A differential equation model of search for randomly arriving and departing targets

In this paper we analyze optimal search strategies in an environment in which multiple, independent targets arrive and depart at random. The analysis revolves around a continuous time differential equation model which captures the time dependent nature of the search process. We explore the impact on optimal strategies of nonzero travel times between regions as well as differing target arrival rates. We derive simple closed form expressions for determining if only one region should be searched.     

A characterization of optimal base‐stock levels for a multistage serial supply chain

In this article, we present a multistage model to optimize inventory control decisions under stochastic demand and continuous review. We first formulate the general problem for continuous stages and use a decomposition solution approach: since it is never optimal to let orders cross, the general problem can be broken into a set of single‐unit subproblems that can be solved in a sequential fashion. These subproblems are optimal control problems for which a differential equation must be solved. This can be done easily by recursively identifying coefficients and performing a line search. The methodology is then extended to a discrete number of stages and allows us to compute the optimal solution in an efficient manner, with a competitive complexity. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 32–46, 2016     

Optimal search plan minimizing the expected risk of the search for a target with conditionally deterministic motion

This article deals with a search problem for a moving target with a rather simple type of motion called factorable conditionally deterministic. A search plan is characterized by (ϕ, T), the elements of which specify how to search and when to stop the search, respectively. The problem is to find the optimal search plan which minimizes the expected risk (the expected search cost minus the expected reward). We obtain conditions for the optimal search plan, and applying the theorems, we derive the optimal search plan in a closed form for the case in which the target moves straight from a fixed point selecting his course and speed randomly.     

Optimal layered search

This article investigates the problem of planning an optimal layered search for a stationary target. A search is layered if it assigns each point in the search space an integer number of glimpses or looks. General necessary and sufficient conditions and an existence theorem are obtained. The special case in which the initial target distribution is bivariate normal is considered in detail.     

Optimal search using two nonconcurrent sensors

Search for a stationary target is considered for a situation in which two sensors are available, but cannot be used simultaneously. The cost (in time) of switching from one sensor to the other is ignored, and each sensor is assumed to have perfect discrimination. For a specified class of searches an optimal allocation of search effort is obtained. In the case of a circular normal prior target location distribution, an example is presented in which one sensor is assumed to have a fixed sweep width and the other a stochastic sweep width. An optimal plan is found for this example. This plan produces an allocation of search effort which is expended in a disk by one sensor and in a bounding annulus by the other.     

A search game taking account of attributes of searching resources

This article deals with a two‐person zero‐sum game called a search allocation game (SAG), in which a searcher and a target participate as players. The searcher distributes his searching resources in a search space to detect the target. The effect of resources lasts a certain period of time and extends to some areas at a distance from the resources' dropped points. On the other hand, the target moves around in the search space to evade the searcher. In the history of search games, there has been little research covering the durability and reachability of searching resources. This article proposes two linear programming formulations to solve the SAG with durable and reachable resources, and at the same time provide an optimal strategy of distributing searching resources for the searcher and an optimal moving strategy for the target. Using examples, we will analyze the influences of two attributes of resources on optimal strategies. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 2008     

基于Theta-D次优控制器设计的相对姿轨耦合控制

针对在轨服务航天器的快速机动和姿轨协同控制的特点,研究了基于姿轨耦合一体化模型的最优控制方法。建立了包括转动和平动的六自由度相对运动耦合非线性模型,连续偏心推力矢量既可以提供位置控制力,也可以输出姿态控制转矩。利用动态模型线性化方法和θ-D构造性优化算法给出相对运动姿轨耦合最优控制问题的数值解法,同时控制服务航天器相对位置和相对姿态,使其直线逼近一个失效慢旋目标。仿真结果证明,由于在动态优化问题中采用了构造性求解,所提方法在保证相对运动稳定和动态性能的前提下计算量小,对未来应用具有一定现实意义。     

不确定环境下无人机区域目标搜索及载荷参数影响

针对不确定环境下无人机区域搜索问题,建立了实时探测更新的搜索方法,提出了机载光电载荷参数优化配置策略。建立了基于二维离散网格的无人机区域搜索模型,采用概率地图描述目标信息的实时获取与更新;引入不确定度指标、目标网格的重访和网格探测次数控制,建立搜索目标函数;建立了基于粒子群算法的搜索路径滚动优化方法;通过对任务区域平均探测时间步数和误判概率的估计分析,建立了机载光电载荷参数优化配置策略。使用蒙特卡洛方法验证了区域搜索方法的有效性和光电载荷参数配置对搜索效率、误判概率的影响。     

一种拦截机动目标的最优制导律设计

引入伪控制变量的概念,建立了线性化的描述导弹与目标相对运动的状态方程.应用线性二次型最优控制理论和改进剩余时间的计算方法,提出了一种拦截高机动目标的最优制导律.通过与比例导引律在平面拦截过程中的仿真结果对比分析,表明所提出的最优制导律在拦截机动目标时更为有效.     

