Testing the quality of control algorithms for complex dynamic systems

A guaranteed approach to testing the quality of control algorithms for complex dynamic systems is considered. The worst perturbations are formed in the process of solving a special differential game problem. An objective quality index is calculated for the proposed control algorithm even in the case when this algorithm is considered as a “blackbox”.     

Least squares based iterative identification algorithms for input nonlinear controlled autoregressive systems based on the auxiliary model

For the difficulty that the information vector in the identification model contains the unknown variables, we substitute these unknown variables with the outputs of the auxiliary model and then develop an auxiliary model based recursive least squares algorithm, an auxiliary model based least squares iterative (AM-LSI) algorithm, and derive an equivalent matrix decomposition based AM-LSI algorithm for input nonlinear controlled autoregressive systems based on the auxiliary model. The simulation results show that the proposed algorithms can estimate the parameters of a class of input nonlinear systems.     

Mathematical model analysis for the dynamic design of machinery

Mathematical models are developed for making a dynamic shock and vibration analysis of a turbine generator on a typical shipboard foundation. The motion response is limited to “one direction at a time” at each mass point, which still allows for two shipboard rotational motions that can be superimposed on each translatory input motion. The usual normal-mode analysis without damping is supplemented by an equivalent transient analysis, wherein the identical peak accelerations are produced corresponding to a common “frequency-spectrum” definition of shock effects. The advantage of the latter analysis is that damping, phasing effects with time and nonlinear elements can be included. The net results is a more realistic summation of dynamic stresses than is found by max-on-max normal-mode summations. The principal consideration has been to keep the model analysis simple enough so that design changes and decisions can be checked out prior to ordering materials or machining parts. Hence, the digital-computer program is used as a new tool in experimental mechanics; a tool which is compatible with the “cut-and-try” philosophy for designing machinery.     

Globally convergent homotopy algorithms for nonlinear systems of equations

Probability-one homotopy methods are a class of algorithms for solving nonlinear systems of equations that are accurate, robust, and converge from an arbitrary starting point almost surely. These new globally convergent homotopy techniques have been successfully applied to solve Brouwer fixed point problems, polynomial systems of equations, constrained and unconstrained optimization problems, discretizations of nonlinear two-point boundary value problems based on shooting, finite differences, collocation, and finite elements, and finite difference, collocation, and Galerkin approximations to nonlinear partial differential equations. This paper introduces, in a tutorial fashion, the theory of globally convergent homotopy algorithms, deseribes some computer algorithms and mathematical software, and presents several nontrivial engineering applications.This work was supported in part by DOE Grant DE-FG05-88ER25068, NASA Grant NAG-1-1079, and AFOSR Grant 89-0497.     

Mathematical characteristics of the pom-pom model

 Recently, in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the pom-pom equations have been derived in the integral/differential form and also in the simplified differential type by McLeish and Larson on the basis of the reptation dynamics with simplified branch structure taken into account. In this study, mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However both versions of the model are Hadamard unstable if we neglect the arm withdrawal in the case of maximum backbone stretch. It is also dissipatively unstable, since the steady shear flow curves exhibit non-monotonic dependence on shear rate. Additionally, in the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms. Received: 14 August 2001 Accepted: 18 October 2001     

Mathematical osteon model for examining poroelastic behaviors

An extended and reasonable stress boundary condition at an osteon exterior wall is presented to solve the model proposed by Rémond and Naili. The obtained pressure and fluid velocity solutions are used to investigate the osteonal poroelastic behaviors. The following results are obtained. (i) Both the fluid pressure and the velocity amplitudes are proportional to the strain amplitude and the loading frequency. (ii) In the physiological loading state, the key role governing the poroelastic behaviors of the osteon is the strain rate. (iii) At the osteon scale, the pressure is strongly affected by the permeability variations, whereas the fluid velocity is not.     

惯性导航系统初始对准与标定最优化方法

从随机闭环控制系统架构出发,提出了基于随机线性控制分离性定理的惯性导航系统初始对准与标定最优化方法.内容包括:系统建模、卡尔曼滤波器设计与稳定性充要条件、随机线性控制系统最优控制律及闭环稳定性充要条件、保证初始对准与标定稳定收敛的设计准则,以及应用于空间稳定惯性导航系统初始对准与标定过程所得到的试验结果.理论分析和实验结果表明,提出的最优化方法是切实可行的,通过调整系统极点配置或全状态修正时间间隔可以实现在容许控制律条件下的最优性,最优闭环控制所产生的系统导航精度比常规的卡尔曼滤波一一开环控制有显著提高.     

自适应交互式多模型AUV组合导航算法（英文）

提出了一种基于期望模式修正(EMA)的改进交互式多模型(IMM)算法。该算法主要解决自主水下航行器(AUV)复杂工作环境下量测噪声统计特性未知或易发生变化时的状态估计问题,其核心思想是将期望模式修正机制和交互式多模型滤波算法相结合,利用状态估计过程中的获取的模型概率进行决策,得到更加接近与系统真实模式的期望模型集合,再通过期望模型集合滤波结果对固定模型集合滤波结果进行修正。与传统的交互式多模型算法相比,提出的基于期望模式修正的交互式多模型算法可以捕捉到系统模式更细微的变化。仿真结果表明,该算法可以大幅提高AUV组合导航系统的估计精度和稳定性。     

自适应交互式多模型AUV组合导航算法

提出了一种基于期望模式修正(EMA)的改进交互式多模型(IMM)算法.该算法主要解决自主水下航行器(AUV)复杂工作环境下量测噪声统计特性未知或易发生变化时的状态估计问题,其核心思想是将期望模式修正机制和交互式多模型滤波算法相结合,利用状态估计过程中的获取的模型概率进行决策,得到更加接近与系统真实模式的期望模型集合,再通过期望模型集合滤波结果对固定模型集合滤波结果进行修正.与传统的交互式多模型算法相比,提出的基于期望模式修正的交互式多模型算法可以捕捉到系统模式更细微的变化.仿真结果表明,该算法可以大幅提高AUV组合导航系统的估计精度和稳定性.     

