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1.
具有年龄结构的捕食种群系统的最优收获策略   总被引:1,自引:0,他引:1  
分析了一类基于年龄结构的食饵-捕食者系统的最优收获问题.证明了系统非负解的存在唯一性、解对控制变量的连续依赖性.讨论了最优策略的存在性,利用法锥和Dubovitskii-Milyutin理论导出了最优性条件.  相似文献   

2.
具空间扩散和年龄结构的时变种群系统的最优收获控制   总被引:1,自引:0,他引:1  
李健全  陈任昭 《应用数学》2006,19(1):152-158
本文讨论了一类具空间扩散和年龄结构的时变种群系统的最优收获控制问题,利用Banach空间的SaksMasur引理,证明了系统最优收获控制的存在性,并利用切向锥、法向锥概念,建立了收获控制为最优的必要条件.  相似文献   

3.
研究了一类非线性种群系统的最优控制问题.利用Ekeland变分原理和共轭系统证明了最优收获的存在性,并借助于法锥概念得到了最优控制的必要性条件.  相似文献   

4.
研究一类具有个体尺度结构的非线性种群控制模型.确立了状态系统模型非负解的存在唯一性,以及状态关于控制变量的连续依赖性.应用紧性推理和极值化序列法证明了最优策略的存在性,借助切锥法锥和共轭系统技巧导出了最优性条件.  相似文献   

5.
一类可再生资源系统的最优动态平衡收获   总被引:2,自引:0,他引:2  
研究一类可再生资源系统的最优利用问题.首先,引进一个新的效用函数,它依赖于收获努力度和资源量,由此导出最优控制问题.其次证明该控制问题最优解的存在性.然后,利用无穷区间上控制问题的最大值原理,得到一个非线性的四维最优系统.通过对上述系统正平衡解的详细分析,借助Hopf分支定理证明了极限环的存在性.之后考虑中心流形上的简化系统,分析极限环的稳定性.最后,解释所得结果的生物经济学意义.  相似文献   

6.
研究一类具有年龄结构n维食物链模型的最优收获控制.利用不动点定理,证明了系统非负解的存在性和唯一性.由Mazur定理,证明了最优控制策略的存在性,同时由法锥概念的特征刻画,还得到了控制问题最优解存在的必要条件.  相似文献   

7.
探究一类具有年龄等级结构的种群模型的边界调控问题,包括系统的能控性和最优控制.应用特征线方法和Gronwall不等式建立状态分布关于控制变量的连续依赖性;基于线性系统的能控性与集值映射不动点方法获得了非线性种群系统的近似能控性;运用Ekeland变分原理证明了最优策略的存在唯一性,构造适当的共轭系统和法向量对最优策略作出精细刻画.数值模拟结果展示了控制策略的可行性.  相似文献   

8.
一般型数字最优预见伺服系统的设计   总被引:2,自引:0,他引:2  
在最优预见伺服系统设计中通常只考虑阶跃型目标值函数.本文研究当自标值信号及干扰信号为多项式或为线性齐次系统的输出时最优预见伺服系统的设计问题,得到了如下三方面的结果:(一)扩大系统的能控性及能观测性条件;(二)最优预见控制器的设计方法;(三)控制规则的简便算法.  相似文献   

9.
一类具有年龄分布和加权的种群系统的最优控制   总被引:1,自引:0,他引:1  
叶山西  赵春 《应用数学》2007,20(3):562-567
本文研究了一类依赖于年龄结构的非线性种群系统的最优控制问题,其生死率依赖于个体年龄和加权规模.应用Ekeland’S变分原理证明了最优解的存在性,并用法锥和共轭系统技巧导出了最优性条件.  相似文献   

10.
年龄相关的半线性种群扩散系统的最优收获控制   总被引:3,自引:1,他引:2  
研究年龄相关的半线性种群扩散系统的最优收获控制问题,证明了最优收获控制的存在性,得到了收获控制为最优的必要条件和由偏微分方程与变分不等式所构成的最优性组,由最优性组确定最优控制.  相似文献   

