遥感卫星小推力轨道转移控制

在太阳同步回归轨道遥感卫星的小推力轨道转移控制问题的研究中,小推力推进与化学推进方式有本质不同,不能再用速度脉冲的方法来设计轨道.针对推力方式不同的问题,采用了一组无奇点的春分点根数表示小推力卫星的动力学模型,从最优控制理论出发,给出了协态变量微分方程和最优推力方向,将轨道转移问题转化为非线性参数优化问题,利用非线性序列二次型规划法求解.对遥感卫星在1天回归和10天回归轨道之间的转移控制问题进行仿真,证明了方法的有效性.     

基于形状规划理论的小行星探测方法

小推力轨迹优化过程的控制率设计是典型的非线性动力学最优控制问题。针对具体的问题背景,直接优化算法和间接优化算法已被广泛应用。为了简化问题的优化模型,采用形状规划理论来模拟小推力的作用轨迹,将动力学最优控制问题转化成多项式的参数优化。结合小行星群的探测,利用粒子群优化与微分进化混合优化算法进行全局优化,为满足精度要求,再采用模式搜索局部优化算法进行二次优化。     

基于混合粒子群算法的远程机动轨道优化设计

研究了粒子群算法在空间飞行器连续推力轨道机动最优化问题.为优化空间飞行器轨道,给出了空间飞行器轨道机动最优化控制问题模型,运动方程用地心惯性坐标系下建立;性能指标选为轨道机动过程中时间最小;控制变量为推力攻角;终端状态受到位置和速度的约束.针对粒子群算法的缺点,提出混合粒子群算法,即将全局寻优能力强的粒子群算法和局部寻优能力强的非线性规划相结合,以提高算法的搜索精度和收敛速度.并将其应用于连续推力空间飞行器轨道机动优化之中.仿真表明混合粒子群算法对于空间飞行器远程机动轨道初始参数取值不敏感,具有一定的鲁棒性,生成的轨道能够较好地满足各种约束条件,并可以应用于空间飞行器连续推力轨道最优机动问题的求解.     

航天器任意椭圆轨道最优转移问题研究

目前航天器最优转移轨道研究中,常忽略摄动力影响,仅考虑能量最优,且采用常值推力控制量,得到的转移轨道精度低,转移时间长,非理论最优。本文考虑地球非球形摄动力J2的影响,建立时间-能量综合最优性能指标,基于变推力控制量,研究了任意椭圆轨道最优转移问题。建立高斯拉格朗日状态方程,应用Pontryagin极小值原理和共轭梯度法求解最优转移问题;研究了J2摄动力对转移轨道根数、推力加速度和最优转移轨道的影响。结果表明:J2摄动力对转移轨道根数和推力加速度都有影响,不能忽略;时间-能量综合最优转移同时考虑轨道转移时间和能量消耗,优化结果更利于工程应用;最优推力加速度不是常值,即采用常值推力控制量得到的并非理论最优转移轨道。     

登月软着陆轨道优化算法研究

月球软着陆轨道优化是月球探测中的关键技术之一,研究了基于燃料最优的定常推力月球探测器软着陆轨道优化问题.在优化算法中,首先对软着陆轨道动力学方程做归一化处理,经过将软着陆轨道离散化,应用函数逼近法拟合推力控制角,从而将轨道优化问题转化为参数优化问题,最后设计了蛙跳算法作为搜索优化方法.仿真结果表明设计的轨道较好地满足了所要求的约束条件,同时蛙跳算法具有很高的优化精度,并且应用比较简便,可以应用于登月软着陆的轨道优化设计任务.     

卫星在降交点地方时不变的最优轨道转移研究北大核心CSCD

卫星在运行时要求降交点地方保持不变,而在卫星变轨前后降交点地方时不变情况下要用有限推力燃料达到最优异面轨道转移问题。针对降交点地方时不变、有限推力等难点,利用虚拟目标卫星的概念,建立了轨道转移的相对运动模型,提出了保证降交点位置不变的变轨初始条件;基于极小值原理将燃料最优变轨问题转化为两点边值问题,并采用共轭梯度法进行数值求解。针对变轨时间固定、连续推力情况,以总冲最小、满足各种约束为指标,进行了异面转移轨道的优化设计验证。仿真结果验证了卫星轨道转移策略和算法达到最优转移。     

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.     

