Model reduction of bilinear systems described by input–output difference equation

A class of single input single output bilinear systems described by their input–output difference equation is considered. A simple expression for the Volterra kernels of the system is derived in terms of the coefficients of difference equation. An algorithm, based on the singular value decomposition of a generalized Hankel matrix, is also developed. The algorithm is then used to find a reduced-order bilinear state-space model. The Hankel approach will be extensively studied under different data length cases and different orders of the state-space models. A numerical example is presented to illustrate the effectiveness of the proposed algorithm.     

Matrix continued fraction expansion and inversion by the generalized matrix Routh algorithm

A generalized matrix Mouth algorithm is established to expand n matrix transfer function into the matrix continued fraction of three matrix Cauer forms. By the use of the generalized matrix Routh algorithm and state-space techniques. a method is established for performing the matrix continued fraction inversion. The procedure is amenable to digital computation.     

Reduced-order modelling of linear discrete-time systems via continued-fraction expansion of a z transfer function about z = 1 and z = a alternately

A new time-domain procedure is suggested for obtaining reduced-order models of linear time-invariant discrete-time systems. The procedure is based on presenting a new form of continued-fraction expansion (CFE) about z = 1 and z = a alternately, and deriving a realization form for the CFE. An algorithm is presented for obtaining the new CFE of the z transfer function of a linear discrete-time system from its state-space model directly, without having to determine the corresponding rational z transfer function. Also presented is a systematic approach to deriving two similarity transformation matrices: one is used to transform a state-space model from a general form to the CFE canonical form, and the other is used to transform a state-space model from the phase-variable canonical form to the CFE canonical form. Finally, an approximate aggregation matrix is constructed to relate the state vector of the original system to that of a reduced model obtained by the present method. The proposed procedure is illustrated with examples.     

Passive Reduced-Order Macromodeling Algorithm for Microelectromechanical Systems

In this paper, we present a passive reduced-order macromodeling algorithm for second-order dynamic systems of linear microelectromechanical systems (MEMS) devices. The proposed reduction algorithm is based on congruent transformations. The system equations of MEMS devices, given by finite-element methods (FEMs), are converted to state-space forms that are compatible with passive Krylov subspace methods. To achieve this, a modified matrix equation is proposed for second-order MEMS dynamics. In addition, the generalized procedure is provided for first-order heat transfer problems and second-order structure dynamic problems to ensure that the discretized FEM system satisfies all the necessary conditions to guarantee the passivity of the reduced-order system. Finally, numerical examples are provided to demonstrate the validity of the proposed passive reduction technique.     

Digital design of variable structure control systems

Reachability conditions are developed for discrete single-input-single-output variable structure control systems described by linear mathematical models in general state-space form to reach a switching function from anywhere in state space. Stability conditions of a sliding mode are investigated. A modified algorithm is proposed to simplify the design procedure. Practical application to a thermal process has been achieved by using the modified algorithm to show the potential for development and practical results are compared with those using the classical PID controller design.     

A PMF-based subspace method for continuous-time model identification. Application to a multivariable winding process

This paper presents a methodology for system identification of continuous-time state-space models from finite sampled input-output signals. The estimation problem of the consecutive time-derivatives and integrals of the input-output signals is considered. The appropriate frequency characteristcs of a linear filtering based on the Poisson moment functionals in regards to the derivative or integral estimation problem is shown. The proposed method combines therefore the Poisson moment functionals technique with subspace based state-space system identification methods. The developed algorithm is based on a generalized singular value decomposition to compensate the noise colouring caused by the linear prefiltering of the input-output data. Rules of thumb are presented to choose the design parameters and new regards to the selection of the Poisson filter cut-off frequency are introduced. Finally, the proposed method is applied to a multivariable winding processes. The experimental results emphasize the applicability of the developed methodology.     

基于CARMA模型多变量系统的j步输出预估

用于广义预测控制（GPC）的单变量j步预估器传统上是在多项式域采用丢番图方程导出的,针对与其等价的状态空间形式预估器,对该预估器的多变量扩展进行了z域分析,得到一个多项式域的基于CARMA模型的多变量j步预估器．该预估器可以简化多变量系统的GPC算法设计,在单变量情形,该预估器即为传统的GPC预估器,最后提供了传统GPC预估器与状态空间形式预估器等价性的严格证明．     

An algorithm for the computation of 2-D eigenvalues

In this paper, a definition for the eigenvalues of two-dimensional (2-D) general discrete state-space models is proposed. This definition is consistent with that known for 2-D Roesser models. Also, a programmable algorithm is developed to compute the 2-D eigenvalues     

两种状态平均法在功率变换器建模的应用比较

以buck变换器为对象,采用广义状态平均法建立功率变换器广义状态空间平均模型,并与状态空间平均法进行对比.用MATLAB软件对两种方法建立的模型进行仿真,仿真结果与用MATLAB/PSB建立的电路精确模型和实际电路输出结果进行比较.得出结论:状态空间平均法适于研究直流分量占主要成分,电路各量变化波动不大的变换器电路.广义状态平均法不仅可以反映电路各量的直流成分,也能反映出其交流成分,对于研究类似谐振变换器或波动较大的变换器电路,非常有效.     

Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms

An algorithm is presented in this paper for computing state-space balancing transformations directly from a state-space realization. The algorithm requires no "squaring up" or unnecessary matrix products. Various algorithmic aspects are discussed in detail. A key feature of the algorithm is the determination of a contragredient transformation through computing the singular value decomposition of a certain product of matrices without explicitly forming the product. Other contragredient transformation applications are also described. It is further shown that a similar approach may be taken, involving the generalized singular value decomposition, to the classical simultaneous diagonalization problem. These SVD-based simultaneous diagonalization algorithms provide a computational alternative to existing methods for solving certain classes of symmetric positive definite generalized eigenvalue problems.     

