液压驱动型四足机器人对角小跑步态本体水平位置控制方法

为了对对角小跑中四足机器人本体的水平位置进行控制,建立基于沿支撑线方向运动分解的机器人近似动力学模型,将本体和对角支撑腿简化为一个七连杆结构和一个线性倒立摆,并且基于线性倒立摆解析模型提出摆动腿落足点位置计算方法,进而实现对本体水平位置的控制。针对液压作动器伸缩速度受限的问题,利用单腿冗余关节将关节角速度优化问题转化为标准二次型规划问题,通过设计二次型规划问题解法,降低对摆动腿关节角速度的需求,并且避免了传统伪逆方法可能产生的腿部奇异位型。仿真和实验结果表明:该方法能够实现在关节角速度受限的情况下,有效跟踪本体水平位置的期望轨迹。     

支持向量顺序回归机的线性规划算法

支持向量顺序回归机是标准支持向量分类机的一个推广，它是一个凸的二次规划问题。本文根据l1范数与l2范数等价关系和优化问题的对偶原理，把凸的二次规划转化成线性规划。由此提了支持向量顺序回归机的线性规划算法，进一步用数值实验验证了此算法的可行性和有效性。并与支持向量顺序回归机相比，它的运行时间缩短了，而且误差i不超过支持向量顺序回归机；     

基于Floyd算法的常规导弹连续波次作战运输规划

为提高常规导弹连续波次作战效能，对常规导弹连续波次作战运输规划问题进行研究。以Floyd算法为基础，首先生成了作战机动区域的交通网络最短路径、距离矩阵；其次将常规导弹连续波次作战运输过程分解为不同阶段，以运输过程中的整体暴露时间最短为目标，构建了初始规划方案0-1整数规划模型；然后考虑道路通行量及地域容量限制，对初始规划方案中存在的地域容量超过限制及单行道路中会车、超车情况进行逐步循环优化，以得到最佳运输规划方案；最后选择了一个作战案例想定，通过Matlab编程对案例进行了求解，得到了针对此案例的最佳运输规划方案，验证了模型的正确性和算法的有效性。     

多UCAV协同作战自主任务规划系统

在分析未来多UCAV协同作战任务的基础上,构建了一个多UCAV协同作战的自主任务规划系统结构,探讨了其运行机制。提出这个系统的核心是自主规划器,它应该具有任务分解、智能信息处理和机载任务规划与重规划能力。设计了自主规划器的初步方案。指出了这个系统下一步研究的任务和方向。     

二次规划法优化设计的应用研究

本文对二次规划法进行应用研究。通过化铣网格加劲壳的二次规划法优化设计和几何规划对偶问题的二次规划解法,提出变量替换梯移法调参改善初始展开点、限制步长法和改进的高斯消元法等措施,给二次规划法的应用提供一些简单有效的方法。计算结果表明,上述处理方法在加快收敛、提高计异精度方面也收到了较好的效果。     

凸优化算法在多导弹协同作战目标识别中的应用

针对多导弹协同作战目标识别的特点,分析了识别要素和识别数学描述,提出了利用凸优化理论建立满足多导弹协同作战系统需求的目标识别模型.通过分解代价函数,将模型转换为凸二次规划问题,并引入惩罚因子,利用牛顿迭代法求解该模型.仿真结果表明该识别模型有较好的识别能力和较强的鲁棒性.     

