillw*-closed?Theanswer,however,is.generallyno.Toovercomethisdifficulty,Ledzewicz-kowalewsforproposedtheconeeptofjointlyregularitybeef.2,whileWalczakproposedtheconceptofsystemofthesamesenseRef.3.Thecontribution…  相似文献   

6.
In this paper we study a bilinear optimal control problem for a diffusive LotkaVolterra competition model with chemo-repulsion in a bounded domain of RN,N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control i...  相似文献   

7.
陈翰馥 《数学学报》1979,22(4):438-447
<正> 随机控制中的二次性能指标是一种十分重要的情况,对离散时间并对状态是线性的系统,问题已得到彻底解决.对连续时间系统,也已多有讨论,但迄今给出的证明还并不完满,所要求的条件也太强. 设(Ω,,P)是概率空间,{},0≤t≤T是以中的零测集完备了的非降  相似文献   

8.
1 IntroductionThroughout this paPer, we denote n an opell bounded domain in Rn with smooth boulldary0fl, let Q = fl x (0,T) and r = 0n x (0,T). Let H = L'(n).We shall study the optimal control problems governed by the following system:y'(t) Ay(t) p(y(t) -- rk(t)) 9 B1u(t) I1(t), (1.1)y(0) = u0,rk'(t) Aop(f) 7(op(f)) = B2u(t) f2(f), (1.2)op(0) = op0with the state constrchtF(y) C W' (1.3)The pay-off functional is given byJ(y, u) = l"[,(,, y) h(u)]dt. (1.4)JoNote that y' and…  相似文献   

9.
设H是可分的Hilbert空间,A是空间H中的无界线性算子,b∈H是非零元。考虑空间H中用一阶发展方程描述的控制系统  相似文献   

10.
61. IntroductionLet (fi, F, P, {R}tZo) be a complete filtered probability space on which a standard onedimensional Brownian motion w(') is defined such that {R}tZo is the natural filtrationgenerated by w(.), augmented by all the p-null sets in i. We consider the following stateequationwhere T E T[0, TI, the set of all {R}tZo-stopping times taking values in [0, T], (E sigLlt (fi;IR"); A, B, C, D are matrix-valued {R}tZo-adapted bounded processes. In the above, u(.) EU[T, T]gLI(T, T…  相似文献   

11.
非自伴椭圆问题的离散强极值原理与区域分解法   总被引:1,自引:0,他引:1  
胡健伟 《计算数学》1999,21(3):283-292
1.引言本文考虑非自伴二阶椭圆型方程的边值问题():其中Q是有界多角形开域,其边界*O充分光滑;并且方程左端微分算子是H’川椭圆的.虽然在一定条件下问题(P)的解满足极值原理,但是,用通常的Galerkin有限元法求解(P)时,得到的解叫的一般并不满足极值原理.特别,当问>>a时,qx)还可能出现剧烈的振荡.即使对自伴问题(即(卫.1)中b一时在三角形线性元的情形,P.G.O。小t和P.-A.Ravlart证明了:如果限定三角形的内角。三。/2-。(其中常数。>则,且网格参数人>0充分小时,则有较弱形式的极值原理:maxfrU(…  相似文献   

12.
In this paper, a kind of partial upwind finite element scheme is studied for twodimensional nonlinear convection-diffusion problem. Nonlinear convection term approximated by partial upwind finite element method considered over a mesh dual to the triangular grid, whereas the nonlinear diffusion term approximated by Galerkin method. A linearized partial upwind finite element scheme and a higher order accuracy scheme are constructed respectively. It is shown that the numerical solutions of these schemes preserve discrete maximum principle. The convergence and error estimate are also given for both schemes under some assumptions. The numerical results show that these partial upwind finite element scheme are feasible and accurate.  相似文献   

13.
丛玉豪  胡洋  王艳沛 《计算数学》2019,41(1):104-112
本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理,本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件,并通过数值算例验证了理论结果的有效性.  相似文献   

14.
In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results.  相似文献   

15.
赵临龙  俞元洪 《数学杂志》2014,34(5):959-967
本文研究三阶中立型分布时滞微分方程的振动问题.利用Riccati变换技巧和积分平均方法,获得了方程每一解振动或者收敛到零点的新准则,最后,给出了说明所得结果应用的例子.  相似文献   

16.
1引言众所周知,某些复杂的工业过程用线性近似动态模型是不适宜的,而且许多对象如工业生产,生态,生物和社会经济等过程可以用双线性模型自然描述,能够在稳态工作点的一个较大领域内描述一大类严重非线性系统的动态特性,描述精度优于传统的线性模型  相似文献   

17.
针对一类单输入单输出非线性多时滞系统,提出了一种自适应模糊跟踪控制方案.该方案结合了自适应控制和H∞控制.构建了自适应时滞模糊逻辑系统用来逼近未知时滞函数;设计了H∞补偿器来抵消模糊逼近误差和外部扰动.根据跟踪误差给出了参数调节规律.证明了误差闭环系统满足期望的H∞跟踪性能.仿真结果表明了该方案的有效性.  相似文献   

18.
§1.引言在[1]、[2]及[3]中考虑了可以用偏微分方程方法处理的一类具有连续轨道的扩散过程的最优控制问题.近来[4]研究了具有跳跃的扩散过程的最优控制问题,证明了 reward函数满足 Bellman 方程.  相似文献   

19.
带随机过程的随机规划问题最优解过程的平稳性与马氏性   总被引:1,自引:0,他引:1  
证明了带随机过程的随机规划问题其最优争集中至少存在一列最优解均为可测的随机过程;且如果问题中的随机过程具有平稳性与马氏性,则此时间问题的最优解过程亦具有相应的特性。  相似文献   

20.
剩用松弛化方法,讨论了一个特定的最优控制存在性问题.在系统初始状态固定的前提下,分别给出了在系统终端状态固定或自由的两种情形下,最优控制存在的判别条件.所涉及的控制问题中,状态方程及性能指标都较为简单,但控制区域及性能指标不具对称性且性能指标中状态变量和控制变量不分离.这与一般文献中基于对称性给出的最优控制不存在的证明以及状态变量和控制变量分离时的存在性结果有非常大的区别.  相似文献   

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