改进遗传人工神经网络在组合导航中的应用

鉴于常规卡尔曼滤波算法组合导航系统数据融合算法中,存在易于发散的缺陷,尝试将遗传优化人工神经网络引入组合导航系统中.针对传统遗传算法存在的易早熟、算法稳定性差、固定的交叉和变异概率影响收敛效果等缺点,采用浮点式编码方式,两两竞争的选择策略、引入突变操作、重新定义交叉算子和自适应的交叉变异算子等措施进行了遗传算法的改进.仿真结果表明,改进后的算法更为有效,并且精度与常规卡尔曼滤波算法相当.     

改进的LMS算法在INS/SMNS组合导航中的应用

在惯导/景象匹配组合导航中,数学模型和噪声统计信息很难准确地给出,且景象匹配导航系统的输出值随机、有限甚至可能存在误匹配,这些都导致了目前适合于该组合的信息融合算法不多,而组合导航中常用的Kalman滤波算法在该系统中也难以收敛.为了寻找新的适合于该系统的信息融合算法,研究了基于最优估计理论的变步长最小均方算法和规格化最小均方算法,并将它们应用于惯导/景象匹配组合导航中.仿真结果表明,这两种算法与固定步长最小均方算法相比,抗干扰能力强;与递推最小二乘算法相比,它们滤波精度相同,但这两种算法结构简单,计算量小,耗时少,所以这两种算法适合于惯导/景象匹配组合导航.     

箭载GPS定位临近地面卫星对流层延迟改正模型

针对经典对流层延迟改正模型无法处理负仰角卫星误差修正的问题,在传统球对称标准大气模型的基础上,采用射线描迹法建立了GPS信号穿透对流层的数学模型,推导了根据对流层折射最低点海拔高度计算对流层延迟改正的计算公式;为求解对流层折射最低点海拔高度,采用最小二乘法求得GPS信号穿透对流层时地心张角与最低点海拔高度之间的线性方程,提出了根据卫星和火箭之间的夹角与地心张角之间的关系进行迭代计算,进而求得最低点海拔高度的方法;最后引入了模型误差因子,评估对流层延迟改正模型的效果。采用火箭飞行试验数据对模型进行验证,结果表明,该模型提供的方法能够消除负仰角卫星大部分对流层延迟,消除的最大延迟可达135 m,消除对流层延迟后的临近地面卫星参与定位计算使最终定位精度提高25 m,计算迭代次数平均10次,尤其适合箭载GPS实时定位。     

一种航天飞行器的INS/CNS自主导航方案

传统的天文导航方法由于受水平基准精度的制约,难以进一步提高定位精度。针对INS/CNS组合导航方法对水平基准依赖的问题,提出了一种新颖的基于星光折射技术的INS/CNS自主组合导航方案。将惯性系下的非线性惯导误差传播方程作为系统状态方程,将星敏感器测得姿态和星光折射信息作为量测,采用UKF滤波算法,构成全面最优的INS/CNS组合导航。仿真结果表明,星敏感器精度为3″时,导航系统的定位精度优于200 m,姿态精度优于3″,导航定位精度随所使用的折射星数目增多明显提高,且方案在系统大角度误差条件下仍然适用。     

空间稳定系统加速度计在线标校

三轴加速度计是惯性导航系统的核心元件之一,其误差对导航精度具有重要影响。提出一种适用于空间稳定系统的加速度计在线标校方法。在三轴加速度计十二系数误差模型基础上,推导比力的模误差与加速度计误差系数之间的关系式。设计一个五维静态Kalman滤波器进行加速度计组合误差系数的在线标定,并讨论了加速度计组合误差的补偿方法。计算机仿真和多组试验结果表明:采用所提方法,空间稳定系统加速度计误差的标校精度达到1×10-5g量级,所用加速度计的长期稳定性优于1.5×10-5g,对实现高精度导航具有实用价值。     

Mathematical model of forced expiration

A one-component model of the lungs suitable for describing the mechanics of forced expiration is proposed. As distinct from similar models mentioned in the literature (see, for example, [2]), this model makes it possible qualitatively and quantitatively to describe not only the flowvolume diagram but also other experimental facts associated with the forced expiration maneuver.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–10, July–August, 1991.     

Mathematical model of inchworm locomotion

Inchworms are caterpillars. Their locomotion, involving arching of much of the central portion of their body length, has not been studied as extensively as the peristaltic locomotion of worms or the crawling locomotion of many other caterpillars. A mathematical model is developed to describe the shapes and bending strains of typical inchworm motions. The inchworm is assumed to travel in a straight line on a rigid horizontal substrate. Two basic types of cycles are considered. In Case I, the inchworm body arches and then reverses that motion in becoming flat again. In Case II, the body arches, then cantilevers upward, and then falls down to a flat shape. A continuum model based on an elastica is adopted. The results may be useful in the development of soft robots exhibiting an inchworm mode of motion.