控制系统最优降阶技术与应用

本文给出一种新的控制系统最优降阶技术并介绍其在控制系统设计中的应用，文中引入的最优降阶的准则是在指定输入信号时，对降阶模型与原始模型之间误差的加权最小积分方差。广西重点讨论连续系统的降阶算法，但结论同样适合于离散时间系统，文中还将通过一个例子来淙本方法和其它传统方法相比的优越性。     

随机过程在指定坐标下的最优截断

提出了随机激励下的一种模型降阶方法.在指定坐标下,选择使输出误差性能指标 最小的分量,并对输出矩阵作最优修正,指出了这种最优截断法的几何正交性,为降阶控制器 设计提供了基础.最后给出了一个可行算法和算例.     

一种复杂系统的最优分数阶内模控制器设计

针对复杂系统提出了一种最优分数阶内模控制器设计方法。引入一种带混沌算子的人群搜索优化算法（Seeker Optimization Algorithm,SOA）将系统模型降阶简化,在此基础上完成了一种新的分数阶内模控制器的设计和参数最优整定。仿真结果表明,降阶模型很好地逼近了原系统,设计的控制器可以使系统具有良好的动态性能及克服参数变化的鲁棒性。     

线性不确定系统的给定阶最优控制器设计

为避免间接法设计降阶控制器的模型近似引起的性能下降,本文在静态输出反馈控制器设计的基础上,直接设计了线性不确定系统的给定阶混合H2/H∞动态反馈控制器.利用系统内外分解方法,得到了最优降阶状态观测器.通过求解降维状态观测器的静态输出反馈,可得到降阶控制的最优反馈增益阵.给定阶控制器由两个Ric cati方程和一个Lyapunov方程参数化表示.最后,通过一个例子,说明了本文提出的给定阶控制器设计方法.     

几种模型降阶方法的仿真对比研究

算法比较研究,比较几种主要模型降阶方法的优缺点,为给工程应用提供方法参考.利用奇异值分解的模型降阶方法具有较好的理论性质,能够保持降阶系统结构特性,但计算成本较高故不适合大规模动态系统的降阶;采用矩匹配的模型降阶方法计算简便,适合大规模系统降阶,但无法保证降阶系统稳定性,也很难求得降阶误差界.最小二乘降阶法同时利用了系统的Gramian矩阵和Krylov子空间理论,结合了二者的优点,使得降阶过程计算简化,保持了降阶系统的结构特性,而且降阶误差进一步减小.仿真算例证明了最小二乘法较前两者具有优越性.     

基于模型降阶的分数阶系统动态性能研究

由于大多数分数阶系统阶次过高,使得系统的控制器设计变得非常困难,会造成系统控制精度变差且动态性能降低等不利因素,而模型降阶技术是解决这一问题的有效工具.首先简要介绍了H2范数模型降阶的一般方法,并提出一种新的降阶模型结构,可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统.仿真结果证明,采用改进型H2范数模型降阶方法不仅保持了原有分数阶模型系统的动态性能而且还提升了原有整数阶模型系统的动态性能.     

电动助力转向系统多领域鲁棒控制模型的降阶方法

随着人们对汽车操纵舒适性、安全性和节能等方面要求的提高,鲁棒控制算法越来越广泛的应用于电动助力转向（EPS）控制系统中．针对高阶鲁棒控制器实时性差、成本高等问题,提出最优平方积分误差（ISE）模型降阶方法．应用该方法对EPS系统鲁棒控制器进行降阶,并与最优Hankel范数降阶法进行比较．仿真结果表明,最优ISE降阶方法具有更好的降阶效果,降阶系统具有很好的鲁棒性．     

复杂高阶对象的预测PID控制

针对复杂高阶对象提出了一种基于数值最优模型降阶方法,并基于这种降阶模型设计了预测PID控制器,将此控制器应用于原始模型能够得到很好地控制效果。数值最优模型降阶算法使高阶对象能近似为一阶加时滞对象或二阶加时滞对象,通过模型阶跃响应和Bode图对比,降阶模型曲线很好地逼近原始模型曲线。预测PID对大时滞对象有着很好地控制效果,模型降阶使得预测PID很好地控制复杂高阶对象,且其结构简单,可调参数少的特点。     

随机马尔可夫切换系统的H∞模型降阶

考虑一类带有时滞的不确定马尔可夫切换系统的H∞模型降阶问题.首先得到了一个矩阵不等式形式的充分条件,使该系统的H∞模型降阶问题对于满足条件的任意不确定性都是可解的;然后依据CCL(conecom plem entarity linearization)方法给出了该问题的求解算法,以及降阶模型的参数化方法.仿真算例说明该方法的有效性.     

