【作者】 袁帅；

【导师】 严质彬；

【作者基本信息】 哈尔滨工业大学 ， 运筹学与控制论， 2011， 硕士

【摘要】 现实世界中的很多系统都会受到外界的干扰,这些干扰持续的时间对于整个系统发生过程来说是非常短暂的,连续的微分方程不能完全准确的反映系统经受短暂干扰而表征出来的动态变化,而脉冲微分方程可以很好的对这一过程进行描述。本文首先针对家禽的养殖捕获问题,介绍了在固定时刻实施脉冲的Logistic脉冲捕获模型和Gompertz脉冲捕获模型,并利用脉冲微分方程最优化的相关理论,以利润函数作为性能指标,对上述两个脉冲捕获模型实行最优控制,进一步得出Logistic脉冲捕获模型的最优脉冲捕获时间和相应的最优捕获量。接下来,设计出几种适合这两类脉冲捕获模型的算法,利用MATLAB7.10实现了对模型决策变量的优化控制,并利用Logistic脉冲捕获模型已经求出的最优脉冲捕获时间和相应的利润函数的解析表达式,来验证这几种算法的有效性和通用性。最后,通过对Logistic脉冲捕获模型的仿真结果与实际值进行误差分析,在这几种算法中寻找出一种最合适的算法,并利用此算法求出Gompertz脉冲捕获模型的最优捕获时刻及最优捕获量的数值解。该算法也验证了改进的利润函数的合理性。本文通过对单种群动力学模型中引入脉冲微分系统的最优控制方法,确定了最优脉冲捕获策略,并利用计算机对模型的优化过程进行仿真,得出了决策变量及性能指标的数值解。更多还原

【Abstract】 Many systems in the real world may suffer disturbances whose duration is very short relative to the entire process. Continuous differential equations can not reflect the dynamic change appearing in the system accurately. But impulsive differential equations can describe this situation exactly.First, we introduce the single species Logistic and Gompertz impulsive capture models. Then, utilizing the theories of optimization problems on impulsive differential equations, we solve the optimization problems for the two models to maximize the profit function, which is taken as the performance index. Further, we get the optimal impulsive capture time and the corresponding capture quantity. We design several algorithms that can be used in the two impulsive capture models to realize the optimal control for decision variables by MATLAB7.10, and use the optimal impulsive capture time and the corresponding profit function analytic solution of Logistic impulsive capture model to verify their effectiveness and validity. Finally, comparing the error between the simulation results and the analytic results, we find out the most suitable algorithm, by which the numerical solution is worked out on the optimal capture time and the optimal capture amount for Gompertz model. This algorithm is verified also suitable for an improved profit function.This paper obtains the optimal capture strategy by introducing optimal control method of impulsive differential systems into single species dynamic model, and gets numerical results for the optimal decision variables and performance index by computer simulation.更多还原