基于智能优化算法的Pendubot轨迹规划与控制方法设计

以垂直Pendubot为研究对象,提出一种基于智能优化算法的轨迹规划与控制方法,以解决Pendubot控制过程中难以从摇起区过渡至平衡区的问题.为Pendubot的驱动连杆规划一条从初始角度到中间角度的正向轨迹和一条从中间角度到目标角度的反向轨迹.欠驱动连杆在系统耦合关系作用下进行运动,对应的Pendubot末端点也运动至相应位置.通过遗传算法优化轨迹参数,将正向和反向轨迹拼合为一条由初始角度到目标角度的驱动连杆轨迹的同时,对应的Pendubot末端点轨迹拼合为一条由垂直向下平衡位置到垂直向上平衡位置的完整轨迹,然后设计跟踪控制器跟踪优化后的驱动连杆轨迹至目标角度,由于耦合关系的存在,Pendubot末端点也运动至垂直向上平衡位置.由于Pendubot受重力作用,其末端点很难长时间稳定在垂直向上平衡位置,故设计镇定控制器,实现Pendubot末端点在垂直向上平衡位置的镇定控制.最后通过仿真实验验证所提出方法的有效性,并通过对比说明所提出方法在奇异点规避、控制器设计和控制效果方面的优势.     

Pendubot的一种分层滑模控制方法

针对Pendubot这类二阶欠驱动系统提出了一种分层滑模控制方法.该方法将系统状态分成两个子系统,分别构造滑动平面,采用Lyapunov方法求取总控制量,该控制量可以实现Pendubot的摆起控制,当系统接近平衡位置附近时,双层滑模控制器退化成单层控制器,这样又保证了Pendubot能够稳定在最终的平衡位置上.从理论上证明了各层滑动平面的渐近稳定性,并且通过仿真实验验证了该方法的有效性以及该控制器对各类扰动的自适应性.     

布尔控制网络的输出稳定与镇定

矩阵的半张量积是将逻辑变量转化为向量研究的主要工具.本文利用半张量积把逻辑控制系统表示为离散时间仿射线性系统,在逻辑系统的状态空间框架下研究了以布尔控制网络为代表的逻辑动态系统的输出稳定与镇定.首先给出布尔网络输出稳定的定义,研究了布尔网络输出稳定的充要条件;其次讨论了布尔控制网络的输出镇定,分别得到了布尔控制网络由常值输入变量、自由控制序列、状态反馈控制序列输出镇定的条件.本文讨论的系统输出稳定与镇定是(部分)变量稳定与镇定的推广.     

带两控制器刚体飞行器的姿态镇定

已知带两控制器的刚体飞行器系统不能被连续的纯状态反馈局部渐近镇定.有效的解 决方法包括时变反馈镇定方法和非连续反馈镇定方法.现有的时变反馈镇定方法设计均较为复 杂.已有的光滑时变反馈方法是非指数收敛的.本文通过引入辅助变量以及采用反馈线性化技术 设计出光滑时变的控制器.该方法设计简单且保证闭环系统状态是指数收敛的.仿真结果证明了 本文方法的有效性.     

伺服问题的二自由度镇定控制器参数化

对于多输入多输出四块线性系统,本文研究了存在跟踪和干扰抑制约束的二自由度镇定控制器参数化问题,给出了一般条件下的伺服问题二自由度镇定控制器参数化表示。     

具有状态和控制约束的受扰离散线性切换系统的反馈控制

本文的主要贡献是针对一类具有重置函数及由外部不能控事件决定动态的离散时间线性切换系统,给出一些稳定性综合结论. 当系统受到外部有界扰动, 及状态和控制量约束时, 在输入到状态稳定性理论框架下, 研究使得系统镇定的线性状态反馈控制器设计方法. 针对这类混杂系统, 本文引入了受控D不变性的概念, 并给出检测某一混杂区域具有受控D不变性的充要条件. 进而, 提出一种能够使得受扰的线性切换系统镇定, 同时保证状态和控制量满足其约束的反馈矩阵的计算方法. 最后, 通过一个由两个子系统构成的数值例子来说明本文技术的应用性.     

基于行为方法的同时镇定

从行为角度研究了动态系统的互联与控制．通过把控制规定为一种互联，得到了使系统镇定的一些新结果，此时，控制器不过是限制对象行为的一个系统．通过潜在变量的消除，得到人们感兴趣的那部分变量的动态特性刻画：即可以通过极点配置变成稳定的．通过定义一个既单且满的Bezout映射，证明了该控制器能镇定系统的多样性.从而使得一个控制器能对两个或两个以上的系统同时镇定．仿真算例验证了设计的正确性和有效性．     

欠驱动机械系统的三类级联规范型

基于欠驱动机械系统的动力学,分析了其驱动模式;为了便于欠驱动机械系统的控制设计,针对具有动能对称性的欠驱动机械系统,提出了一种闭环全局坐标变换方案.该方案将欠驱动机械系统的动力学转换成具有结构特征的级联规范型（即严格反馈、严格前馈和非三角级联非线性系统）,并分别给出了Pendubot、倒立摆系统和TORA （Translational Oscillator with Rotational Actuator） 系统的级联规范型.     