互连线高效时域梯形差分模型降阶算法

为了进一步提高现有互连电路模型降阶方法的精度和效率,提出一种基于时域梯形法差分的互连线模型降阶方法.首先将互连电路的时域方程用梯形法差分离散后获得一种关于状态变量的递推关系,形成了一个非齐次Krylov子空间;然后利用非齐次Arnoldi算法求得非齐次Krylov子空间的正交基,再通过正交基对原始系统进行投影得到降阶系统.该算法可以保证时域差分后降阶系统和原始系统的状态变量在离散时间点的匹配,保证时域降阶精度,同时也保证了降阶过程的数值稳定性及降阶系统的无源性.与现有的时域模型降阶方法相比,文中算法可降低计算复杂度;与频域降阶方法相比,由于避免了时频域转换误差,其在时域具有更高的精度.     

Optimal control problem regularization for the Markov process with finite number of states and constraints

The optimal control problem is considered for a system given by the Markov chain with integral constraints. It is shown that the solution to the optimal control problem on the set of all predictable controls satisfies Markov property. This optimal Markov control can be obtained as a solution of the corresponding dual problem (in case if the regularity condition holds) or (in other case) by means of proposed regularization method. The problems arising due to the system nonregularity along with the way to cope with those problems are illustrated by an example of optimal control problem for a single channel queueing system.     

随机观测时滞系统的最优估计

研究了在观测中存在Markov跳跃时滞的离散时间系统的线性最小方差状态估计问题. 首先, 通过引入跳跃时滞的示性函数, 将带有跳跃时滞的观测方程转化为带有乘性噪声的定常时滞系统. 进一步采用状态扩维的方法, 将定常时滞系统转化为无时滞的Markov跳跃系统. 最后, 基于得到的无时滞系统, 采用Hilbert空间已有的几何论知识, 设计线性最优状态估计器, 得出基于Riccati方程的滤波器的表达式, 并证明了所得滤波器的渐渐收敛性.     

Improving Phoneme Classification Performance Using Observation Context–Dependent Segment Models

This article describes a novel method that models the correlation among acoustic observations in contiguous speech segments. The basic idea behind the method is that acoustic observations are conditioned not only on the phonetic context but also on the preceding acoustic segment observation. The correlation between consecutive acoustic observations is modeled by mean trajectory polynomial segment models (PSM). This method is an extension of conventional segment modeling approaches in that it describes the correlation of acoustic observations not only inside segments but also between contiguous segments. It is also a generalization of phonetic context (e.g., triphone) modeling approaches because it can model acoustic context and phonetic context at the same time. Using the proposed method in a speaker-independent phoneme classification test resulted in a 7 to 9% relative reduction of error rate as compared with the traditional triphone segmental model system and a 31% reduction as compared with a similar triphone hidden Markov model (HMM) system.     

An analytical representation of conformal mapping for genus-zero implicit surfaces and its application to surface shape similarity assessment

This paper develops an analytical representation of conformal mapping for genus-zero implicit surfaces based on algebraic polynomial functions, and its application to surface shape similarity assessment. Generally, the conformal mapping often works as a tool of planar or spherical parameterization for triangle mesh surfaces. It is further exploited for implicit surface matching in this study. The method begins with discretizing one implicit surface by triangle mesh, where a discrete harmonic energy model related to both the mesh and the other implicit surface is established based on a polynomial-function mapping. Then both the zero-center constraint and the landmark constraints are added to the model to ensure the uniqueness of mapping result with the Möbius transformation. By searching optimal polynomial coefficients with the Lagrange–Newton method, the analytical representation of conformal mapping is obtained, which reveals all global and continuous one-to-one correspondent point pairs between two implicit surfaces. Finally, a shape similarity assessment index for (two) implicit surfaces is proposed through calculating the differences of all the shape index values among those corresponding points. The proposed analytical representation method of conformal mapping and the shape assessment index are both verified by the simulation cases for the closed genus-zero implicit surfaces. Experimental results show that the method is effective for genus-zero implicit surfaces, which will offer a new way for object retrieval and manufactured surface inspection.     

