季节性和综合害虫管理策略实施时间对害虫控制的影响(英文)

通过建立具有季节变化和综合脉冲控制效应的非自治捕食与被捕食模型,我们得到了保证害虫根除的临界条件,即得到了保证害虫根除周期解全局稳定的充分条件.进而我们讨论了季节性变化以及最优的害虫控制策略实施时间对临界条件的影响.结论显示当害虫种群数量具有季节波动时,系统存在使得临界值达到最小的最优控制策略实施时间.     

一类周期种群系统的稳定性分析及最优控制问题

本文讨论了一类线性时变周期种群系统的稳定性和最优控制问题.利用Lyapunov函数.对系统的稳定性进行了分析.给出了系统稳定的充分条件.并且利用Banach空间理论,证明了最优收获控制的存在性和唯一性.并且给出了最优控制所满足的必要性条件.     

具有放牧率的某些概周期生态模型

文［１］研究了具有放牧率的周期生态模型的周期解的存在性、唯一性与稳定性等问题．本文考虑更加广泛的生态模型,即具有放牧率的概周期生态系统的概周期解的存在性、稳定性,通过利用指数型二分性和不动点方法,得到一些新结果．     

具有毒素作用和年龄结构的种群模型的最优控制（英文）

本文研究了污染环境下具有年龄结构的三竞争种群的最优控制问题。即讨论了小环境容量下具有年龄结构和毒素作用的种群模型。利用不动点定理研究了该模型解的存在唯一性;采用法锥技巧得到了控制的最优性条件;同时利用Ekeland's变分原理得到了最优控制的存在性。     

关于一类二次微分系统的概周期解及周期解（英文）

周期解及概周期解问题在生物科学和其他领域具有重要价值.探究一类二次微分系统的周期解及概周期解,分析了附有周期系数系统的周期解的存在性,证明了附有概周期系数系统的概周期解的存在唯一性及全局吸引性.     

一种非线性多阶段动力系统的最优控制及数值优化

针对间歇发酵过程的非线性多阶段动力系统,建立了以初始浓度为控制变量、以生产强度为性能指标的最优控制模型.证明了非线性多阶段动力系统的主要性质、最优控制的存在性及达到最优解的必要条件.构造了优化算法并应用于实际数据计算,其数值结果表明了本文模型与算法的有效性.     

具有时滞的两种群Schoener竞争模型的正周期解的存在性

应用重合度理论讨论了具有时滞的周期Schoener竞争模型,得到了系统正周期解存在的充分条件．     

具有脉冲效应的时滞捕食系统的正周期解

提出了一个具有脉冲效应的周期时滞捕食系统,运用叠合的方法研究了该系统的周期解的存在性．结论表明在一定的条件下捕食者和食饵周期变化．     

具有经济阈值的植物疾病模型

研究了具有经济阈值和人文控制策略的植物疾病模型．根据某一参数的三种情况分析了唯一的正的周期解的存在性,并利用定性理论给出了在该参数某种范围下周期解全局稳定的充分条件,同时得到在其它两种情况下周期解的不稳定性．文章所得结论推广了综合疾病管理中植物疾病模型的经典结论．     

时标上具有HollingⅢ型功能反应的捕食模型的周期解

研究了时标上一类具有Holling型功能反应的捕食模型.运用时标上连续拓扑度定理,得到了系统存在周期解的充分条件,从而使系统的连续时间情形和离散时间情形的周期解问题得到了统一,该方法可广泛应用于研究微分方程和差分方程的周期解的存在问题.     

一类生物种群投资的最优采收控制

在原有的Gauss白噪声刻画环境噪声项的基础上,考虑环境不可预知的跳跃性变化,运用Lévy白噪声建立了有界环境中的随机生物种群模型.并且,引入随机奇异控制来描述投资者的最优采收策略.进一步地,构造一族有着不同起点的控制问题,利用动态规划的思想,给出了最优采收控制问题解的充分条件,进而,将随机控制问题的求解转化为确定型偏微分方程的求解.     

Allee Effect and Control of Lake System Invasion

We consider the model of invasion prevention in a system of lakes that are connected via traffic of recreational boats. It is shown that in presence of an Allee effect, the general optimal control problem can be reduced to a significantly simpler stationary optimization problem of optimal invasion stopping. We consider possible values of model parameters for zebra mussels. The general N-lake control problem has to be solved numerically, and we show a number of typical features of solutions: distribution of control efforts in space and optimal stopping configurations related with the clusters in lake connection structure.     

Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations

The Lotka–Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting both species as the control variable. We analyse the optimal hunting problem paying special attention to the nature of the optimal state and control trajectories in long time intervals. To do that, we apply recent theoretical results on the frame to show that, when the time horizon is large enough, optimal strategies are nearly steady-state. Such path is known as turnpike property. Some experiments are performed to observe such turnpike phenomenon in the hunting problem. Based on the turnpike property, we implement a variant of the single shooting method to solve the previous optimisation problem, taking the middle of the time interval as starting point.     

