一类害虫治理的数学模型研究

针对害虫治理的实际问题,建立了一类具有连续时滞饱和反应增长率的状态反馈控制模型.首先,定性分析了平衡点存在的条件;其次,依据半连续动力系统理论,利用Dulac函数和环域定理证明了唯一的正平衡点是全局稳定的;最后,采用微分方程几何理论和后继函数法,获得了阶1周期解存在的充分条件,同时用几何方法获得一种新的存在唯一阶1周期解的条件.     

具有状态脉冲效应的阶段结构的害虫防治模型动力性分析(英文)

本文对符合实际的具有状态脉冲效应的阶段结构的害虫防治模型进行研究,给出半连续动力系统、半连续动力系统的后继函数等的定义,根据动力系统的基本理论,采用脉冲微分方程几何理论的方法研究模型定义的半连续动力系统各种几何性质,得到系统存在阶1周期解的充分条件,阶1周期解全局轨道渐近稳定性的充分条件.获得的理论结果说明我们可以经过一次脉冲、两次脉冲、多次脉冲就能完全控制害虫使之不超过阖值.最后,我们用数值模拟的方法说明结果的正确性.     

Modelling Fuzzy Control Problems with Toll Sets

We shall introduce in this paper toll sets and apply it to dynamical and control systems. We shall reformulate viability theorems for 'fuzzy controlled problem". 'Fuzzification" of dynamical and control systems led us to use indicators instead of characteristic functions for imbedding subsets into functions. Therefore, instead of obtaining the genuine fuzzy sets by a convexification procedure, we obtain the 'toll sets", the membership function being a cost function taking values between 0 and . Hence we can define 'fuzzy" or 'toll" – differential inclusions and control systems and solve the viability problem or the toll viability problem by building fuzzy controllers which regulate viable solutions (satisfying at each instant viability and toll viability constraints).     

基于喷洒杀虫剂及释放病虫的脉冲控制害虫模型

基于喷洒杀虫剂及释放病虫的综合控制害虫策略,建立了具有脉冲控制的微分方程模型.利用脉冲微分方程的F loquet理论、比较定理,证明了害虫灭绝周期解的全局渐近稳定性与系统的持久性.     

具阶段结构害虫防治模型的脉冲效应

对于用微分方程描述的种群生态动力系统，其研究结果已十分丰富，但自然界中的许多变化规律都呈现出脉冲效应，因此用脉冲微分方程描述某些运动状态在固定或不固定时刻的快速变化或跳跃更切合实际，尤其在刻画种群生长和流行病动力学行为方面，脉冲微分方程的描述显得更科学更真实，具有脉冲效应的种群动力学模型的研究目前还处于刚刚起步阶段，本对符合实际的有脉冲效应的具阶段结构的常系数害早防治模型进行了研究，得到了系统存在周期解的充分条件，系统存在唯一周期解的充分条件，系统周期解轨道渐近稳定的充分条件。     

一类具有脉冲控制的害虫管理SI数学模型研究

研究一类具有脉冲控制的害虫管理SI数学模型,运用Floquet理论证明了系统害虫灭绝周期解的全局渐近稳定性,并对所得结论进行了数值模拟.     

一类带有连续投放和脉冲控制的害虫管理SI数学模型

研究一类具有连续投放和脉冲控制的害虫管理SI数学模型,证明了连续投放系统正平衡点的全局渐近稳定性,讨论了脉冲控制系统的持续性,并对所得结论进行了数值模拟.     

Modelling of a Switching Control Hydraulic System

Modelling of a hydraulic system featuring a specific type of switching control is presented. Despite conventional hydraulic drive technology where rather smooth changes of pressure and flow rate are intended and where oscillations constitute undesired phenomena, switching control provokes oscillations as an indispensable element to achieve high energetic efficiency with valve control. The system under study is one which comprises a novel switching valve, a long line with considerable wave propagation dynamics, a hydraulic cylinder, and the valve's dynamics.     

害虫综合防治建模驱动“半连续动力系统理论”兴起

以害虫综合防治数学建型为启迪,对生物数学研究的一些相关问题开展了一系列的研究.从实际问题出发,我们分别建立了"常微分方程模型"以及对应的"周期脉冲控制模型";随着害虫综合防治常态化管理和环境污染常态化防治的兴起,我们建立了"状态脉冲反馈控制系统"模型,简称"半连续动力系统"模型,提出了"半连续动力系统"相关的概念,创建了其基本理论,并且作了系统性的研究,例如:半连续动力系统的周期解以及周期解的稳定性、同宿轨和同宿分支、异宿轨和异宿分支以及"双边控制系统"等概念及其判定定理的研究;进一步将"半连续动力系统"相应的理论和方法应用于生物数学其他方面的一些相关问题的研究.本文以数学模型为载体,归纳总结了近十多年来对生物数学的研究历程,指出了当前研究中尚待解决的问题.     

LP Modelling for the Time Optimal Control Problem of the Heat Equation

To find a control function which puts the heat equation in an unknown minimum time into a stationary regime is considered. Using an embedding method, the problem of finding the time optimal control is reduced to one consisting of minimizing a linear form over a set of positive measures. The resulting problem can be approximated by a finite dimensional linear programming (LP) problem. The nearly optimal control is constructed from the solution of the final LP problem. To find the lower bound of the optimal time a search algorithm is proposed. Some examples demonstrate the effectiveness of the method.     