基于BIC准则模型选择的光纤光栅波长温度拟合研究

针对现有光纤光栅温度解调系统的波长温度信息,提出将多项式拟合和BIC准则应用到光纤光栅温度解调系统中,该方法具有实时性好、易实现等特点,保证了工程性应用的前提。现场试验数据结果表明,6次多项式模型在模型参数和误差要求上最佳,同时,此时的误差为后续研究提供了参考。     

Approximation of infinite-dimensional systems

A Fourier series-based method for approximation of stable infinite-dimensional linear time-invariant system models is discussed. The basic idea is to compute the Fourier series coefficients of the associated transfer function T_d(Z) and then take a high-order partial sum. Two results on H^∞ convergence and associated error bounds of the partial sum approximation are established. It is shown that the Fourier coefficients can be replaced by the discrete Fourier transform coefficients while maintaining H^∞ convergence. Thus, a fast Fourier transform algorithm can be used to compute the high-order approximation. This high-order finite-dimensional approximation can then be reduced using balanced truncation or optimal Hankel approximation leading to the final finite-dimensional approximation to the original infinite-dimensional model. This model has been tested on several transfer functions of the time-delay type with promising results     

New bound characteristics of NARX model in the frequency domain

New results about the bound characteristics of both the generalized frequency response functions (GFRFs) and the output frequency response for the NARX (Non-linear AutoRegressive model with eXogenous input) model are established. It is shown that the magnitudes of the GFRFs and the system output spectrum can all be bounded by a polynomial function of the magnitude bound of the first order GFRF, and the coefficients of the polynomial are functions of the NARX model parameters. These new bound characteristics of the NARX model provide an important insight into the relationship between the model parameters and the magnitudes of the system frequency response functions, reveal the effect of the model parameters on the stability of the NARX model to a certain extent, and provide a useful technique for the magnitude based analysis of nonlinear systems in the frequency domain, for example, evaluation of the truncation error in a volterra series expression of non-linear systems and the highest order needed in the volterra series approximation. A numerical example is given to demonstrate the effectiveness of the theoretical results.     

Optimized Sinusoid Synthesis via Inverse Truncated Fourier Transform

It was shown that sinusoid synthesis can be implemented efficiently by an inverse Fourier transform on consecutive frames where all but a small number of coefficients per oscillator are dropped. This leads to a compromise between computational complexity and approximation accuracy. The method can be improved by two approaches. First, optimal coefficients can be found by minimizing the average approximation error. Second, the optimal window function can be found through an iterative process. The gain in signal-to-noise ratio (SNR) is between 10 and 40 dB and can be used to reduce computational complexity while satisfying required synthesis quality.     

Optimal control of quasi-linear systems of the diffusion type under incomplete information on the state

The problem of optimal control for a stochastic state-linear control system with coefficients of diffusion depending on the vector of state and control with quadratic criterion of the control quality is investigated. We assume that only a part of components of the state vector of the system are measured. On the basis of the Lyapunov-Lagrange method, we propose a method for searching for an optimal control strategy depending on known components of the state vector. The problem of synthesis of a control is reduced to solving a boundary-value problem for a system of ordinary differential equations of the Riccati type. Several model examples with different awareness about the system state are analyzed.     

The computer method of variable piecewise polynomial approximation of functions and solutions of ordinary differential equations

The authors present a computer method of piecewise polynomial approximation of functions and solution of Cauchy problem for systems of ordinary differential equations based on the Newton polynomial. The approximating polynomial on a subinterval is converted to the form with numerical coefficients, the degree of the polynomial and the number of subintervals varies. The method is shown to uniformly converge at the rate of geometric progression under conditions of double continuous differentiability of the function and of the right-hand side of the system. The approximate solution of the system is continuous, continuously differentiable, and is characterized by low error rate, in particular, when solving stiff problems.