搜索路径给定时的搜索对策问题及其应用

搜索路径给定时的最优搜索方案问题,也可以理解为是关于搜索者和目标的二人对策问题,主要讨论了当搜索路径给定时的单个搜索者和单个目标的搜索对策问题。首先根据问题的特点,利用动态规划和迭代的方法,确定关于目标逃逸路径混合策略的最优分区,证明该分区是多面体凸集;针对目标不同逃逸路径的分区,求出搜索者的最大期望收益,再将问题转化为二人有限零和对策,计算出搜索者的支付矩阵,确定最优搜索策略。最后结合海军护航行动,对我舰载直升机搜索小型海盗船进行分析和计算,说明搜索路径给定时的最优搜索对策对于双方的资源分配和提高搜索效率具有一定的应用价值。     

越肩发射次最优火控系统设计

在非线性导弹火力控制设计方面 ,相关黎卡提方程 (SDRE)理论证明是一种系统而高效的方法。对于越肩发射火控系统而言 ,在攻击载机后方目标的过程中 ,机载设备往往只能获取目标的角度信息 ,即非完全目标信息。本文基于非完全目标信息 ,采用非线性 SDRE状态调节器理论 ,设计越肩发射次最优火控系统 ,求得系统的局部渐进稳定次优解 ,用以实现“越肩”火控过程     

Optimal lot sizing and inspection policy for an EMQ model with imperfect inspections

An EMQ model with a production process subject to random deterioration is considered. The process can be monitored through inspections, and both the lot size and the inspection schedule are subject to control. The “in-control” periods are assumed to be generally distributed and the inspections are imperfect, i.e., the true state of the process is not necessarily revealed through an inspection. The objective is the joint determination of the lot size and the inspection schedule, minimizing the long-run expected average cost per unit time. Both discrete and continuous cases are examined. A dynamic programming formulation is considered in the case where the inspections can be performed only at discrete times, which is typical for the parts industry. In the continuous case, an optimum inspection schedule is obtained for a given production time and given number of inspections by solving a nonlinear programming problem. A two-dimensional search procedure can be used to find the optimal policy. In the exponential case, the structure of the optimal inspection policy is established using Lagrange's method, and it is shown that the optimal inspection times can be found by solving a nonlinear equation. Numerical studies indicate that the optimal policy performs much better than the optimal policy with periodic inspections considered previously in the literature. The case of perfect inspections is discussed, and an extension of the results obtained previously in the literature is presented. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 165–186, 1998     

带落角约束的再入机动弹头的复合导引律

针对再入机动弹头垂直打击目标的要求,研究了具有末端落角约束的复合导引律.该导引律包括俯冲平面内的制导方程和转弯平面内的制导方程,通过在最优导引律的基础上引入滑模变结构控制,增强导引律的鲁棒性.为了减小控制量的抖振和能量损耗,提出了采用RBF(径向基函数)神经网络自适应调节切换项增益的方案,数学仿真验证了该方案的有效性.仿真结果还表明,与最优导引律相比,复合导引律在外界干扰的影响下仍能保持较高的制导精度.     

Incremental approximation of optimal allocations

This paper concerns the approximation of optimal allocations by δ allocations. δ allocations are obtained by fixing an increment δ of effort and deciding at each step upon a single cell in which to allocate the entire increment. It is shown that δ allocations may be used as a simple method of approximating optimal allocations of effort resulting from constrained separable optimization problems involving a finite number of cells. The results are applied to find δ allocations (called δ plans) which approximate optimal search plans. δ plans have the property that as δ → 0, the mean time to find the target using a δ plan approaches the mean time when using the optimal plan. δ plans have the advantage that. they are easily computed and more easily realized in practice than optimal plans which tend to be difficult to calculate and to call for spreading impractically small amounts of effort over large areas.     