Modelling the Effects of Prepaid Monetary Incentives on Mail-Survey Response

This paper presents a statistical model relating the impact of prepaid monetary incentives on response rates from mail surveys. The model supports the use of monetary incentives, but inclusion of incentive value made an insignificant contribution to the model. A cost-benefit model was developed to estimate the economic worth of incentives when a researcher is attempting to achieve a target sample size.     

Modelling and Optimal Receding-horizon Control of Maritime Container Terminals

The main objective of this paper consists in modelling, optimizing, and controlling container transfer operations inside intermodal terminals. More specifically, maritime container terminals are here considered, involving three kinds of transportation modes, i.e., maritime, rail, and road transport. Generally speaking, an intermodal port terminal can be seen as a system of container flows with two interfaces, towards the hinterland and towards the sea, respectively. Moreover, inside a terminal, unloading operations of inbound containers, container storage, and loading operations of outbound containers are carried out. A simple model for maritime container terminals is proposed in this paper. In the model, a system of queues represents the standing of containers and their movements inside the terminal. The dynamic evolutions of these queues are described by discrete-time equations, where the state variables represent the queue lengths and the control variables take into account the utilization of terminal resources such as load/unload handling rates. On the basis of the proposed model, an optimization problem is defined that consists in minimizing the transfer delays of containers in the terminal. The problem is stated as an optimal control problem whose solution is sought by adopting a receding-horizon strategy.      

Modelling and Control of a Hydraulic Actuated Large Scale Manipulator

This contribution deals with the modelling and control of an elastic manipulator. The arm is actuated by a hydraulic ram due to the significant weight. The overall goal is to achieve good tracking of the tip, as well as to reject disturbances, which act on the flexible arm. The controller design is based on two approaches. A flatness‐based feedforward control takes care of the tracking behaviour, and a passivity‐based feedback law stabilizes the trajectories and suppresses the elastic vibrations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effects of Modelling on Log Bucking Solution Techniques

Log bucking is an industrial problem of subdividing longer logs into smaller logs such that potential revenue is maximized. The model has been solved using dynamic programming predominately, and branch-and-bound to a lesser extent. This research considers the effect of modelling assumptions that have been used to accommodate the solution techniques. Three levels of increasing model detail are considered. An examination of the nature and amount of error is made by using a model of lesser detail instead of a more precise model. The main experiment is used to show the differences in solution accuracy for the three dynamic programming strategies when compared with the accuracy of solutions generated by using branch-and-bound. The final analysis considers the cost in terms of time to solution for each solution technique to produce highly comparable solution accuracy.     

具非线性传染率与生物化学控制的害虫管理S-I模型

讨论了具有非线性传染率与脉冲控制的害虫管理S-I传染病模型,此模型考虑的是脉冲投放病虫和喷洒农药.不但得到了系统的所有解的一致完全有界,而且得到了害虫灭绝的边界周期解的全局渐进稳定和系统的一致持久的条件.为实际的害虫管理提供了可靠的理论依据.     

Modelling the $Wolbachia$ Strains for Dengue Fever Virus Control in the Presence of Seasonal Fluctuation

Consider that infection with $Wolbachiacan$ limit a mosquito''s ability to transmit Dengue fever virus through its saliva, a mathematical model describing the transmission of Dengue fever between vector mosquitoes and human, incorporating $Wolbachia$-carrying mosquito population and seasonal fluctuation, is proposed. Firstly, the stability and bifurcation of this model are investigated exactly in the case where seasonality can be neglected. Further, the basic reproductive number $\mathcal{R}_0^s$ for this model with seasonal variation is obtained, that is, if $\mathcal{R}_0^s$ is less than unity the disease is extinct and $\mathcal{R}_0^s$ is greater than unity the disease is uniformly persistent. Finally, numerical simulations verify the theoretical results. Theoretical results suggest that, compared with the mosquito reduction strategies (such as the elimination of mosquito breeding sites, killing of adult mosquitoes by spraying), introducing $Wolbachia$ strains is as effectual to fight against the transmission of Dengue virus.     

Modelling,Synthesis, and Simulation of Supervisory Process Control Systems

Modelling, synthesis, and simulation issues of the supervisory systems in process control are investigated in the paper. Petri nets are used as a basic modelling framework for the supervisory part of the system. It is shown how the final verification effort can be minimised by applying formal synthesis methods. A straightforward approach to the industrial implementation of the developed solutions is suggested by means of sequential function chart representation. A batch process cell case study is used to illustrate the described concepts. Corresponding continuous and discrete event models of the process cell units are developed and a co-ordinating supervisor is designed by the method of place invariants. The system is simulated by the continuous simulation tool Matlab-Simulink, which is enhanced for simulation of the sequential control logic represented by sequential function chart.     

First Principles Modelling of a Pasteurisation Plant for Model Predictive Control

This paper investigates the physical modelling of an industrial pasteuriser plant from a control-oriented point of view. The investigated pasteuriser is based on plate heat exchangers (PHE) of type Clip 10-RM and brazed heat exchangers (BHE) of type CB76 from Alfa Laval. The traditionally highly complex and over parameterised models established for design, dimensioning, and scientific purposes are not suitable for use within a control strategy in their present form. In this paper, a simplified first order first principles (FP) model of the PHE sections as well as the BHE heaters constructing the pasteuriser are developed. An integrated model of the entire pasteuriser is then constructed combining the first principles model obtained for different pasteuriser components. The pasteuriser model parameters are identified, and the model is validated using data obtained during five test protocol sessions performed on an industrial process. Finally an example of a model predictive control (MPC) strategy, using the developed model, is briefly introduced, results are shown and conclusions are drawn.