解一类弱间断最优控制问题的一个自适应拟谱方法

针对弱间断最优控制问题,提出一种自适应拟谱方法.利用一些点序列分割时间区间为若干子区间;控制和状态函数使用分段连续多项式逼近;以数值解的收敛性为基础,证明分割时间区间的点序列可以收敛到弱间断点;依据柯西收敛原理,弱间断点位置可以由前述点序列的变化来估计,据此设计误差指示量以调整子区间和逼近多项式次数.在数值算例中,通过与两种拟谱方法比较,所提出方法在精度和效率上都有更好的表现.     

解最优控制问题结合同伦法的自适应拟谱方法

针对弱间断最优控制问题和Bang-Bang最优控制问题,提出一种结合同伦法的自适应拟谱方法.Chebyshev拟谱方法转换原问题成为非线性规划问题.基于同伦法思想,同伦参数改变路径约束的界限,得到一系列比较光滑的最优控制问题.通过解这些问题得到原问题的不光滑解.文中证明了弱间断情况下数值解的收敛性.依据这收敛性和同伦参数,误差指示量可以捕捉不光滑点.本文方法与其他方法在数值算例中的对比表明,本文方法在精度和效率上都有明显优势.     

解一类最优控制问题的一种自适应拟谱方法

提出一种解常微分方程最优控制问题的自适应拟谱方法.对状态函数和控制函数使用不同次数的多项式逼近.设计了一个自适应算法决定不同的次数,并给出了理论分析.数值算例比较了本文方法与一种常用的拟谱方法.     

线性—二次型最优控制问题的Chebyshev—Legendre拟谱方法

介绍了一种求解线性—二次型最优控制问题的拟谱方法.使用Legendre展开式逼近控制和状态函数,采用Chebyshev-Gauss-Lobatto（CGL）点作为插值点,对原问题进行离散,从而将最初的最优控制问题化归为一个与之等价的二次规划（QP）问题,对应QP问题的未知量分别为状态和控制函数的Legendre展开式系数.通过求解QP问题得到原问题的数值解.整个离散过程使用快速Legendre变换（FLT）以及相关的一些技巧,能方便计算出函数在各个CGL点上的函数值.数值实验结果表明用该方法解决这类最优控制问题的有效性和高精度.     

动态平衡运量配流问题及其稳态伴随解算法

动态平衡运量配流问题的建模和求解是发展智能车辆导驶系统的理论基础.本文对多起点单讫点交通网络建立了连续时间最优控制模型,该模型的最优解对应于动态用户平衡解.文中提出的稳态伴随解算法避免了解复杂的两点边界值问题,可以获得原问题的近似解.该算法利用了交通网络和计算机网络的结构特性,计算速度较高,可用于城市交通流的实时控制.     

二维非线性反应扩散方程的局部间断Galerkin谱元法

本文提出了二维非线性反应扩散方程的局部间断Galerkin谱元法.在空间方向上采用了Legendre-Galerkin Chebyshev谱配置法,即在每个子区域上,该格式按Legendre-G alerkin谱方法形成,子区域交界面处的跳跃项利用数值流量进行处理,非线性项采用在Chebyshev-GaussLobatto点上的插值进行计算.时间方向上采用四阶低存储Runge-Kutta方法.文中给出了半离散格式下的稳定性和收敛性分析,以及单区域和多区域算法的数值算例,并与间断Galerkin有限元方法进行比较.     

基于自适应EKF的弱GNSS信号跟踪算法

弱GNSS信号跟踪技术是卫星导航接收机关键技术之一,跟踪技术的好坏将直接影响卫星导航接收机在弱信号条件下的跟踪性能;在动态环境和先验信息不充分的情况下,由于扩展卡尔曼滤波(EKF)的固定设计使其不能满足要求,针对此不足引入一种自适应扩展卡尔曼滤波(AEKF)的信号跟踪算法;该自适应滤波算法能够实时监测残差或滤波器新息的动态变化,来修正观测噪声方差和状态噪声方差,以此调整滤波器增益,观测值和控制预测值在滤波结果中的权重;理论分析和结果表明,该算法能够充分利用观测信号的统计特性,克服了传统EKF算法不足,获得更好的跟踪性能。     

旋转曲面变换PSO 算法解非线性最优控制问题

针对利用粒子群优化算法进行多极值点函数优化时,存在陷入局部极小点和搜寻效率低的问题.提出旋转曲面变换方法,将被优化函数映射到一个同胚曲面上.它将当前局部极小点变换为全局最大点,并保持被优化函数值在当前局部极小点以下部分的形状不变,从而克服陷入局部极小点的问题.最后将其用于解一个非线性系统的最优控制问题,实验结果证明了该方法的可行性和有效性.     

