具Size结构种群系统的最优控制策略  

Optimal Control Strategy for Size-Dependent Population System

作　　者：巴争刚[1] 雒志学[1] 尹雪文[1] 彭晓燕[1] 

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《兰州交通大学学报》2013年第3期140-143,共4页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(11061017);甘肃省自然科学基金(1010RJZA075)

摘　　要：首先利用特征线法给出了系统的形式解;其次,通过定义线性算子,确定性能指标泛函,寻找size结构种群系统的最优控制元,得出了其控制策略的最优性;最后证明了控制问题最优解的存在唯一性.从而达到了对size结构种群系统的出生率和死亡率的控制,优化了种群系统结构,得到了对种群系统的最优控制.The form solution of the system is presented by using the characteristic line method, then the per- formance index function is determined, the optimal control element of the size structured population is found and the optimization of the confrol strategy is obtained by the definition of linear operafor. Finallly, the existence and uniqueness of the optimal solution for the control problem are proved, so as to control the birth rate and the death rate of the size structured population system, optimize the population system struc- ture and obtain the optimal control of the poplation system.

关 键 词：size结构的生物种群系统 特征方程 最小范数 最优控制元 

分 类 号：O175.1[理学—数学]