基于受控拉格朗日函数的永磁同步电动机控制器设计

本文将基于受控拉格朗日函数(CL)的控制器设计方法应用到高阶、强耦合、非线性的永磁同步电动机 (PMSM)的控制问题中. 利用期望的受控能量来构造受控拉格朗日函数, 并在广义力中引入速度一次项的保守力, 得到原始方程与受控方程相匹配的条件. 通过求解匹配条件中的偏微分方程, 得到的非线性光滑反馈控制律可同时 实现位置与速度的全局渐近镇定. 最后, 利用LaSalle不变定理对其进行证明. 仿真结果表明了控制律的有效性.     

一类随机分布参数系统反馈控制的镇定

研究一类随机分布参数系统的镇定.主要方法是将所考虑的系统的解随机场关于空间变量的积分形式上视为相应的随机常微分方程的解过程,通过构造一个关于空间变量平均的Lyapunov函数来达到运用It^o微分公式研究该系统的镇定性的目的.并获得了若干构造性的代数判据.     

Approximation of Escape Time for Lagrangian Systems With Fast Noise

This note is concerned with the large deviations asymptotics estimate of the mean escape time for Lagrangian systems subjected to fast Gaussian noise. The solution to the Hamilton-Jacobi equation of the associated variational problem is derived as a sum of two terms dependent on kinetic and potential energy of the system, respectively. A closed-form solution for classes of linear and nonlinear systems is obtained. An application to a controlled pointing problem is discussed as an example.     

On unconditional conservation of kinetic energy by finite-difference discretizations of the linear and non-linear convection equation

In the past the development of kinetic energy conserving finite-difference methods mostly focused on second-order accurate central methods defined on uniform grids. Nowadays the need for high-order accurate discretizations, to perform for instance accurate numerical simulations of turbulent flow, calls for the development of novel kinetic energy conserving discretization schemes. Instead of choosing a fixed basis discretization up front, in this paper a different, more general, approach is applied. For a Cartesian mesh, sets of conditions are presented such that all discretizations of the linear or non-linear convection equation which obey these conditions, unconditionally conserve kinetic energy.For the linear convection equation it is shown that on a uniform grid it is necessary and sufficient for a discretization to be central in order to be fully conservative, that is: such discretizations not only unconditionally conserve kinetic energy but also unconditionally conserve momentum. On non-uniform grids an algorithm is introduced that can be used to generate fully conservative discretizations that are at least first-order accurate.The derivation of the discretization conditions for the non-linear convection equation is performed in the two-dimensional (2D) linear case. Some examples on uniform grids and on non-uniform grids are presented. It is shown that on uniform grids no upper limit exists with respect to the accuracy of the kinetic energy conserving method. For the higher-dimensional linear and non-linear convection equation the same set of conditions, which ensure the unconditional conservation of kinetic energy, are found as in the 2D linear case. Other results too are found to be straightforward generalizations of the corresponding 2D linear results.It is shown that the fourth-order unconditionally kinetic energy conserving discretization on a staggered mesh introduced in this paper is well suited to simulate the initial development of an inviscid shear layer instability in a divergence-free flow.     

Kinetic model of radiation-induced gas conductivity

A kinetic equation for low-energy electrons induced in gas by ionizing radiation is studied. The kinetic equation takes into account elastic, inelastic, and ionization collisions between electrons and gas molecules, as well as the interaction with an external electric field. The process of the conduction current generation is considered. A small parameter is calculated as a ratio of the energy accumulated by an electron between collisions to the thermal energy. An approximate solution is constructed of the kinetic equation for electron concentration and flow. The study resulted in obtaining quadrature formulas for the calculation of electron conduction of an ionized gas in the model of a radiation-induced electromagnetic field.     