Using the filtered CARMA and CARIMA models for state-space self-tuning control

Design procedures of state-space self-tuning controllers are described for both the filtered CARMA and CARIMA models. While closely resembling the generalized approach of Clarke-Kanjilal-Mohtadi (CKM), the proposed methods use the minimum possible dimension for the associated implicit-delay state-space model, and practical issues such us feedforward for linearization, regulation, servo-following, disturbance and offset elminution are considered. The resulting conipart-mental design allows the adjustment of tuning parameters to affecl different control characteristics. For the state-space self-tuners based on the filtered CARIMA model, two different forms can be distinguished: the normal form resembles the controller configuration based on the CARMA model, while the integrating form resembles the CKM self-tuner. Satisfactory results are observed in a simulation study of using the proposed self-tuners to control the steam temperature of a solar central receiver.     

Nested Monte Carlo EM algorithm for switching state-space models

Switching state-space models have been widely used in many applications arising from science, engineering, economic, and medical research. In this paper, we present a Monte Carlo Expectation Maximization (MCEM) algorithm for learning the parameters and classifying the states of a state-space model with a Markov switching. A stochastic implementation based on the Gibbs sampler is introduced in the expectation step of the MCEM algorithm. We study the asymptotic properties of the proposed algorithm, and we also describe how a nesting approach and the Rao-Blackwellized forms can be employed to accelerate the rate of convergence of the MCEM algorithm. Finally, the performance and the effectiveness of the proposed method are demonstrated by applications to simulated and physiological experimental data.     

A note on the estimation of variances in state-space models using the maximum a posteriori procedure

This note examines an estimation procedure for the unknown parameters in a state-space model proposed by Tsang, Glover, and Bach. The method is based on the maximum a posteriori (MAP) principle. Contrary to the claims of Tsang et al. it is shown that the algorithm performs very poorly compared to maximum likelihood. Some insight into the shortcomings of the MAP procedure is obtained by comparing it to the computation of maximum likelihood estimators by the EM algorithm.     

基于状态空间模型广义预测控制的并行算法

本文首先基于脉动阵列经，提出了一种实时参数辨识的并行算法，然后推导出基于状态空间模型广义预测控制的两种新算法，这两种算法都可以通过阵列结构并行实现。     

A Wiener-type recurrent neural network and its control strategy for nonlinear dynamic applications

This paper presents a Wiener-type recurrent neural network with a systematic identification algorithm and a control strategy for the identification and control of unknown dynamic nonlinear systems. The proposed Wiener-type recurrent network resembles the conventional Wiener model that consists of a dynamic linear subsystem cascaded with a static nonlinear subsystem. The novelties of our network include: (1) the two subsystems are integrated into a single network whose output is expressed by a nonlinear transformation of a linear state-space equation; (2) the characteristics of the trained network can be analyzed by its associated state-space equation using the well-developed theory of linear systems; and (3) the size of the network structure is determined by the number of state variables (or the system order) of the unknown systems to be identified. To effectively identify a given unknown system from its input–output data, we have developed a systematic identification algorithm that consists of an order determination procedure, a parameterization procedure, and an online learning procedure. The false nearest neighbors algorithm was adopted to acquire a minimal embedding dimension from the input–output data as the system order, and then the eigensystem realization algorithm (ERA) was used to initialize a best-fit state-space representation according to the acquired system order. To improve the overall identification performance, we have derived an online parameter learning algorithm based on an ordered derivatives and momentum terms. Subsequently, a simple feedback linear controller was designed to control the unknown dynamic nonlinear systems without much complexity. Computer simulations and comparisons with some existing recurrent networks have conducted to confirm the effectiveness and superiority of the proposed Wiener-type network, identification algorithm and control strategy.     

Generalized predictive control for non-uniformly sampled systems

In this paper, we study digital control systems with non-uniform updating and sampling patterns, which include multirate sampled-data systems as special cases. We derive lifted models in the state-space domain. The main obstacle for generalized predictive control (GPC) design using the lifted models is the so-called causality constraint. Taking into account this design constraint, we propose a new GPC algorithm, which results in optimal causal control laws for the non-uniformly sampled systems. The solution applies immediately to multirate sampled-data systems where rates are integer multiples of some base period.     

Nonlinear system identification under missing observations: The case of unknown model structure

This article presents an algorithm for identification of nonlinear state-space models when the “true” model structure of a process is unknown. In order to estimate the parameters in a state-space model, one needs to know the model structure and have an estimate of states. An approximation of the model structure is obtained using radial basis functions centered around a maximum a posteriori estimate of the state trajectory. A particle filter approximation of smoothed states is then used in conjunction with expectation maximization algorithm for estimating the parameters. The proposed approach is extended to handle missing observations and illustrated through a real application.     

Least squares based iterative identification for a class of multirate systems

This paper studies modeling and identification problems for multi-input multirate systems with colored noises. The state-space models are derived for the systems with different input updating periods and furthermore the corresponding transfer functions are obtained. To solve the difficulty of identification models with unmeasurable noises terms, the least squares based iterative algorithm is presented by replacing the unmeasurable variables with their iterative estimates. Finally, the simulation results indicate that the proposed iterative algorithm has advantages over the recursive algorithms.