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.

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.

考虑耐久性的PEM燃料电池有轨电车自适应优化控制策略

针对燃料电池/锂电池/超级电容混合储能有轨电车在动态负载、启停循环、怠速循环、大功率运行时质子交换膜(PEM)燃料电池寿命衰减情况,提出Pontryagin极小值原理(PMP)与耐久性结合的能量管理策略。通过启停控制策略控制燃料电池的启动与停止,有效降低燃料电池启动次数;利用储能系统总体氢气消耗为经济性代价,燃料电池性能衰退指数为耐久性代价,构建联合代价函数;在满足期望条件下,实现协态变量随荷电状态实时变化的在线适应;将所提策略与传统极小值策略和状态机策略进行仿真对比。结果表明:城市循环工况中所提策略较于传统Pontryagin策略燃料电池峰值电流降低了33.2%,氢气消耗下降了12.50%;郊区循环工况中所提策略较传统Pontryagin策略峰值电流降低了21.88%,氢气消耗下降了40.39%。所提管理策略在不同工况下均有良好的适应能力,解决了传统PMP只能离线应用的缺点,将启停次数控制在较低水平,具有延寿燃料电池的能力。

基于庞特里亚金极小值原理的柴电混合动力船舶能量管理策略

提升混合动力船舶的能源利用率,制定合适的能量管理策略以实现功率合理分配、减小船舶燃油消耗、节约成本,是混合动力船舶的亟需解决的关键技术问题。本文基于Matlab/Simulink仿真建模软件,建立对象船舶的动力系统仿真模型,研究不同功率需求下对柴油发电机和超级电容的控制要求。考虑动力源特性和船舶功率需求,本文提出了一种基于庞特里亚金极小值的能量管理策略对目标船舶进行合理的功率分配。仿真结果表明:基于庞特里亚金极小值原理的能量管理策略能够优化船舶柴油机组原动机的工作状态,使其在比油耗较低的点工作。在该策略的控制下,航行工况内的柴油发电机组原动机平均比油耗为207.2 g/(kW·h),总燃油消耗量为204.1 kg。本文方法不仅对船舶减小燃油消耗具有积极的作用,同时对提高船舶运行经济性具有重要意义。

多约束月面盘旋飞跃轨迹优化控制方法

针对无平移发动机月球探测器的多约束盘旋飞跃问题,给出了燃耗最优轨迹。盘旋飞跃划分为垂直上升段、平移段、垂直下降段,垂直上升段与垂直下降段的最优控制均为Bang-Bang形式。研究平移段最优轨迹时,考虑位置、速度、角速度等约束,首次把优化问题的控制变量由推力转化为角速度,然后基于Pontryagin极小值原理得到了最优角速度的初步形式,接着通过对奇异点连续性、控制变量切换次数的研究,得到最优角速度的最终形式由最大边值与最小边值组成且发生两次切换,最后提供了一种求解切换点的数值方法。仿真结果表明,该算法精度高、复杂度低,适用于在线轨迹优化。

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.

基于极小值原理的混动瞬时优化能量管理策略

以发动机瞬时燃油消耗最小为目标建立性能泛函,通过发动机、电机、电池数学模型建立Hamilton目标函数,采用最优控制的Pontryagin极小值原理解析目标函数,在控制集范围内搜索使目标函数达到最小值的最优控制变量,从而计算出控制电机扭矩与发动机扭矩的最优控制值。

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.

计及飞行任务与能耗分析的航空燃料电池推进系统能量管理策略

为改善航空燃料电池推进系统的燃料消耗情况并提升系统运行效率,该文提出一种考虑多飞行任务模式与外部最大能耗的综合能量管理方法。在优化常规极小值原理策略的基础上,针对飞行器飞行工况的变化率进行区间划分,改变系统目标函数系数。采用最大外部能耗算法求解超级电容的充放电电压与母线电压的偏差量来实时调整哈密顿函数中的协态变量。最后,通过求解目标函数来控制燃料电池系统的输出功率。基于实时仿真硬件在环测试平台的验证结果表明,所提算法相对于传统的等效氢耗和庞特里亚金最小值原理算法,分别将系统等效氢耗降低了4.6%和3.2%,将系统的平均运行效率提升了10.3%和5.5%,在减少燃料电池系统所承受的应力同时,提升了系统输出的稳定性。

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.