Image reconstruction using an adaptive simultaneous algebraic reconstruction technique in computed tomography

The simultaneous algebraic reconstruction technique(SART) is a vintage algorithm for computed tomography(CT) image reconstruction, but it has many problems such as slow convergence speed, edge blur, and ringing effect. The relaxation parameter is an important factor affecting the performance of the algorithm, and we find that the edge region does not need the same relaxation factor as the uniform region, so an adaptive simultaneous algebraic reconstruction technique based on fuzzy entropy is proposed. After preliminary SART reconstruction, by quoting fuzzy entropy for edge detection of the reconstructed image which is used as prior information, a monotonous increasing function that defines the relaxation factor is constructed based on the neighborhoodhomogeneous measurement(NHM). Therefore, the proposed approach can select the relaxation factor adaptively by the local character of the image. Experimental results show that the new algorithm can solve the problem of edge blurring and suppress the ringing effect effectively in CT image reconstruction.     

A high-order Lie groups scheme for solving the recovery of external force in nonlinear system

In this paper, we develop the high-order Lie group scheme to estimate a real-time external force exerted on nonlinear system. For estimating a real-time data, the equations of motion and the supplemental data are combined into a set of differential algebraic equations (DAEs), which is solved by an implicit Lie group differential algebraic equations method (LGDAE) and a Newton iterative algorithm. However, an explicit LGDAE cannot work, and an implicit scheme cannot avoid a lot of iterative numbers and overcome numerical instability under a long time span and noisy-level effect. Because the original implicit LGDAE cannot satisfy the constraint of the cone structure, Lie group and Lie algebra at each time step, solutions highly dependent on ones cannot easily converge by a large time step. Therefore, we develop a high-order explicit LGDAE to avoid iterative numbers and numerical instability, and at the same time combined with higher order sliding modes to obtain real-time external force. The accuracy and efficiency of the novel scheme is validated by comparing the estimation results with the previous literature.     

包络环面蜗杆的高效磨削方法研究

提出了用双锥面砂轮替代现有的平面砂轮和锥面砂轮磨削包络环面蜗杆以提高蜗杆磨削效率的新方法,采用合理论对这种方法所加工蜗杆副的啮合性能分析的结果表明：该加工方法适用于各种传动比的环面蜗杆副加,加工效率高,能实现蜗杆的双面磨削而重新调整磨头,且所加工传动副啮合性能好,传动精度高,砂轮修整容易。     

Well-posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon

This paper is concerned with a stochastic linear-quadratic (LQ) problem in an infinite time horizon with multiplicative noises both in the state and the control. A distinctive feature of the problem under consideration is that the cost weighting matrices for the state and the control are allowed to be indefinite. A new type of algebraic Riccati equation – called a generalized algebraic Riccati equation (GARE) – is introduced which involves a matrix pseudo-inverse and two additional algebraic equality/inequality constraints. It is then shown that the well-posedness of the indefinite LQ problem is equivalent to a linear matrix inequality (LMI) condition, whereas the attainability of the LQ problem is equivalent to the existence of a “stabilizing solution” to the GARE. Moreover, all possible optimal controls are identified via the solution to the GARE. Finally, it is proved that the solution to the GARE can be obtained via solving a convex optimization problem called semidefinite programming.     

用分片代数曲面构造管道曲面的过渡曲面

借助围绕一个顶点处代数曲面的光滑拼接条件,提出并研究了用分片代数曲面构造三通管道的过渡曲面问题。首先对空间区域进行适当的剖分以确定分片代数曲面的定义区域。然后,通过求解一个线性方程组来构造出光滑拼接的分片代数曲面,同时还了在代数曲面片的Ｂ－Ｂ表示下,Ｂｅｚｉｅｒ纵标对过渡曲面的形状的局部控制问题。结果表明,用分片代数曲面构造过渡曲面不仅可以降低曲面的次数,而且更有利于曲面形状的控制。     

不确定线性系统混合H2/H∞鲁棒输出反馈控制

解决了在系统状态空间模型的状态与输出矩阵中含有范数有界 参数不确定线性系统的混合Ｈ２／Ｈ∞鲁棒输出反馈控制问题,所推导的满阶控制器对于所有呆容许的参数不确定都能满足给定的Ｈ∞干扰衰减水平,且为最坏情形Ｈ２代价函数提供了一个最优的上界,所得的结果需要求解一个含有尺度参数的修正代数Ｒｉｃｃａｔｉ方程以及三个含有尺度参数的交叉耦合非线性方程,而且也给出了一个求解这些含有尺度参数非线性方程的数值算法。     

区间约束的非基本代数操作

本文定义了区间约束的非基本代数操作的语法和语义,用基本代数读作表达了非基本代数读作, 并证明了表达式的正确性     

连续小推力航天器轨道交会问题的制导律设计

使用高比冲的小推力推进系统为执行机构,设计空间交会问题的燃料最优时间连续制导律.首先给出轨道交会问题的数学模型,并给出最优控制问题的目标函数和约束条件;然后利用直接法将控制变量离散化,通过参数寻优得到对应燃料最优的控制变量参数和转移时间常数;最后针对点火时刻误差问题,分析了实际轨迹与名义最优轨迹的偏差,并利用微分代数工具求取部分控制变量的修正值,以保证航天器满足轨道交会的终端位置约束.     

数值积分的校正公式

利用代数精度概念,求出校正公式中间点的具体数值,从而重新推导了几个校正公式。本文的方法适用于各类数值积分公式。