带乘性噪声和延时观测广义系统的多步最优预测器

本文研究了状态空间描述的离散广义系统最优预测器的设计问题,该系统带有即时和延时观测,所有观测中带有乘性噪声.论文在两个基本假设条件下采用标准的奇异值分解方法给出了受限等价时滞系统,对于此类系统没有采用状态增广方法,而是采用新息重组分析理论给出了多步预测器.因为延时观测的存在,所给出的多步预测器包含了两套递推的广义系统黎卡提方程.本文给出了一个数学算例验证了所提方法的正确性和有效性,并给出了四幅图片,根据算例可以看出一般情况下预测的步数越少,预测的结果越好.本文方法可以进一步来研究更复杂的一些问题,如延时广义系统的H_∞滤波和控制问题.     

State-space analysis and identification for a class of hysteretic systems

In this paper we present results on the twin subjects of system analysis and system identification for a class of state-space realizable dynamic systems under the influence of hysteresis. The class of systems in question consists of models in the form of a linear time-invariant dynamic system in series with a differential model of hysteresis. It will be demonstrated that under fairly light constraints on the differential model of hysteresis, it is possible to design a series of experiments leading towards the identification of the full state-space realization. The approach is tested successfully on a high-precision mechanical translation system affected by hysteresis.     

-output feedback of infinite-dimensional systems via approximation

As in the finite-dimensional case, a state-space based controller for the infinite-dimensional disturbance-attenuation problem may be calculated by solving two Riccati equations. These operator Riccati equations can rarely be solved exactly. We approximate the original infinite-dimensional system by a sequence of finite-dimensional systems. The solutions to the corresponding finite-dimensional Riccati equations are shown to converge to the solution of the infinite-dimensional Riccati equations. Furthermore, the corresponding finite-dimensional controllers yield performance arbitrarily close to that obtained with the infinite-dimensional controller.     

Discrete state-space modeling for linearnth-order constant coefficient distributed-parameter systems

A systematic procedure is developed for state-space modeling and solving the dynamic behavior of any linearn order constant coefficient distributed-parameter system with two or more independent variables. The state-space model is a set of first-order linear difference equations and is also referred to as a discrete multidimensional state-space model. Transformation of a continuous distributed-parameter system into a discrete state-space model is based on the multidimensional Laplace-bilinear mapping technique. A procedure is outlined for converting the initial and boundary conditions of the system into a set of discrete conditions appropriate for the statespace model. Convergence of the state-space model's solution to the exact solution depends on the sampling rates of the independent variables and the ratio of increments. A few examples when state-space modeling of a distributed-parameter system is useful are: to estimate optimal feedback or optimal feedforward gains in active control applications; model reference optimal-distributed tracking systems; optimal tracking of desired trajectories; realtime system identification.     

Parameterization and identification of multivariable state-space systems: A canonical approach

In this paper, the problem of determining a canonical state-space representation for multivariable systems is revisited. A method is derived to build a canonical state-space representation directly from data generated by a linear time-invariant system. Contrary to the classic construction methods of canonical parameterizations, the technique developed in this paper does not assume the availability of any observability or controllability indices. However, it requires the -matrix of any minimal realization of the system to be non-derogatory. A subspace-based identification algorithm is also introduced to estimate such a canonical state-space parameterization directly from input–output data.     

Realization theory of discrete-time linear switched systems

The paper presents realization theory of discrete-time linear switched systems. We present necessary and sufficient conditions for an input–output map to admit a discrete-time linear switched system realization. In addition, we present a characterization of minimality of discrete-time linear switched systems in terms of reachability and observability. Further, we prove that minimal realizations are unique up to isomorphism. We also discuss algorithms for converting a linear switched system to a minimal one and for constructing a state-space representation from input–output data. The paper uses the theory of rational formal power series in non-commutative variables.     

分数阶线性定常系统的稳定性及其判据

介绍了分数阶微分方程和分数阶系统 ,给出分数阶线性定常系统的传递函数描述和状态空间描述 .给出了分数阶线性定常系统的稳定性条件 ,并结合分数阶状态方程给出定理的证明 .直接从复分析中的辐角原理出发 ,推导出分数阶线性定常系统 2个有效的稳定性判据 :分数阶系统奈奎斯特判据和分数阶系统对数频率判据 .通过实例验证了其有效性     

Data driven local coordinates for multivariable linear systems and their application to system identification

In this paper we introduce a new parametrization for state-space systems: data driven local coordinates (DDLC). The parametrization is obtained by restricting the full state-space parametrization, where all matrix entries are considered to be free, to an affine plane containing a given nominal state-space realization. This affine plane is chosen to be perpendicular to the tangent space to the manifold of observationally equivalent state-space systems at the nominal realization. The application of the parametrization to prediction error identification is exemplified. Simulations indicate that the proposed parametrization has numerical advantages as compared to e.g. the more commonly used observable canonical form.     

Flow estimation of boundary layers using DNS-based wall shear information

This article investigates the problem of obtaining a state-space model of the disturbance evolution that precedes turbulent flow across aerodynamic surfaces. This problem is challenging since the flow is governed by nonlinear, partial differential-algebraic equations for which there currently exists no efficient controller/estimator synthesis techniques. A sequence of model approximations is employed to yield a linear, low-order state-space model, to which standard tools of control theory can be applied. One of the novelties of this article is the application of an algorithm that converts a system of differential-algebraic equations into one of ordinary differential equations. This enables straightforward satisfaction of boundary conditions whilst dispensing with the need for parallel flow approximations and velocity–vorticity transformations. The efficacy of the model is demonstrated by the synthesis of a Kalman filter that clearly reconstructs the characteristic features of the flow, using only wall velocity gradient information obtained from a high-fidelity nonlinear simulation.     

Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise

In the present paper, the identification and estimation problem of a single-input–single-output (SISO) fractional order state-space system will be addressed. A SISO state-space model is considered in which parameters and also state variables should be estimated. The canonical fractional order state-space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification. The identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state-space system recursively. Another subject that will be addressed in this paper is a novel fractional order Kalman filter suitable for the systems with coloured measurement noise. The promising performance of the proposed methods is verified using two stable fractional order systems.     

Left invertibility of discrete systems with finite inputs and quantised output

The aim of this article is to address left invertibility for dynamical systems with inputs and outputs in discrete sets. We study systems which evolve in discrete time within a continuous state-space. Quantised outputs are generated by the system according to a given partition of the state-space, while inputs are arbitrary sequences of symbols in a finite alphabet, which are associated to specific actions on the system. Our main results are obtained under some contractivity hypotheses. The problem of left invertibility, i.e. recovering an unknown input sequence from the knowledge of the corresponding output string, is addressed using the theory of iterated function systems (IFS), a tool developed for the study of fractals. We show how the IFS naturally associated to a system and the geometric properties of its attractor are linked to the invertibility property of the system. Our main result is a necessary and sufficient condition for left invertibility and uniform left invertibility for joint contractive systems. In addition, an algorithm is proposed to recover inputs from output strings. A few examples are presented to illustrate the application of the proposed method.     

Model reduction for state-space symmetric systems

In this paper, the model reduction problem for state-space symmetric systems is investigated. First, it is shown that several model reduction methods, such as balanced truncation, balanced truncation which preserves the DC gain, optimal and suboptimal Hankel norm approximations, inherit the state-space symmetric property. Furthermore, for single input and single output (SISO) state-space symmetric systems, we prove that the H_∞ norm of its transfer functions can be calculated via two simple formulas. Moreover, the SISO state-space symmetric systems are equivalent to systems with zeros interlacing the poles (ZIP) under mild conditions.     

Model reduction for state-space symmetric systems

In this paper, the model reduction problem for state-space symmetric systems is investigated. First, it is shown that several model reduction methods, such as balanced truncation, balanced truncation which preserves the DC gain, optimal and suboptimal Hankel norm approximations, inherit the state-space symmetric property. Furthermore, for single input and single output (SISO) state-space symmetric systems, we prove that the H_∞ norm of its transfer functions can be calculated via two simple formulas. Moreover, the SISO state-space symmetric systems are equivalent to systems with zeros interlacing the poles (ZIP) under mild conditions.     

State feedback and estimation of well-posed systems

The class of well-posed systems includes many systems modeled by partial differential equations with boundary control and point sensing as well as many other systems with possibly unbounded control and observation. The closed-loop system created by applying state-feedback to any well-posed system is well-posed. A state-space realization of the closed loop is derived. A similar result holds for state estimation of a well-posed system. Also, the classical state-feedback/estimator structure extends to well-posed systems. In the final section state-space realizations for a doubly coprime factorization for well-posed systems are derived.This research was partially supported by the Fields Institute, which is funded by grants from the Ontario Ministry of Colleges and Universities and the Natural Sciences and Engineering Research Council of Canada, and by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Modeling of a dynamic dual-input dual-output fast steeringmirror system

A modeling method is proposed for a dynamic fast steering mirror (FSM) system with dual inputs and dual outputs. A physical model of the FSM system is derived based on first principles, describing the dynamics and coupling between the inputs and outputs of the FSM system. The physical model is then represented in a state-space form. Unknown parameters in the state-space model are identified by the subspace identification algorithm, based on the measured input-output data of the FSM system. The accuracy of the state-space model is evaluated by comparing the model estimates with measurements. The variance-accounted-for value of the state-space model is better than 97%, not only for the modeling data but also for the validation data set, indicating high accuracy of the model. Comparison is also made between the proposed dynamic model and the conventional static model, where improvement in model accuracy is clearly observed. The model identified by the proposed method can be used for optimal controller design for closed-loop FSM systems. The modeling method is also applicable to FSM systems with similar structures.     

Learning control system analysis and design based on 2-D system theory

The connections between two research areas, intelligent control systems and multi-dimensional systems, are established. Two-dimensional (2-D) system theory is used to analyze a class of learning control system. The 2-D state-space model of a learning control system is given. A class of learning control laws is proposed and the convergence of the learning process can be checked based on a 2-D model of the learning control system. The theory and methods proposed in this paper not only provide the learning control system with powerful tools for analysis and design, but also offer a multi-dimensional system theory with a new field of application as well as some new problems for further exploration.The original version of this paper was presented at the 2nd International Symposium on Robotics and Manufacturing (ISRAM), Albuquerque, New Mexico, 16–18 November 1988. The published proceedings of this meeting may be ordered from: CAD Laboratory for Systems/Robotics, EECE Dept., UNM, Albuquerque, NM 87131, U.S.A.     

Subspace identification of multivariable linear parameter-varying systems

A subspace identification method is discussed that deals with multivariable linear parameter-varying state-space systems with affine parameter dependence. It is shown that a major problem with subspace methods for this kind of system is the enormous dimension of the data matrices involved. To overcome the curse of dimensionality, we suggest using only the most dominant rows of the data matrices in estimating the model. An efficient selection algorithm is discussed that does not require the formation of the complete data matrices, but processes them row by row.     

Weak and strong stabilisation of bilinear systems in a Banach space

In this paper, we study the feedback stabilisation of homogeneous bilinear systems on a Banach state-space. Sufficient conditions for weak and strong stabilisation are given. A decay rate of the stabilised state is explicitly estimated. Applications to heat and transport equations are provided.