A Numerical Method to Solve Identification Problem for the Lower Coefficient and the Source in the Convection–Reaction Equation

We consider the problem of identifying simultaneously the kinetic reaction coefficient and source function depending only on a spatial variable in one-dimensional linear convection–reaction equation. As additional conditions, a non-local integral condition for the solution of the equation and condition of final overdetermination are given. This problem belongs to the class of combined inverse problems. By integrating the equation with the use of additional integral condition, the problem is transformed to a coefficient inverse problem with local conditions. The derivative with respect to the spatial variable is discretized and a special representation is proposed to solve the resultant semi-discrete problem. As a result, for each discrete value of the spatial variable, the semi-discrete problem splits into two parts: a Cauchy problem and a linear equation with respect to the approximate value of the unknown kinetic coefficient. To determine the source function, an explicit formula is also obtained. The numerical solution of the Cauchy problem uses the implicit Euler method. Numerical experiments are carried out on the basis of the proposed method.     

带输入饱和的欠驱动吊车非线性信息融合控制

针对欠驱动吊车系统的控制问题,提出了一种非线性信息融合控制方法. 通过融合二次型性能指标函数中包含的未来参考轨迹和控制能量的软约束信息,以及吊车系统状态方程和输出方程的硬约束信息,获得协状态和控制量的最优估计. 针对控制量输入饱和的问题,提出了一种控制能量软约束信息自适应调节算法,使求出的控制量满足限制要求. 信息融合控制方法基于被控对象的离散模型设计,具有易于实现的特点. 仿真结果表明了该方法的有效性.     

不确定拟哈密顿系统的随机最优控制

本文提出了不确定拟哈密顿系统、基于随机平均法、随机极大值原理和随机微分对策理论的一种随机极大极小最优控制策略.首先,运用拟哈密顿系统的随机平均法,将系统状态从速度和位移的快变量形式转化为能量的慢变量形式,得到部分平均的It随机微分方程;其次,给定控制性能指标,对于不确定拟哈密顿系统的随机最优控制,根据随机微分对策理论,将其转化为一个极小极大控制问题;再根据随机极大值原理,建立关于系统与伴随过程的前向-后向随机微分方程,随机最优控制表达为哈密顿控制函数的极大极小条件,由此得到最坏情形下的扰动参数与极大极小最优控制;然后,将最坏扰动参数与最优控制代入部分平均的It随机微分方程并完成平均,求解与完全平均的It随机微分方程相应的Fokker-Planck-Kolmogorov(FPK)方程,可得受控系统的响应量并计算控制效果;最后,将上述不确定拟哈密顿系统的随机最优控制策略应用于一个两自由度非线性系统,通过数值结果说明该随机极大极小控制策略的控制效果.     

Note on nonstability of the linear functional equation of higher order

We provide a complete solution of the problem of Hyers-Ulam stability for a large class of higher order linear functional equations in single variable, with constant coefficients. We obtain this by showing that such an equation is nonstable in the case where at least one of the roots of the characteristic equation is of module 1. Our results are related to the notions of shadowing (in dynamical systems and computer science) and controlled chaos. They also correspond to some earlier results on approximate solutions of functional equations in single variable.     

Issues and challenges in orbital-free density functional calculations

Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudopotential calculations and, if the latter, construction of the pseudopotential. Another is the stability, speed, and accuracy of solution algorithms. Underlying both is the fundamental issue of satisfactory quality of the approximate functionals (kinetic energy and exchange–correlation). We address both computational issues and illustrate them by some comparative performance testing of our recently developed modified-conjoint generalized gradient approximation kinetic energy functionals. Comparisons are given for atoms, diatomic molecules, and some simple solids.     

Optimization of kinetic energy of a micro-object by impulse fields

The generalization is performed of the Schrodinger equation for the kinetic energy of a micro-object to potential fields with the structure of distribution of the first order of singularity. This made it possible to solve the problem of minimization of the kinetic energy of a micro-object at the prescribed level of its observation in the class of potentials concentrated in a limited volume with a smooth surface. It was found that the singular component of the optimal potential is a simple layer concentrated at the volume boundary. Graphs are displayed of some affine transformations of the squares of optimal wave functions and appropriate potentials.     

神经网络多步预测控制及其在精馏塔中的应用研究

本文提出一种基于多神经网络并行预测模型的多变量协调预测控制,利用预测误差实时反馈校正各个神经网络预测模型的参数,对于对象的时变、未建模干扰及模型失配引起的误差均有很好的适应性。针对存在耦合的被控对象,本文在优化性能指标中采用多变量协调优化策略,对被控变量集及操作变量集优化,使被控变量达到优化值和使部分操作变量达到优化值。在单步预测控制的基础上,提出基于多RBF神经网络并行预测模型的多变量协调预测控制,提高了预测控制的鲁棒性及抗干扰能力。将此方法应用于精馏塔控制中,在保证主要产品质量合格的前提下,对操作变量进行约束,使部分操作变量达到优化值,从而减少能耗,提高经济效益。仿真结果表明,基于神经网络预测模型的多变量协调预测控制具有很好的动态特性、鲁棒性及显著的节能降耗效果。