火力分配的优化算法

火力分配问题可以看成是一个 0-1规划问题,传统的 0-1规划算法比较复杂、运算量大,优化算法对 0-1规划问题经过枚举、可重复排列和m位n进制数的转换,使运算次数从 2m×n次减少到nm次。该算法有两个特点:一是精简幅度大,将 0-1规划问题转化为可重复排列数的问题时,可以将 2m×n个情况转化为nm个情况;二是通用性强,利用可重复排列数转化为m位n进制数,将不通用的不定次循环问题转化为一次循环问题。利用优化算法可以很容易地解决任务分配、火力分配、弹药运输等问题。     

自燃推进剂液体火箭发动机燃烧室设计简化模型

本文提出了一个自燃推进剂液体火箭发动机燃烧室设计简化模型。与 Priem 基本模型不同,本文考虑了燃料分解反应,液滴二次雾化以及燃烧室截面上混合比和流强的不均匀性对燃烧效率的影响。文中导出了计算所需的全部公式,提出了计算程序。应用本方法计算了 C 发动机的燃烧效率。计算效率与试验结果相当符合,其误差在1～5%以内。文中还给出了燃料总蒸发速率和单位长度上的蒸发速率随该发动机燃烧室轴向距离变化的曲线。曲线表明,分解反应,液滴二次雾化和液滴尺寸分布对蒸发速率的影响很大。最后讨论了本模型使用的条件。     

多目标传感器协同探测的资源优化问题

针对反导作战传感器任务规划问题,提出了一种对多目标任务分解的传感器协同探测任务规划方法。首先将整个预警任务分解为元任务,并以分解的元任务为核心,建立基于元任务的任务规划模型,在此基础上,以探测收益为代价函数,分析任务规划模型及算法流程。仿真结果表明,该方法不仅保持了较高的元任务加权探测收益值,而且能够给出较为合理的任务规划方案。     

面向无人机海上侦察任务的自适应粒度分解策略研究

无人机海上侦察作战任务自动规划的前提是任务分解,分解策略的通用性和分解粒度的合理性直接影响任务规划的速度和实际效果。对无人机海上侦察任务具有随机性强、复杂度高、动态性明显等特点,提出了一种基于军事领域知识库的无人机海上侦察任务自适应粒度分解策略,构建了无人机海上侦察领域知识图谱和自适应粒度任务分解模型,并以海上编队护航背景下的无人机侦察任务为例,实施了任务分解策略验证,结果表明分解策略较传统任务分解方法具有更佳的稳定性和适应性。     

采用PWPF调节器的再入飞行器最优控制分配方法

针对具有反作用控制系统(Reaction Control System,RCS)和气动舵两类控制机构的再入飞行器,提出一种基于脉宽脉频(Pulse-Width Pulse-Frequency,PWPF)调节器的最优控制分配方法。将RCS的输入信号转化为连续变化量,RCS与气动舵的控制分配问题被描述为二次规划问题,并采用有效集方法对其求解。采用离散法和PWPF调节器将优化结果转化为RCS的开关机状态。与混合整数规划问题相比,连续二次规划问题更容易求解,计算速度更快。通过对二次规划问题的重构,该算法能有效地应对故障情况。     

Concave minimization over a convex polyhedron

A general algorithm is developed for minimizing a well defined concave function over a convex polyhedron. The algorithm is basically a branch and bound technique which utilizes a special cutting plane procedure to' identify the global minimum extreme point of the convex polyhedron. The indicated cutting plane method is based on Glover's general theory for constructing legitimate cuts to identify certain points in a given convex polyhedron. It is shown that the crux of the algorithm is the development of a linear undrestimator for the constrained concave objective function. Applications of the algorithm to the fixed-charge problem, the separable concave programming problem, the quadratic problem, and the 0-1 mixed integer problem are discussed. Computer results for the fixed-charge problem are also presented.     

