基于二维Roesser模型与范数优化迭代学习控制的市域铁路列车速度追踪研究

ATO(列车自动运行)技术通过控制算法实现列车运行速度自动调节,通过对控制算法进行优化,可使列车运行速度更加贴合目标速度。轨道交通列车作为具有高度重复性的非线性动力学系统,在固定线路的时间轴和批次轴具有二维动态演化的特性,因此考虑将二维模型迭代学习控制应用于轨道交通列车。不同车厢在列车运行时所受空气阻力不同,将列车车厢分为头、中、尾三类,求解基于多质点模型的列车动力学方程,对其进行线性化处理,得到列车的状态空间方程;应用二维系统理论,将其转换为二维Roesser模型;设计范数优化迭代学习控制算法,将其作为二维模型的输入信号,验证了新建立的二维模型具有渐进稳定性。同时,选择市域铁路D型列车组作为研究对象,通过对速度、位移追踪仿真,验证了优化后算法的可行性;并选择了两种常用的一维系统ILC(迭代学习控制)进行速度追踪仿真,通过比较三者的追踪误差,验证了优化后算法的追踪性能优于其余两者。

广义2-D Roesser模型的状态滤波器

研究了状态和测量同时受白噪声干扰时广义随机2-D Roesser模型的状态滤波器设计问题。将Kalman滤波器的设计推广至广义2-D Roesser模型。通过逐行扫描法,模能重构的广义2-D Roesser模型的滤波问题得到了解决,获得了状态向量的最优滤波的计算公式。计算步骤和例子说明了设计的滤波器的有效性。

2－DRoesser模型的静态干扰解耦

本文讨论了２－ＤＲｏｅｓｓｅｒ模型［１］（ＲＭ）的静态干扰解耦问题［２］（简称为２－ＤＤＤＰ），即寻求２－Ｄ状态反馈使相应的闭环系统具有抗干扰的能力，得到了问题有解的充分条件和计算相应反馈阵的算法．

2-D Roesser模型状态反馈特征结构配置

基于Sylvester矩阵方程的显示通解提出了上(下)块三角的状态反馈特征结构配置的参数化方法。给出了状态反馈控制律及闭环特征向量的参数化表达式,它们都依赖于参数向量{f1ijk}及{f2ijk},这组参数向量表征了系统的设计自由度,通过合理地选择这些自由度可以满足系统的其它性能指标,为系统的进一步设计提供了方便。数值例子显示了其有效性。

广义2-D系统Roesser模型的可接受输入序列研究

通过将有限矩形上的广义 2 - D Roesser模型转化为等价的代数方程 ,给出了有限矩形上所有输入均为该系统的可接受输入的充要条件 ;利用 2 - D Z-变换以及多项式矩阵的性质 ,给出了无限矩形上所有输入均可接受的充要条件。证明了当系统的输入矩阵行满秩时 ,只要系统在某个有限矩形上的所有输入均为可接受输入 ,则在无限矩形上的所有输入也均为可接受输入。基于矩阵的初等行变换 ,提出了确定广义 2 - D系统 Roesser模型可接受输入序列集合的方法。

2－D广义Roesser模型的约化

本文讨论了将２－Ｄ广义Ｒｏｅｓｓｅｒ模型化成正常模型以及将非主项系统化成主项系统的问题，给出了解决这些问题的几个判别条件和具体方法，然后以实例对结果进行了说明．本文给出的各种方法主要是通过系统的等价变换，计算量不大．

将Roesser模型转换成F-M Ⅱ模型的一种新方法的研究

本文针对2维方框图理论,研究了由Roesser模型到F-M Ⅱ模型的转换方法,提出了一种新的模型转换方法。该方法依据2维方框图理论以及Roesser模型与F-M Ⅱ模型之间的关联,可由Roesser模型的实现矩阵直接求解出F-M Ⅱ模型的实现矩阵,且得到系统实现矩阵更灵活,有利于系统的分析设计。对比运用求状态方程实现模型之间的转换,省去了中间的求导环节,简化了计算步骤,使多维系统模型之间的转化更加便捷高效。将此方法运用于雷达系统中,能够提高系统的分析效率。

Kalman Filter for Generalized 2-D Roesser Models

The design problem of the state filter for the generalized stochastic 2-D Roesser models, which appears when both the state and measurement are simultaneously subjected to the interference from white noise, is discussed. The well-known Kalman filter design is extended to the generalized 2-D Roesser models. Based on the method of “scanning line by line”,the filtering problem of generalized 2-D Roesser models with mode-energy reconstruction is solved. The formula of the optimal filtering, which minimizes the variance of the estimation error of the state vectors, is derived. The validity of the designed filter is verified by the calculation steps and the examples are introduced.

