Pontryagin’s Maximum Principle for a Advection-Diffusion-Reaction Equation

In this paper we investigate optimal control problems governed by a advection-diffusion-reaction equation. We present a method for deriving conditions in the form of Pontryagin’s principle. The main tools used are the Ekeland’s variational principle combined with penalization and spike variation techniques.

Real-Time Co-optimization of Gear Shifting and Engine Torque for Predictive Cruise Control of Heavy-Duty Trucks

Fuel consumption is one of the main concerns for heavy-duty trucks.Predictive cruise control(PCC)provides an intriguing opportunity to reduce fuel consumption by using the upcoming road information.In this study,a real-time implementable PCC,which simultaneously optimizes engine torque and gear shifting,is proposed for heavy-duty trucks.To minimize fuel consumption,the problem of the PCC is formulated as a nonlinear model predictive control(MPC),in which the upcoming road elevation information is used.Finding the solution of the nonlinear MPC is time consuming;thus,a real-time implementable solver is developed based on Pontryagin’s maximum principle and indirect shooting method.Dynamic programming(DP)algorithm,as a global optimization algorithm,is used as a performance benchmark for the proposed solver.Simulation,hardware-in-the-loop and real-truck experiments are conducted to verify the performance of the proposed controller.The results demonstrate that the MPC-based solution performs nearly as well as the DP-based solution,with less than 1%deviation for testing roads.Moreover,the proposed co-optimization controller is implementable in a real-truck,and the proposed MPC-based PCC algorithm achieves a fuel-saving rate of 7.9%without compromising the truck’s travel time.

一类具有Beddington-DeAngelis功能反应捕食系统收获模型的稳定性

研究一类具有双线性密度制约及Beddington-DeAngelis功能反应的捕食系统收获模型.运用微分方程定性稳定性理论讨论系统正平衡点的性态,得到其局部渐近稳定及全局渐近稳定的充分条件,利用Pontryagin最大值原理得到系统的最优收获策略.

SGKW轨道在线生成技术研究

天基对地打击动能武器(SGKW)用于从太空对地面高价值战略目标进行快速、准确的打击。针对作战实时性要求,探讨了SGKW的轨道在线生成技术。首先,利用庞特里亚金极大值原理将时间最短打击轨道的最优控制问题转化为两点边值问题。由于约束条件中存在优化参数,一种基于"遗传算法+序列二次规划"的组合优化算法被用于求解伴随变量初值和再入点参数。为了提高轨道生成的速度,在大量离线优化数据的基础上建立了BP神经网络预测模型,其预测值通过序列二次规划算法稍加修正,即可满足相应任务的落点精度要求。仿真结果验证了上述方案的有效性。

基于B-S模型金融衍生品可转债定价的研究

作为一种新型的融资渠道,可转债近几年在资本市场上有了飞速发展,针对可转债的价值组成,将其分成纯债券、转换和期权价值三部分,并分别介绍了三种价值的度量方法,利用最小价值原理和B-S定价公式对选取的9只上市可转债理论价值进行估计,发现计算出的结果普遍比市价低,最后基于这个发现讨论产生这种偏差的原因.

Mathematical Model and Simulation of Harmful Invasive Plant Control

Plant invasion refers to the phenomenon that some plants grow too fast due to they are far away from the original living environment or predators, affecting the local environment. With the development of tourism and trade, the harm caused by invasive plants will be more and more serious. Therefore, it is necessary to ex- plore an effective method for controlling plant invasion through qualitative and quan- titative research. In this paper, the models were established for the early and late harmful plant invasion control. The huge computation was completed by the com- puter programming to obtain the optimal solutions of the models. The real meaning of the optimal solution was further discussed. Through numerical simulations and discussion, it could be concluded that the quantitative research on the invasive plant control had a certain application value.

