A COLLISION-AVOIDANCE CONTROL ALGORITHM FOR SPACECRAFT PROXIMITY OPERATIONS BASED ON IMPROVED ARTIFICIAL POTENTIAL FUNCTION 1)

针对航天器近距离操作的安全问题,提出了一种基于人工势函数改进的碰撞规避控制算法.根据航天器与目标、障碍物之间的实时状态, 利用人工势函数算法,计算航天器的实时加速度, 规划航天器的轨迹. 为改进人工势函数方法的适用性,提出三个方面的改进措施: 首先, 在人工势函数算法中, 为提高碰撞预警的准确性,减少额外机动, 碰撞预警采用碰撞概率代替相对距离. 其次, 为了提高对接安全,降低接近目标航天器的相对速度, 利用相对速度的安全接近走廊来计算目标排斥力.最后, 针对大多航天器不能提供任意连续变化推力的情况, 设置两种实用的推力形式,如bang-bang控制的推力形式和恒定变化率的推力形式, 代替连续变推力形式.通过对不同算例的比较,成功地揭示了主要任务参数(如碰撞预警方法、速度安全边界和实际加速度形式)对近距离操作安全的影响.结果表明, 该方法可以提高航天器近距离操作的安全性、效率性, 并且结构简单,实时性强.     

无人机自主防碰撞控制器设计

为了使无人机能够有效地规避突发静态障碍物,提出一种基于EKF-OSA的自主防碰撞控制器设计方法。首先建立无人机与障碍物的相对运动方程,采用扩展卡尔曼滤波算法(EKF)估计障碍物状态,并提出突发静态障碍物碰撞规避规则;然后,设计一种基于提前一步(OSA)优化方法的导引律。仿真结果验证了所提方法的有效性。     

中断角度跟踪的战斗机机动控制方法

基于跟踪雷达角度自动跟踪系统特性,提出了战斗机中断雷达角度跟踪的机动轨迹控制策略。推导了跟踪雷达角度自动跟踪系统的系统传递函数,研究了跟踪误差产生机理。以二维平面内导弹攻击为例,分析了导弹与战斗机的二阶相对运动模型。在此基础上,基于闭环反馈控制思想,提出了战斗机通过机动实现角度拖引,中断雷达角度跟踪的控制方法,推导了战斗机的机动轨迹控制律,给出了其解析形式。通过数值仿真,分析了该方法的适用性,为战斗机飞行员制定决策提供了依据。     

On shortest crucial words avoiding abelian powers

Let k≥2 be an integer. An abeliankth power is a word of the form X₁X₂?X_k where X_i is a permutation of X₁ for 2≤i≤k. A word W is said to be crucial with respect to abelian kth powers if W avoids abelian kth powers, but Wx ends with an abelian kth power for any letter x occurring in W.Evdokimov and Kitaev (2004) [2] have shown that the shortest length of a crucial word on n letters avoiding abelian squares is 4n−7 for n≥3. Furthermore, Glen et al. (2009) [3] proved that this length for abelian cubes is 9n−13 for n≥5. They have also conjectured that for any k≥4 and sufficiently large n, the shortest length of a crucial word on n letters avoiding abelian kth powers, denoted by ?_k(n), is k²n−(k²+k+1). This is currently the best known upper bound for ?_k(n), and the best known lower bound, provided in Glen et al., is 3kn−(4k+1) for n≥5 and k≥4. In this note, we improve this lower bound by proving that for n≥2k−1, ?_k(n)≥k²n−(2k³−3k²+k+1); thus showing that the aforementioned conjecture is true asymptotically (up to a constant term) for growing n.     

循迹小车的追踪与避障

介绍了采用灰度传感器的自循迹小车的设计与实现,并加以追踪与避障的功能。采用与白色地面反差很大的黑色路线引导小车按既定路线前进,若接近开关检测到物体时,实现追踪功能。通过改编程序,同样利用这两个接近开关可实现避障功能,即遇到障碍物时,自动转弯。     

Joint Optimization for Congestion Avoidance in Cognitive Radio WMNs under SINR Model

Due to limited spectrum resources and differences in link loads, network congestion is one of the key issues in cognitive radio wireless mesh networks. In this letter, a congestion avoidance model with power control, channel allocation, and routing under the signal‐to‐interference‐and‐noise ratio is presented. As a contribution, a nested optimization scheme combined with a genetic algorithm and linear programming solver is proposed. Extensive simulation results are presented to demonstrate the effectiveness of our algorithm.     

分期付款购房模型及其抛物障碍问题

考虑常数利率条件下的分期付款购房模型,若风险资产市场价格服从几何布朗运动,则合约可以运用美式期权定价方法给出合理的价格.该文给出了分期付款购房合约定价的偏微分方程方法,得到一个一维抛物障碍问题,同时给出了贷款合约价格函数所联系的自由边界,并讨论了自由边界的单调性与有界性.     

The Obstacle Problems for Second Order Fully Nonlinear Elliptic Equations with Neumann Boundary Conditions

In this paper we prove the existence theorem of the strong solutions to the obstacle problems for second order fully nonlinear elliptic equations with the Neumann boundary conditions F(x, u, Du, D²u) ≥ 0, x ∈ Ω u ≤ g, x ∈ Ω (u - g)F(x, u, Du, D²u) = 0, x ∈ Ω D_vu = φ(x, u), x ∈ ∂Ω where F(x, z, p, r) satisfies the natural structure conditions and is concave with respect to r, p, and φ(x, z) is nondecreasing in z, and g(x) satisfies the consistency condition.     

临近空间飞行器自动防撞技术探讨

在分析机载平台空中防撞系统的发展历程和技术特点的基础上,提出了在临近空间飞行器上采用自动防撞技术。对所提出的自动防撞技术的基本功能、主要技术特点以及自动防撞技术的基本工作原理进行了描述,同时,阐述了临近空间飞行器自动防撞技术研究中几个需要解决的关键技术。