基于形状法和伪谱法的小推力借力优化研究

小推力借力飞行轨道优化是一个多变量多约束的非线性优化问题,根据形状法和伪谱法,提出一种混合优化策略,分为全局优化和局部优化两个阶段进行。在全局优化阶段采用LT-PGA模型,即通过求解形状法小推力Lambert问题,搜索满足约束条件的小推力发射窗口,得到发射、借力和到达时间点。在局部优化阶段采用伪谱法得到推力控制率,用连接点设置解决借力行星处状态量的不连续问题。数值仿真结果表明,改进方法不用事先指定推力开关机序列,优化效率高,为初始设计阶段小推力借力飞行的轨道优化问题提供有益参考。     

LQ最优控制系统加权矩阵Q的一种数值算法

利用ＬＱ最优控制逆问题的参数化解,将求解对称、非负定加权矩阵Ｑ的问题变为一类Ｆ－范数优化问题,给出一种求解ＬＱ最优控制指标函数中的加权矩阵Ｑ的简便而系统的方法。算法的优点在于任意给定一组自变量,通过解这类优化问题就可求得满足闭环特征要求的加权矩阵Ｑ,而且具有良好的收敛性。     

船舶动力定位系统推力分配策略研究

针对船舶动力定位系统推力分配过程中推进系统的燃油消耗大、推进器磨损严重、推力误差存在等现象,提出一种以带权重的伪逆算法为基础、合理高效地解决船舶推力分配问题的方法.整个推力优化分配的目标是使推进系统的能耗最小,同时考虑推进器的方位角变化速率,推进器的推力禁区、推力饱和限制等情况,静态解决方法给出了基于最小能量的各推力的优化方向,在考虑禁止角情况下,全回转推进器方向角可以缓慢变化,而动态解决方法提供了动态能力.两者结合后,成为一种以能量优化为目的的推力分配算法.经仿真验证,静态和动态相结合的推力分配算法要比纯静态的算法消耗更少的能量,而且误差更小,应用前景比较广泛.     

3 种伪谱最优控制方法的积分形式及统一性证明

为了进一步提高伪谱最优控制方法的计算精度, 削弱微分形式伪谱法对状态变量近似误差的放大幅度, 研究基于积分形式的伪谱最优控制方法. 依次给出3 种伪谱法的积分伪谱离散形式, 证明当Lagrange 多项式对状态变量的近似误差等于零时, Gauss 伪谱法和Radau 伪谱法的积分形式与微分形式是等价的, 而Legendre 伪谱法的积分形式与微分形式是不等价的, 并分析了其不等价的原因.

     

Three-dimensional trajectory optimization of soft lunar landings from the parking orbit with considerations of the landing site

Minimum fuel, three-dimensional trajectory optimization from a parking orbit considering the desired landing site is addressed for soft lunar landings. The landing site is determined by the final longitude and latitude; therefore, a two-dimensional approach is limited and a three-dimensional approach is required. In addition, the landing site is not usually considered when performing lunar landing trajectory optimizations, but should be considered in order to design more accurate and realistic lunar landing trajectories. A Legendre pseudospectral (PS) method is used to discretize the trajectory optimization problem as a nonlinear programming (NLP) problem. Because the lunar landing consists of three phases including a de-orbit burn, a transfer orbit phase, and a powered descent phase, the lunar landing problem is regarded as a multiphase problem. Thus, a PS knotting method is also used to manage the multiphase problem, and C code for Feasible Sequential Quadratic Programming (CFSQP) using a sequential quadratic programming (SQP) algorithm is employed as a numerical solver after formulating the problem as an NLP problem. The optimal solutions obtained satisfy all constraints as well as the desired landing site, and the solutions are verified through a feasibility check.     

网格缩减的自适应hp伪谱法

针对控制变量不连续的最优控制问题,本文提出一种自适应更新的忉伪谱法,这种方法在(Legendre Gauss Radau,LGR)点处取配点,能够以较小的网格规模获得较高的精度.通过计算相对误差估计,判断网格规模是增加还是缩减,若相对容许误差大于给定值,则增加网格区间数或网格配点数提高解的精度,反之则合并网格或减小网格配点数缩减网格规模提高计算效率.将hp伪谱法应用于最优控制问题,仿真验证了hp伪谱法的优越性.     