一类新不确定2-D Roesser模型的鲁棒H_∞控制

讨论了具有广义Frobenius范数有界参数不确定性的2-D Roesser模型的鲁棒H∞控制问题.借助线性矩阵不等式(LMI)给出了2-D Roesser模型鲁棒H∞控制问题可解性的一个充分条件,并利用这个条件,通过解一系列LMI设计出了所期望的γ—次优H∞状态反馈控制律.

2-D Roesser模型的有界实引理和鲁棒H_∞控制

讨论具有时不变、模有界、参数不确定性的 2-D Roesser 模型的鲁棒 H_∞控制问题,目的在于设计一种状态反馈控制器,使所得的闭环系统对所有允许的不确定性均具有期望的 H_∞性能指标．借助线性矩阵不等式(LMI)建立了不同形式的 2-D Roesser 的有界实引理, 并在此基础上给出了鲁棒 H_∞控制问题可解性的一个充分条件。最后利用这个条件,通过解矩阵不等式设计出所期望的状态反馈控制器．

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional（2D） systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded（polytope type） uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.

Stability analysis of nonlinear Roesser-type two-dimensional systems via a homogenous polynomial technique

This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional （2D） systems. Firstly, the fuzzy modeling method for the usual one-dimensional （1D） systems is extended to the 2D ease so that the underlying nonlinear 2D system can be represented by the 2D Takagi Sugeno （TS） fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conser- vative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach.

Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional （2D） systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed result.

Non-Fragile Controller Design for 2-D Discrete Uncertain Systems Described by the Roesser Model

This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be norm-bounded. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A new linear matrix inequality (LMI) based sufficient condition for the existence of such controllers is established. Finally, a numerical example is provided to illustrate the applicability of the proposed method.

广义Roesser模型的广义特征值及配置

本文给出了广义Roesser模型的广义特征值定义,得出了它的配置方法,相应地给出了实例.

二维线性系流 Roesser 模型鲁棒稳定性参数扰动上界的数值算法

本文对二维线性系统Ｒｏｅｓｓｅｒ模型鲁棒稳定性参数扰动上界进行了深入的讨论，据此给出了参数扰动上界的数值算法．

基于2-D Roesser模型的时滞系统迭代学习控制稳定性分析

本文讨论了多种类型时滞系统的迭代学习控制问题.针对状态时滞和输入时滞系统分别建立相应的2-D Roesser模型,并通过Roesser模型进行收敛性分析.分析表明,两类系统是否稳定与控制律中引入的伪偏导项无关.伪偏导项虽然不能决定系统是否收敛,但能够影响系统的收敛速度.而且该设计思想不仅对连续时滞系统有效,对于离散时滞系统依然有效.最后的仿真算例验证了算法的有效性.

Practical Exponential Stability of Two Dimensional Nonlinear Switched Positive Systems in the Roesser Model

This paper deals with the practical exponential stability of two-dimensional(2-D)nonlinear switched positive systems with impulse,disturbance and all modes unstable.Under the mode-dependent interval dwell time switching,new criteria such that 2-D nonlinear switched positive systems achieve practical exponential stability are derived.Furthermore,the explicit upper bound and convergence rate of the system state are estimated explicitly.Numerical examples indicate the correctness and effectiveness of the obtained results.

真三维显示系统的Roesser模型及其性能分析

文章用多维系统控制理论的思想方法研究光学显示问题,为了对真三维显示系统进行建模,并分析其性能,针对体空间中每个体素点的分布情况,将三维位置坐标和一维时间坐标相结合,建立四维Givone-Roesser(GR)模型对真三维显示系统进行状态空间表示.阐述了真三维显示系统工作过程,对其进行实时性分析,简化了系统矩阵.介绍了定点量化模型,推导出该系统经量化后全局渐近稳定的充分必要条件.实验结果表明,一个尺寸为4*4*4和8*8*8的真三维显示系统中,体素点的状态向量会收敛到0,因此是渐近稳定的.文章提出的Roesser模型表示方法既能简化系统数学表达,又有利于系统分析与设计,便于微控制器的软件实现,实时性与稳定性分析可广泛应用到真三维显示系统分析与设计中,具有极高的应用价值.

2-D奇异时滞系统的稳定性

研究用Roesser模型表示的 2 -D奇异时滞系统的稳定性。通过变换 ,将2 -D奇异时滞Roesser模型化为等价的 2 -D奇异一般模型 ,给出了 2