In this paper, we build an epidemiological model to investigate the dynamics of the spread of dengue fever in human population. We apply optimal control theory via the Pontryagins Minimum Principle together with the R...In this paper, we build an epidemiological model to investigate the dynamics of the spread of dengue fever in human population. We apply optimal control theory via the Pontryagins Minimum Principle together with the Runge-Kutta solution technique to a “simple” SEIRS disease model. Controls representing education and drug therapy treatment are incorporated to reduce the latently infected and actively infected individual populations. The overall thrust is the minimization of the spread of the disease in a population by adopting an optimization technique as a guideline.展开更多
The purpose of the present paper is to apply the Pontryagin Minimum Principle to mathematical models of cancer growth. In [1], I presented a discrete affine model T of cancer growth in the variables C for cancer, GF f...The purpose of the present paper is to apply the Pontryagin Minimum Principle to mathematical models of cancer growth. In [1], I presented a discrete affine model T of cancer growth in the variables C for cancer, GF for growth factors and GI for growth inhibitors. One can sometimes find an affine vector field X on whose time one map is T. It is to this vector field we apply the Pontryagin Minimum Principle. We also apply the Discrete Pontryagin Minimum Principle to the model T. So we prove that maximal chemo therapy can be optimal and also that it might not depending on the spectral properties of the matrix A, (see below). In section five we determine an optimal strategy for chemo or immune therapy.展开更多
根据柴油发动机台架试验结果,分析排气背压对发动机性能的影响,在设计插电式柴电混合动力汽车(plug-in hybrid electric vehicle,PHEV)控制策略时考虑排气背压对油耗与排放的影响因素.以排气背压和蓄电池荷电状态为状态变量,利用庞特里...根据柴油发动机台架试验结果,分析排气背压对发动机性能的影响,在设计插电式柴电混合动力汽车(plug-in hybrid electric vehicle,PHEV)控制策略时考虑排气背压对油耗与排放的影响因素.以排气背压和蓄电池荷电状态为状态变量,利用庞特里亚金极小值原理,求解以插电式混合动力汽车油耗与颗粒物排放量的多目标泛函,从而得到整车油耗与排放综合最优控制策略.在MATLAB/Simulink仿真平台下建立了包含柴油颗粒过滤器(diesel particle filter,DPF)压力损失和捕集效率模型的整车动力学模型,对上述所得最优控制策略进行验证,并与二阶段(charge-depleting and charge-sustaining,CD–CS)控制策略和无排气背压状态最优控制策略进行对比.仿真结果表明,本文建立的最优控制策略相对于其它两种控制策略均能明显降低排气背压升高对发动机性能的影响,有效地改善了整车燃油经济性和排放性.最后通过台架试验对所提出的最优控制策略的有效性进行验证,结果表明,采用该控制策略优化后的等效燃油消耗量与颗粒物(particulate matter,PM)排放量分别降低了9.68%和32%.展开更多
文摘In this paper, we build an epidemiological model to investigate the dynamics of the spread of dengue fever in human population. We apply optimal control theory via the Pontryagins Minimum Principle together with the Runge-Kutta solution technique to a “simple” SEIRS disease model. Controls representing education and drug therapy treatment are incorporated to reduce the latently infected and actively infected individual populations. The overall thrust is the minimization of the spread of the disease in a population by adopting an optimization technique as a guideline.
文摘The purpose of the present paper is to apply the Pontryagin Minimum Principle to mathematical models of cancer growth. In [1], I presented a discrete affine model T of cancer growth in the variables C for cancer, GF for growth factors and GI for growth inhibitors. One can sometimes find an affine vector field X on whose time one map is T. It is to this vector field we apply the Pontryagin Minimum Principle. We also apply the Discrete Pontryagin Minimum Principle to the model T. So we prove that maximal chemo therapy can be optimal and also that it might not depending on the spectral properties of the matrix A, (see below). In section five we determine an optimal strategy for chemo or immune therapy.
文摘根据柴油发动机台架试验结果,分析排气背压对发动机性能的影响,在设计插电式柴电混合动力汽车(plug-in hybrid electric vehicle,PHEV)控制策略时考虑排气背压对油耗与排放的影响因素.以排气背压和蓄电池荷电状态为状态变量,利用庞特里亚金极小值原理,求解以插电式混合动力汽车油耗与颗粒物排放量的多目标泛函,从而得到整车油耗与排放综合最优控制策略.在MATLAB/Simulink仿真平台下建立了包含柴油颗粒过滤器(diesel particle filter,DPF)压力损失和捕集效率模型的整车动力学模型,对上述所得最优控制策略进行验证,并与二阶段(charge-depleting and charge-sustaining,CD–CS)控制策略和无排气背压状态最优控制策略进行对比.仿真结果表明,本文建立的最优控制策略相对于其它两种控制策略均能明显降低排气背压升高对发动机性能的影响,有效地改善了整车燃油经济性和排放性.最后通过台架试验对所提出的最优控制策略的有效性进行验证,结果表明,采用该控制策略优化后的等效燃油消耗量与颗粒物(particulate matter,PM)排放量分别降低了9.68%和32%.