球约束凸二次规划的一个算法

针对球约束凸二次规划问题,利用Lagrange对偶将其转化为无约束优化问题,然后运用单纯形法对其求解,获得原问题的最优解。最后,对文中给出的算法给出了论证。     

Concise RLT forms of binary programs: A computational study of the quadratic knapsack problem

The reformulation‐linearization technique (RLT) is a methodology for constructing tight linear programming relaxations of mixed discrete problems. A key construct is the multiplication of “product factors” of the discrete variables with problem constraints to form polynomial restrictions, which are subsequently linearized. For special problem forms, the structure of these linearized constraints tends to suggest that certain classes may be more beneficial than others. We examine the usefulness of subsets of constraints for a family of 0–1 quadratic multidimensional knapsack programs and perform extensive computational tests on a classical special case known as the 0–1 quadratic knapsack problem. We consider RLT forms both with and without these inequalities, and their comparisons with linearizations derived from published methods. Interestingly, the computational results depend in part upon the commercial software used. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Nonlinear programming the choice of direction by gradient projection

Rosen's method of Gradient Projection chooses a search direction which is not necessarily the direction of steepest ascent. However, the projection of the gradient onto a “suitably chosen subspace” does yield the direction of steepest ascent. The suitable choice is easily recognized as a result of some theorems relating gradient projection to steepest ascent. These results lead to a modification of Rosen's method. The modification improves the choice of search direction and usually yields the steepest ascent direction without solving a quadratic programming problem.     

Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling

In urban rail transit systems of large cities, the headway and following distance of successive trains have been compressed as much as possible to enhance the corridor capacity to satisfy extremely high passenger demand during peak hours. To prevent train collisions and ensure the safety of trains, a safe following distance of trains must be maintained. However, this requirement is subject to a series of complex factors, such as the uncertain train braking performance, train communication delay, and driver reaction time. In this paper, we propose a unified mathematical framework to analyze the safety‐oriented reliability of metro train timetables with different corridor capacities, that is, the train traffic density, and determine the most reliable train timetable for metro lines in an uncertain environment. By employing a space‐time network representation in the formulations, the reliability‐based train timetabling problem is formulated as a nonlinear stochastic programming model, in which we use 0‐1 variables to denote the time‐dependent velocity and position of all involved trains. Several reformulation techniques are developed to obtain an equivalent mixed integer programming model with quadratic constraints (MIQCP) that can be solved to optimality by some commercial solvers. To improve the computational efficiency of the MIQCP model, we develop a dual decomposition solution framework that decomposes the primal problem into several sets of subproblems by dualizing the coupling constraints across different samples. An exact dynamic programming combined with search space reduction strategies is also developed to solve the exact optimal solutions of these subproblems. Two sets of numerical experiments, which involve a relatively small‐scale case and a real‐world instance based on the operation data of the Beijing subway Changping Line are implemented to verify the effectiveness of the proposed approaches.     

A method for quadratic programming

A solution to the quadratic programming is presented with the constraint of the form Ax ≥ b using the linear complementary problem approach.     

The conjugate gradient technique for certain quadratic network problems

We consider a class of network flow problems with pure quadratic costs and demonstrate that the conjugate gradient technique is highly effective for large-scale versions. It is shown that finding a saddle point for the Lagrangian of an m constraint, n variable network problem requires only the solution of an unconstrained quadratic programming problem with only m variables. It is demonstrated that the number of iterations for the conjugate gradient algorithm is substantially smaller than the number of variables or constraints in the (primal) network problem. Forty quadratic minimum-cost flow problems of various sizes up to 100 nodes are solved. Solution time for the largest problems (4,950 variables and 99 linear constraints) averaged 4 seconds on the CBC Cyber 70 Model 72 computer.     

A generalized recursive algorithm for a class of non-stationary regeneration (scheduling) problems

Recent efforts in the field of dynamic programming have explored the feasibility of solving certain classes of integer programming problems by recursive algorithms. Special recursive algorithms have been shown to be particularly effective for problems possessing a 0–1 attribute matrix displaying the “nesting property” studied by, Ignall and Veinott in inventory theory and by Glover in network flows. This paper extends the class of problem structures that has been shown amenable to recursive exploitation by providing an efficient dynamic programming approach for a general transportation scheduling problem. In particular, we provide alternative formulations lor the scheduling problem and show how the most general of these formulations can be readily solved vis a vis recursive techniques.