Flexible predictive power-split control for battery-supercapacitor systems of electric vehicles using IVHS

The utilization of traffic information received from intelligent vehicle highway systems(IVHS) to plan velocity and split output power for multi-source vehicles is currently a research hotspot. However, it is an open issue to plan vehicle velocity and distribute output power between different supply units simultaneously due to the strongly coupling characteristic of the velocity planning and the power distribution. To address this issue, a flexible predictive power-split control strategy based on IVHS is proposed for electric vehicles(EVs) equipped with battery-supercapacitor system(BSS). Unlike hierarchical strategies to plan vehicle velocity and distribute output power separately, a monolayer model predictive control(MPC) method is employed to optimize them online at the same time. Firstly, a flexible velocity planning strategy is designed based on the signal phase and time(SPAT) information received from IVHS and then the Pontryagin’s minimum principle(PMP) is adopted to formulate the optimal control problem of the BSS. Then, the flexible velocity planning strategy and the optimal control problem of BSS are embedded into an MPC framework, which is online solved using the shooting method in a fashion of receding horizon. Simulation results verify that the proposed strategy achieves a superior performance compared with the hierarchical strategy in terms of transportation efficiency, battery capacity loss, energy consumption and computation time.

Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem

A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer—a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.

Parametric Iteration Method for Solving Linear Optimal Control Problems

This article presents the Parametric Iteration Method (PIM) for finding optimal control and its corresponding trajectory of linear systems. Without any discretization or transformation, PIM provides a sequence of functions which converges to the exact solution of problem. Our emphasis will be on an auxiliary parameter which directly affects on the rate of convergence. Comparison of PIM and the Variational Iteration Method (VIM) is given to show the preference of PIM over VIM. Numerical results are given for several test examples to demonstrate the applicability and efficiency of the method.

Modelling the Optimal Control of Transmission Dynamics of <i>Mycobacterium ulceran</i>Infection

This paper examines optimal control of transmission dynamics of Mycobacterium ulceran (MU) infection. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations, optimal control and computer simulation. The basic reproduction number of the reduced model system is obtained by using the next generation operator method. It is found that by using Ruth Hurwitz criteria, the disease free equilibrium point is locally asymptotically stable and using centre manifold theory, the model shows the transcritical (forward) bifurcation. Optimal control is applied to the model seeking to minimize the transmission dynamics of MU infection on human and water-bugs. Pontryagin’s maximum principle is used to characterize the optimal levels of the controls. The results of optimality are solved numerically using MATLAB software and the results show that optimal combination of two controls (environmental and health education for prevention) and (water and environmental purification) minimizes the MU infection in the population.

Analysis of Listeriosis Transmission Dynamics with Optimal Control

Listeriosis is an illness caused by the germ Listeria monocytogenes. Generally, humans are infected with listeriosis after eating contaminated food. Listeriosis mostly affects people with weakened immune systems, pregnant women and newborns. In this paper, a model describing the dynamics of Listeriosis is developed and analysed using ordinary differential equations. The model was analysed both quantitatively and qualitatively for its local and global stability, basic reproductive number and parameter contributions to the basic reproductive number to understand the impact of each parameter on the disease spread. The Listeriosis model has been extended to include time dependent control variables such as treatment of both humans and animals, vaccination and education of humans. Pontryagin’s Maximum Principle was introduced to obtain the best optimal control strategies required for curbing Listeriosis infections. Numerical simulation was performed and the results displayed graphically and discussed. Cost effectiveness analysis was conducted using the intervention averted ratio (IAR) concepts and it was revealed that the most effective intervention strategy is the treatment of infected humans and animals.

Time-optimal Trajectories for a Car-like Robot

这份报纸为完成时间最佳的轨道的足够的家庭在基于几何最佳的控制理论歧管的 3-dimensional 连接机器人的任何二种配置提供一个新几何方法。我们为分析非线性的问题的这种特殊类型提供一个新观点。从 Pontryagin 的最小的原则(PMP ) 和谎言代数学基于切换的功能和他们的衍生物的结构的特征，我们造一个特殊坐标系统并且介绍新向量。我们发现在这新向量的旋转轨道和最佳的控制轨道之间的一对一的印射。而且，我们定义表示位置和这向量的旋转方向的切换的向量，并且得出一个结论规定起始、最后的切换的向量能特别地决定一条最佳的轨道。另外，它是能直接被使用选择一条时间最佳的轨道的一个条件被提供的第一次。