Species preservations in an optimal harvest model with random prices

In this paper, we consider an optimal harvest model in which the objective is to maximize the expected return. The unit price of biomass is assumed constant until a random time when the price increases by a given amount. Furthermore, due to obvious environmental protection requirements, it is assumed that the fishery population is bounded from below for all time so as to reduce the danger of species extinction. Clearly, this problem is an optimal control problem in which a random parameter is involved. However, due to its special structure, it is shown that the problem is convertible into a deterministic optimal control problem and hence is solvable by an existing optimal control software package, MISER. The practical implication of several computed results obtained by this approach is discussed. They are also compared with other related results in the literature.     

Predictive algorithms for neuromuscular control of human locomotion.

The problem of quantifying muscular activity of the human body can be formulated as an optimal control problem. The current methods used with large-scale biomechanical systems are non-derivative techniques. These methods are costly, as they require numerous integrations of the equations of motion. Additionally, the convergence is slow, making them impractical for use with large systems. We apply an efficient numerical algorithm to the biomechanical optimal control problem. Using direct collocation with a trapezoidal discretization, the equations of motion are converted into a set of algebraic constraint equations. An augmented Lagrangian formulation is used for the optimization problem to handle both equality and inequality constraints. The resulting min-max problem is solved with a generalized Newton method. In contrast to the prevalent optimal control implementations, we calculate analytical first- and second-derivative information and obtain local quadratic convergence. To demonstrate the efficacy of the method, we solve a steady-state pedaling problem with 7 segments and 18 independent muscle groups. The computed muscle activations compare well with experimental EMG data. The computational effort is significantly reduced and solution times are a fraction of those of the non-derivative techniques.     

Optimal risk management of human alveolar echinococcosis with vermifuge

In this study, we develop a bioeconomic model of human alveolar echinococcosis (HAE) and formulate the optimal strategies for managing the infection risks in humans by applying optimal control theory. The model has the following novel features: (i) the complex transmission cycle of HAE has been tractably incorporated into the framework of optimal control problems and (ii) the volume of vermifuge spreading to manage the risk is considered a control variable. With this model, we first obtain the stability conditions for the transmission dynamics under the condition of constant control. Second, we explicitly introduce a control variable of vermifuge spreading into the analysis by considering the associated control costs. In this optimal control problem, we have successfully derived a set of conditions for a bang-bang control and singular control, which are mainly characterized by the prevalence of infection in voles and foxes and the remaining time of control. The analytical results are demonstrated by numerical analysis and we discuss the effects of the parameter values on the optimal strategy and the transmission cycle. We find that when the prevalence of infection in foxes is low and the prevalence of infection in voles is sufficiently high, the optimal strategy is to expend no effort in vermifuge spreading.     

An integrated scheduling and control model for multi-mode projects

In today’s highly competitive uncertain project environments, it is of crucial importance to develop analytical models and algorithms to schedule and control project activities so that the deviations from the project objectives are minimized. This paper addresses the integrated scheduling and control in multi-mode project environments. We propose an optimization model that models the dynamic behavior of projects and integrates optimal control into a practically relevant project scheduling problem. From the scheduling perspective, we address the discrete time/cost trade-off problem, whereas an optimal control formulation is used to capture the effect of project control. Moreover, we develop a solution algorithm for two particular instances of the optimal project control. This algorithm combines a tabu search strategy and nonlinear programming. It is applied to a large scale test bed and its efficiency is tested by means of computational experiments. To the best of our knowledge, this research is the first application of optimal control theory to multi-mode project networks. The models and algorithms developed in this research are targeted as a support tool for project managers in both scheduling and deciding on the timing and quantity of control activities.     

Stability analysis and optimal vaccination of an SIR epidemic model

Almost all mathematical models of diseases start from the same basic premise: the population can be subdivided into a set of distinct classes dependent upon experience with respect to the relevant disease. Most of these models classify individuals as either a susceptible individual S, infected individual I or recovered individual R. This is called the susceptible-infected-recovered (SIR) model. In this paper, we describe an SIR epidemic model with three components; S, I and R. We describe our study of stability analysis theory to find the equilibria for the model. Next in order to achieve control of the disease, we consider a control problem relative to the SIR model. A percentage of the susceptible populations is vaccinated in this model. We show that an optimal control exists for the control problem and describe numerical simulations using the Runge-Kutta fourth order procedure. Finally, we describe a real example showing the efficiency of this optimal control.     

Pontryagin's principle for control problems in age-dependent population dynamics

In this paper, Pontryagin's principle is proved for a fairly general problem of optimal control of populations with continuous time and age variable. As a consequence, maximum principles are developed for an optimal harvesting problem and a problem of optimal birth control.     

Minimal time control of fed-batch bioreactor with product inhibition

This paper is devoted to the minimal time control problem for fed-batch bioreactors, in presence of an inhibitory product, which is released by the biomass proportionally to its growth. We first consider a growth rate with substrate saturation and product inhibition, and we prove that the optimal strategy is fill and wait (bang-bang). We then investigate the case of the Jin growth rate which takes into account substrate and product inhibition. For this type of growth function, we can prove the existence of singular arc paths defining singular strategies. Several configurations are addressed depending on the parameter set. For each case, we provide an optimal feedback control of the problem (of type bang-bang or bang-singular-bang). These results are obtained gathering the initial system into a planar one by using conservation laws. Thanks to Pontryagin maximum principle, Green’s theorem, and properties of the switching function, we obtain the optimal synthesis. A methodology is also proposed in order to implement the optimal feeding strategies.