采用伪谱法的再入飞行器最优反馈制导方法

将伪谱最优反馈控制理论应用于再入飞行器制导研究,使用伪谱法进行在线轨道重构,实时反馈更新当前轨道控制量迎角和倾斜角,达到实时最优反馈制导的目的,并采用无量纲化、弹性约束和自适应反馈更新等策略保证算法的实时性。再入飞行仿真表明,轨道重构可以满足实时性要求,阵风干扰下飞行器能达到所要求的终端约束条件,并且制导指令不会出现增加控制难度的抖动现象。     

多引力场小推力引力借力轨道设计与优化

采用序贯法设计优化小推力引力借力轨道(low-thrust gravity-assist,LTGA)时,设计步骤复杂且优化结果最优性条件难以保证.本文提出一种多引力场LTGA问题联立求解框架.首先对多引力场环境和探测器动力学模型进行统一描述和处理.设计初始化策略,利用Radau伪谱法将发射窗口、借力顺序、初始轨道搜索以及轨道优化联立求解,简化设计步骤.利用hp自适应网格精细化策略保证优化结果最优性条件.该联立框架用于求解地木转移任务,得到地球–火星–地球–木星的转移方案.本文提出的联立求解框架,简化了设计步骤,保证了优化结果的最优性条件,得到比序贯求解更优的转移方案.     

Pseudospectral analysis of buckling and free vibration of rectangular Mindlin plates

A study of buckling and free vibration of rectangular Mindlin plates is presented. The analysis is based on the pseudospectral method, which uses basis functions that satisfy the boundary conditions. The equations of motion are collocated to yield a set of algebraic equations that are solved for the critical buckling load and for the natural frequencies in the presence of the in-plane loads. Numerical examples of rectangular plates with SS-C-SS-C boundary conditions are provided for various aspect ratios and thickness ratios, which show good agreement with those of the classical plate theory when the thickness ratio is very small. This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin Jinhee Lee received B.S. and M.S. degrees from Seoul National University and KAIST in 1982 and 1984, respectively. He received his Ph.D. degree from the University of Michigan, Ann Arbor in 1992 and joined the Dept. of Mechanical and Design Engineering of Hongik University in Choongnam, Korea. His research interests include inverse problems, pseudospectral method, vibration and dynamic systems.     

基于Radau伪谱法的非线性最优控制问题的收敛性

在过去的10年里,伪谱方法(如Legendre伪谱法、Gauss伪谱法、Radau伪谱法)逐步成为求解不同领域中非线性最优控制问题的一种高效、灵活的数值解法.本文从最优控制问题解的存在性、收敛性以及解的可行性3个方面对采用Radau伪谱法求解一般非线性最优控制问题解的收敛性进行研究.证明了原最优控制问题的离散解存在、存在收敛到原最优控制问题解上的离散解和离散形式的收敛解是原最优控制问题的最优解.在此基础上,证明了Radau伪谱法的收敛性.本文结论与现有文献相比,去掉了一些必要条件,更适合一般的非线性时不变系统.     

基于Radau伪谱法的重复使用运载器再入轨迹优化

为了提高数值解法的收敛速度,本文利用Radau伪谱法求解重复使用运载器的再入轨迹优化问题.该方法在一组Legendre-Gauss-Radau点上构造全局Lagrange插值多项式对状态变量和控制变量进行逼近,在动力学方程中状态变量对时间的导数可由插值多项式的导数来近似,故可将动力学方程约束转化为在Legendre-Gauss-Radau点上的代数微分方程约束.因此,可将连续时间的最优控制问题转化为有限维的非线性规划(NLP)问题,之后通过稀疏NLP求解器SNOPT即可对其进行求解.最后的仿真结果显示,通过该方法优化后的再入轨迹成功满足过程约束与边界约束.由于该方法的高效率和高精度特性,可将其应用于轨迹快速优化工程实际问题中.     