11.
An interpretation of some chaotic systems as the result of optimal decisions is presented. First, a generalized discrete-time two-person game is introduced that may be solved by use of dynamic programming. Then, a specific game of this type is formulated whose optimal solution transforms an originally linear discrete-time system into a well-known discrete-time chaotic system. Finally, a particular continuous-time optimal control problem is formulated, whose optimal feedback solution transforms an originally linear continuous-time system into a well-known continuous-time chaotic system.  相似文献   

12.
The Pontryagin maximum principle is used to develop an original algorithm for finding an optimal control in a macroeconomic problem. Numerical results are presented for the optimal control and optimal trajectory of the development of a regional economic system. For an optimal control satisfying a certain constraint, an invariant of a macroeconomic system is derived.  相似文献   

13.
In the present treatment, a nonlinear system of anN-person nonzero-sum differential game is linearized with respect to the controls. It is shown that the optimal trajectory and the optimal costs of the linearized system lead, under certain conditions, to an approximation of the optimal trajectory and the optimal costs of the original nonlinear system.  相似文献   

14.
An optimal control problem for a system involving an interval parameter is considered. The concepts of a universal optimal state and a universal optimal control are introduced. The existence and uniqueness of a universal solution to the interval optimal control problem is proved, and an algorithm for its determination is presented. The interval optimal control problem for a system described by the boundary value problem for a second-order ordinary differential equation is solved as an example.  相似文献   

15.
讨论了一类具终端观测且与年龄相关的非线性时变种群扩散系统的最优分布控制问题利用偏微控制理论和先验估计,证明了系统最优分布控制的存在性,得到了控制为最优的一阶必要条件,并进而讨论了系统的最优反馈控制问题.  相似文献   

16.
An optimal control problem for a coupled nonlinear parabolic population system is considered. The existence and uniqueness of the positive solution for the system is shown by the method of upper and lower solutions. An explicit prior bound of solutions to the system is given by considering an auxiliary coupled linear system. The existence of the optimal control is proved and the characterization of the optimal control is established.  相似文献   

17.
In this paper, we consider the problem of determining optimal operating conditions for a data processing system. The system is burned‐in for a fixed burn‐in time before it is put into field operation and, in field operation, it has a work size and follows an age‐replacement policy. Assuming that the underlying lifetime distribution of the system has a bathtub‐shaped failure rate function, the properties of optimal burn‐in time, optimal work size and optimal age‐replacement policy will be derived. It can be seen that this model is a generalization of those considered in the previous works, and it yields a better optimal operating conditions. This paper presents an analytical method for three‐dimensional optimization problem. An algorithm for determining optimal operating conditions is also given. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

18.
In this paper, we establish the existence of the optimal control for an optimal control problem where the state of the system is defined by a variational inequality problem with monotone type mappings. Moreover, as an application, we get several existence results of an optimal control for the optimal control problem where the system is defined by a quasilinear elliptic variational inequality problem with an obstacle.  相似文献   

19.
We address a rate control problem associated with a single server Markovian queueing system with customer abandonment in heavy traffic. The controller can choose a buffer size for the queueing system and also can dynamically control the service rate (equivalently the arrival rate) depending on the current state of the system. An infinite horizon cost minimization problem is considered here. The cost function includes a penalty for each rejected customer, a control cost related to the adjustment of the service rate and a penalty for each abandoning customer. We obtain an explicit optimal strategy for the limiting diffusion control problem (the Brownian control problem or BCP) which consists of a threshold-type optimal rejection process and a feedback-type optimal drift control. This solution is then used to construct an asymptotically optimal control policy, i.e. an optimal buffer size and an optimal service rate for the queueing system in heavy traffic. The properties of generalized regulator maps and weak convergence techniques are employed to prove the asymptotic optimality of this policy. In addition, we identify the parameter regimes where the infinite buffer size is optimal.  相似文献   

20.
研究一类具有离散时滞和年龄结构的生物种群模型的最优收获策略,其状态方程由一阶偏泛函微分方程描述.运用极值化序列方法和Mazur定理证明了最优控制的存在性,借助非线性泛函分析中的切锥-法锥和共轭系统技巧导出了最优性条件.通过对共轭系统的细致分析,确立了最优控制的唯一性,给出了最优解的特征刻画.  相似文献   

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