Pseudospectral methods for optimal motion planning of differentially flat systems

The article presents some preliminary results on combining two new ideas from nonlinear control theory and dynamic optimization. We show that the computational framework facilitated by pseudospectral methods applies quite naturally and easily to Fliess' implicit state variable representation of dynamical systems. The optimal motion planning problem for differentially flat systems is equivalent to a classic Bolza problem of the calculus of variations. We exploit the notion that derivatives of flat outputs given in terms of Lagrange polynomials at Legendre-Gauss-Lobatto points can be quickly computed using pseudospectral differentiation matrices. Additionally, the Legendre pseudospectral method approximates integrals by Gauss-type quadrature rules. The application of this method to the two-dimensional crane model reveals how differential flatness may be readily exploited.     

针铁矿法沉铁过程双层结构优化控制

针铁矿沉铁过程是锌冶炼过程中一个非常重要的环节,其中最重要的是控制氧气添加量,因此本文提出一种针铁矿沉铁过程双层结构优化控制方法.上层定义氧气利用率衡量理论消耗量与实际添加量的差别,以过程氧气利用率最高为目标优化设定级联反应器出口二价铁离子浓度下降梯度,下层以过程氧气消耗最少和出口离子浓度与上层设定值误差最小为优化目标,过程动态模型和工艺条件为约束,求解构造的非线性优化控制问题得到各反应器最优氧气添加速率.为减少不确定性干扰对系统的影响,采用一种模型参数自适应校正的方法对模型参数进行校正保证优化控制器的性能.最后根据过程离子浓度采样值计算过程实际氧气利用率作为上层优化参数重更新反应器出口二价铁离子浓度最优设定值.由于下层优化问题约束多且约束多呈非线性,采用Legendre伪谱法求解下层优化问题.仿真结果表明,所提出的双层结构优化控制方法能实现过程准确控制,减少过程氧气消耗.     

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.     

A symplectic local pseudospectral method for solving nonlinear state‐delayed optimal control problems with inequality constraints

In this paper, a symplectic local pseudospectral (PS) method for solving nonlinear state‐delayed optimal control problems with inequality constraints is proposed. We first convert the original nonlinear problem into a sequence of linear quadratic optimal control problems using quasi‐linearization techniques. Then, based on local Legendre‐Gauss‐Lobatto PS methods and the dual variational principle, a PS method to solve these converted linear quadratic constrained optimal control problems is developed. The developed method transforms the converted problems into a coupling of a system of linear algebraic equations and a linear complementarity problem. The coefficient matrix involved is sparse and symmetric due to the benefit of the dual variational principle. Converged solutions can be obtained with few iterations because of the local PS method and quasi‐linearization techniques are used. The proposed method can be applied to problems with fixed terminal states or free terminal states, and the boundary conditions and constraints are strictly satisfied. Numerical simulations show that the developed method is highly efficient and accurate.     

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.     

On the convergence of nonlinear optimal control using pseudospectral methods for feedback linearizable systems

We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. In contrast to the existing results, the optimal controller addressed in this paper is allowed to be discontinuous. This generalization requires a substantial modification to the existing convergence analysis in terms of both the framework as well as the notion of convergence around points of discontinuity. Although the nonlinear system is assumed to be feedback linearizable, the optimal control does not necessarily linearize the dynamics. Such problems frequently arise in astronautical applications where stringent performance requirements demand optimality over feedback linearizing controls. We prove that a sequence of solutions obtained using the Legendre pseudospectral method converges to the optimal solution of the continuous‐time problem under mild conditions. Published in 2007 by John Wiley & Sons, Ltd.     

迭代学习控制在线性时变系统终端控制问题中的应用研究

An iterative learning control algorithm based on shifted Legendre orthogonal polynomials is proposed to address the terminal control problem of linear time-varying systems. First, the method parameterizes a linear time-varying system by using shifted Legendre polynomials approximation. Then, an approximated model for the linear time-varying system is deduced by employing the orthogonality relations and boundary values of shifted Legendre polynomials. Based on the model, the shifted Legendre polynomials coefficients of control function are iteratively adjusted by an optimal iterative learning law derived. The algorithm presented can avoid solving the state transfer matrix of linear time-varying systems. Simulation results illustrate the effectiveness of the proposed method.