The United States Coast Guard Computer-Assisted Search Planning system (CASP)

This paper provides an overview of the Computer-Assisted Search Planning (CASP) system developed for the United States Coast Guard. The CASP information processing methodology is based upon Monte Carlo simulation to obtain an initial probability distribution for target location and to update this distribution to account for drift due to currents and winds. A multiple scenario approach is employed to generate the initial probability distribution. Bayesian updating is used to reflect negative information obtained from unsuccessful search. The principal output of the CASP system is a sequence of probability “maps” which display the current target location probability distributions throughout the time period of interest. CASP also provides guidance for allocating search effort based upon optimal search theory.     

Optimization in mixed-integer space with a single linear bound

The search for an optimal point in a mixed-integer space with a single linear bound may be significantly reduced by a procedure resembling the Lagrangian technique. This procedure uses the coefficients of the linear bound to generate a set of necessary conditions that may eliminate most of the space from further consideration. Enumerative or other techniques can then locate the optimum with greater efficiency. Several methods are presented for applying this theory to separable and quadratic objectives. In the maximization of a separable concave function, the resulting average range of the variables is approximately equal to the maximum (integer) coefficient of the constraint equation.     

Discrete search allocation game with false contacts

This paper deals with a two‐person zero‐sum game called a search allocation game, where a searcher and a target participate, taking account of false contacts. The searcher distributes his search effort in a search space in order to detect the target. On the other hand, the target moves to avoid the searcher. As a payoff of the game, we take the cumulative amount of search effort weighted by the target distribution, which can be derived as an approximation of the detection probability of the target. The searcher's strategy is a plan of distributing search effort and the target's is a movement represented by a path or transition probability across the search space. In the search, there are false contacts caused by environmental noises, signal processing noises, or real objects resembling true targets. If they happen, the searcher must take some time for their investigation, which interrupts the search for a while. There have been few researches dealing with search games with false contacts. In this paper, we formulate the game into a mathematical programming problem to obtain its equilibrium point. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Lanchester-type models of warfare and optimal control

The optimization of the dynamics of combat (optimal distribution of fire over enemy target types) is studied through a sequence of idealized models by use of the mathematical theory of optimal control. The models are for combat over a period of time described by Lanchester-type equations with a choice of tactics available to one side and subject to change with time. The structure of optimal fire distribution policies is discussed with reference to the influence of combatant objectives, termination conditions of the conflict, type of attrition process, and variable attrition-rate coefficients. Implications for intelligence, command and control systems, and human decision making are pointed out. The use of such optimal control models for guiding extensions to differential games is discussed.     

卫星导航系统功率增强子星座优化设计与性能分析

卫星功率增强技术是提高区域导航信号抗干扰性能的一种有效措施,在卫星导航全星座中优选出卫星数量少、服务性能优的功率增强子星座,是新一代卫星导航系统建设迫切需要解决的问题。因此提出基于卫星数最少准则的功率增强子星座优化设计方法,详细介绍设计流程、数学模型及最优解搜索策略;定义了可用性水平、精度水平和覆盖范围等指标评估功率增强子星座性能;以GPS为例,分别针对覆盖点目标和区域目标两种应用背景进行功率增强子星座优化设计及性能评估。分析结果表明:全球范围内任意目标点进行功率增强需要12～17颗卫星;实现对我国沿海地区的连续覆盖需要18颗功率增强卫星;覆盖整个亚太地区则需要全星座24颗卫星都具备功率增强能力,这样才能满足其连续性和精度要求,此时最优功率增强子星座的服务范围可扩充至全球区域。     

运动视觉平台点目标定位误差分析和平台最优运动轨迹设计

对运动视觉平台点目标定位问题进行了研究,介绍了基于视觉共线方程的目标定位方法,分析了共线方程关于视线约束的实质。在观测视线相关坐标系推导了视线方向角矢量对目标定位误差的影响规律,分析了多观测对定位误差的影响,并基于最小化目标定位误差推导了视觉平台的最优运动轨迹,利用简单明了的分析方法得到了与已有文献优化Fisher信息矩阵方法一致的结论。利用仿真和试验对定位误差和最优轨迹进行了验证,证实了定位误差理论分析和最优运动轨迹设计的正确性。