窗口长度自适应调整的策略迭代最优控制

在系统模型参数未知的最优控制问题中, 策略迭代能否快速收敛到最优控制策略的关键在于值函数的估计. 为了提升值函数的估计精度以及收敛速度, 本文提出一种窗口长度自适应调整的策略迭代最优控制算法. 充分利用一段时间内的历史样本数据, 通过影响力函数构建窗口长度与值函数估计性能之间的定量关系, 根据数据窗口长度对估计性能影响力的不同, 实现窗口长度的自适应调整. 最后, 将本文所提方法应用到连续发酵过程, 结果表明, 本文所提方法能够加快最优控制策略的收敛, 克服参数变化或外部扰动对控制性能的影响, 从而提升控制精度.     

三阶偏微分方程的时空间断Galerkin谱方法

本文提出了三阶偏微分方程的时空间断Galerkin谱方法.该方法在空间方向上采用局部间断Galerkin谱方法,即在每个子区域上,该格式按Legendre-Galerkin谱方法形成,子区域交界面处的跳跃项利用数值流量进行处理.在时间方向上采用多区域Legendre-tau谱方法.文中将该全离散格式分别应用到线性与非线性方程中,并分别给出了数值算例.理论分析部分给出了三阶线性偏微分方程在全离散格式下的收敛性分析.     

A Discontinuous Spectral Element Model for Boussinesq-Type Equations

We present a discontinuous spectral element model for simulating 1D nonlinear dispersive water waves, described by a set of enhanced Boussinesq-type equations. The advective fluxes are calculated using an approximate Riemann solver while the dispersive fluxes are obtained by centred numerical fluxes. Numerical computation of solitary wave propagation is used to prove the exponential convergence.     

Analysis of a Discontinuous Least Squares Spectral Element Method

This paper addresses the development of a Discontinuous Spectral Least-Squares method. Based on pre-multiplication with a mesh-dependent function a discontinuous functional can be set up. Coercivity of this functional will be established. An example of the approximation to a continuous solution and a solution in which a jump is prescribed will be presented. The discontinuous least-squares method preserves symmetry and positive definiteness of the discrete system.     

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.

     

Time-optimal reorientation for rigid satellite with reaction wheels

This article introduces a time-optimal reorientation manoeuvre controller with saturation constraints on both reaction wheels’ torques and angular momentum. The proposed control scheme consists of two parts. The first part is an open-loop time-minimum reorientation trajectory generated by the Legendre pseudospectral method. Actuator dynamics, saturations on control torques and angular momentums of reaction wheels are taken into account in generating the open-loop optimal trajectory. The second part is a closed-loop tracking control law to track the optimised reference trajectory based on attitude error dynamics with reaction wheel dynamics. Numerical simulations show that reaction wheel dynamics play an important role in attitude manoeuvres. The proposed controller performs better for rest-to-rest reorientation manoeuvre than other existing methods.     

Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes

We present a new two-step “intermediate mortar” approach that efficiently extends the Mortar Element Method (MEM) to 3D meshes with nonconforming discretizations. The technique utilizes projection matrices derived in 2D, thereby avoiding the need to explicitly form large matrices for the 3D cases. The method also allows more flexibility for both h- and p-type adaptation. Parallel implementations with OpenMP and multithreading compiler directives are used to solve a moving heat source problem on SGI Origin and Cray MTA machines. Numerical results demonstrate the advantages of adaptive nonconforming meshes with MEM over uniformly fine meshes.     

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.     

A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems

This paper presents a new approach for the efficient solution of singular optimal control problems (SOCPs). A novel feature of the proposed method is that it does not require a priori knowledge of the structure of solution. At first, the SOCP is converted into a binary optimal control problem. Then, by utilising the pseudospectral method, the resulting problem is transcribed to a mixed-binary non-linear programming problem. This mixed-binary non-linear programming problem, which can be solved by well-known solvers, allows us to detect the structure of the optimal control and to compute the approximating solution. The main advantages of the present method are that: (1) without a priori information, the structure of optimal control is detected; (2) it produces good results even using a small number of collocation points; (3) the switching times can be captured accurately. These advantages are illustrated through a numerical implementation of the method on four examples.     

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

This article aims at proposing a successive Chebyshev pseudospectral convex optimization method for solving general nonlinear optimal control problems (OCPs). First, Chebyshev pseudospectral discrete scheme is used to discretize a general nonlinear OCP. At the same time, a convex subproblem is formulated by using the first-order Taylor expansion to convexify the discretized nonlinear dynamic constraints. Second, a trust-region penalty term is added to the performance index of the subproblem, and a successive convex optimization algorithm is proposed to solve the subproblem iteratively. Noted that the trust-region penalty parameters can be adjusted according to the linearization error in iterative process, which improves convergence rate. Third, the Karush–Kuhn–Tucker conditions of the subproblem are derived, and furthermore, a proof is given to show that the algorithm will iteratively converge to the subproblem. Additionally, the global convergence of the algorithm is analyzed and proved, which is based on three key lemmas. Finally, the orbit transfer problem of spacecraft is used to test the performance of the proposed method. The simulation results demonstrate the optimal control is bang-bang form, which is consistent with the result of theoretical proof. Also, the algorithm is of efficiency, fast convergence rate, and high accuracy. Therefore, the proposed method provides a new approach for solving nonlinear OCPs online and has great potential in engineering practice.