Direct Trajectory Optimization and Costate Estimation of Infinite-horizon Optimal Control Problems Using Collocation at the Flipped Legendre-Gauss-Radau Points

A pseudospectral method is presented for direct trajectory optimization and costate estimation of infinite-horizon optimal control problems using global collocation at flipped Legendre-Gauss-Radau points which include the end point +1. A distinctive feature of the method is that it uses a new smooth, strictly monotonically decreasing transformation to map the scaled left half-open interval τ∈(-1, +1] to the descending time interval t ∈ (+∞, 0]. As a result, the singularity of collocation at point +1 associated with the commonly used transformation, which maps the scaled right half-open interval τ∈[-1, +1) to the increasing time interval [0,+∞), is avoided. The costate and constraint multiplier estimates for the proposed method are rigorously derived by comparing the discretized necessary optimality conditions of a finite-horizon optimal control problem with the Karush-Kuhn-Tucker conditions of the resulting nonlinear programming problem from collocation. Another key feature of the proposed method is that it provides highly accurate approximation to the state and costate on the entire horizon, including approximation at t = +∞, with good numerical stability. Numerical results show that the method presented in this paper leads to the ability to determine highly accurate solutions to infinite-horizon optimal control problems.      

New computational treatment of optical wave propagation in lossy waveguides

In this paper, the optical wave propagation in lossy waveguides is described by the Helmholtz equation with the complex refractive-index, and the Chebyshev pseudospectral method is used to discretize t...     

A MODEL OF THE VISCOUS WALL REGION OF TURBULENT SHEAR FLOWS

The viscous wall region of a fully developed turbulent pipe flow is investigated using a nonlinear, time-dependent, three-dimensional model. In the model, the velocity field is assumed to satisfy periodic boundary conditions in the longitudinal and spanwise directions, the velocity vanishes at the pipe wall, the velocity fluctuations are assumed to vanish at large distances from the wall, and a law of the wall profile is imposed on the longitudinal and spanwise average of the longitudinal component of velocity outside the viscous wall region. The model equations are solved using pseudospectral methods and the computed mean velocity profile, fluctuation intensities, and turbulence production rate are found to be in good agreement with experiment in the viscous wall region. It is found that the bulk of turbulence production is generated by length scales larger than 40 in the spanwise direction and 200 in the longitudinal direction.     

A Hermite‐Lobatto Pseudospectral Method for Optimal Control

A pseudospectral (PS) method based on Hermite interpolation and collocation at the Legendre‐Gauss‐Lobatto (LGL) points is presented for direct trajectory optimization and costate estimation of optimal control problems. A major characteristic of this method is that the state is approximated by the Hermite interpolation instead of the commonly used Lagrange interpolation. The derivatives of the state and its approximation at the terminal time are set to match up by using a Hermite interpolation. Since the terminal state derivative is determined from the dynamic, the state approximation can automatically satisfy the dynamic at the terminal time. When collocating the dynamic at the LGL points, the collocation equation for the terminal point can be omitted because it is constantly satisfied. By this approach, the proposed method avoids the issue of the Legendre PS method where the discrete state variables are over‐constrained by the collocation equations, hence achieving the same level of solution accuracy as the Gauss PS method and the Radau PS method, while retaining the ability to explicitly generate the control solution at the endpoints. A mapping relationship between the Karush‐Kuhn‐Tucker multipliers of the nonlinear programming problem and the costate of the optimal control problem is developed for this method. The numerical example illustrates that the use of the Hermite interpolation as described leads to the ability to produce both highly accurate primal and dual solutions for optimal control problems.     

Propagation of Radar Pulses from a Horizontal Dipole in Variable Dielectric Ground: A Numerical Approach

We numerically investigate the propagation of radar type short pulses from a horizontal dipole in the presence of some simple models of inhomogeneous ground with a flat surface. We use 3-dimensional (3-D) pseudospectral time domain (PSTD) and 2-D finite difference time domain forward modeling to determine the range and azimuth dependence of electric field components and to simulate events in a moveout profile. The models are: (i) a uniform half space with either high or low conductivity; (ii) a vertical dielectric wedge; (iii) a surface thin layer with a monocline wedge overlaid on the dielectric half space. Our homogeneous results agree with the analytical solutions, and more clearly show the significant vertical electric field component, which occurs for all models. The incorporation of an anomalous dielectric quadrant does not affect the air wave and only complicates ground wave propagation near the boundary. Modeling of a monocline dielectric wedge shows predictable subsurface reflections and refractions, some of which are highly dispersive events, depending on the direction of propagation. We present two field examples that appear to demonstrate some of our findings. We conclude that air waves make suitable references for moveout profiles regardless of dielectric complications, and that our results provide some insight into the interpretation of unique events seen in moveout profiles.