Mathematical Analysis of Nipah Virus Infections Using Optimal Control Theory

The optimal use of intervention strategies to mitigate the spread of Nipah Virus (NiV) using optimal control technique is studied in this paper. First of all we formulate a dynamic model of NiV infections with variable size population and two control strategies where creating awareness and treatment are considered as controls. We intend to find the optimal combination of these two control strategies that will minimize the cost of the two control measures and as a result the number of infectious individuals will decrease. We establish the existence for the optimal controls and Pontryagin’s maximum principle is used to characterize the optimal controls. The numerical simulation suggests that optimal control technique is much more effective to minimize the infected individuals and the corresponding cost of the two controls. It is also monitored that in the case of high contact rate, controls have to work for longer period of time to get the desired result. Numerical simulation reveals that the spread of Nipah virus can be controlled effectively if we apply control strategy at early stage.

Study of optimal control problems for hybrid dynamical systems

From the viewpoint of continuous systems, optimal control problem is proposed for a class of controlled Hybrid dynamical systems. Then a mathematical method- HDS minimum principle is put forward, which can solve the above problem. The HDS minimum principle is proved by means of Ekeland＇ s variational principle.

Application of Optimal Control to the Epidemiology of Dengue Fever Transmission

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.

PERIODIC OPTIMAL CONTROL PROBLEMS GOVERNED BY SEMILINEAR PARABOLIC EQUATIONS WITH IMPULSE CONTROL

This paper is concerned with periodic optimal control problems governed by semi- linear parabolic differential equations with impulse control. Pontryagin＇s maximum principle is derived. The proofs rely on a unique continuation estimate at one time for a linear parabolic equation.

Optimal Control of Heterogeneous-Susceptible-Exposed-Infectious-Recovered-Susceptible Malware Propagation Model in Heterogeneous Degree-Based Wireless Sensor Networks

Heterogeneous wireless sensor networks(HWSNs)are vulnerable to malware propagation,because of their low configuration and weak defense mechanism.Therefore,an optimality system for HWSNs is developed to suppress malware propagation in this paper.Firstly,a heterogeneous-susceptible-exposed-infectious-recovered-susceptible(HSEIRS)model is proposed to describe the state dynamics of heterogeneous sensor nodes(HSNs)in HWSNs.Secondly,the existence of an optimal control problem with installing antivirus on HSNs to minimize the sum of the cumulative infection probabilities of HWSNs at a low cost based on the HSEIRS model is proved,and then an optimal control strategy for the problem is derived by the optimal control theory.Thirdly,the optimal control strategy based on the HSEIRS model is transformed into corresponding Hamiltonian by the Pontryagin’s minimum principle,and the corresponding optimality system is derived.Finally,the effectiveness of the optimality system is validated by the experimental simulations,and the results show that the infectious HSNs will fall to an extremely low level at a low cost.

Optimal Campaign in Leptospirosis Epidemic by Multiple Control Variables

In this paper, we consider a leptospirosis epidemic model to implement optimal campaign by using multiple control variables. First, we show the existence of the control problem. Then we derive the conditions under which it is optimal to eradicate the leptospirosis infection and examine the impact of a possible educatioal/vaccinaction campaign using Pontryagin’s Maximum Principle. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. The results obtained from the numerical simulations of the model show that a possible educational/vaccinaction combined with effective treatment regime would reduce the spread of the leptospirosis infection appreciably.

Prey Predator Fishery Model with Stage Structure in Two Patchy Marine Aquatic Environment

In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system with stage structure in an aquatic environment that consists of two zones namely unreserved zone (fishing permitted) and reserved zone (fishing is strictly prohibited). In this model we introduce a stage structure in which predators are split into two kinds as immature predators and mature predators. It is assumed that immature predators cannot catch the prey and their foods are given by their parents (mature predators). It is also assumed that the fishing of immature predators prohibited in the unreserved zone and predator species are not allowed to enter inside the reserved zone. The local and global stability analysis has been specified. Biological and Bionomical equilibriums of the system are derived. Mathematical formulation of the optimal harvesting policy is given and its solution is derived in the equilibrium case by using Pontryagin’s maximum principle.

Motion Equation and Solution of Mushroom Cloud

Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.