系统辨识算法的复杂性、收敛性及计算效率研究

实践中经常会遇到大型计算问题和优化问题, 使得求解问题算法的复杂性、计算量和计算精度等成为突出问题, 特别是大规模非线性多变量系统的辨识. 对此, 提出几个有趣的研究课题: 1) 利用信息滤波技术和多新息辨识理论研究能提高辨识精度的大规模系统辨识理论与方法; 2) 利用递阶辨识原理研究维数高、变量数目多、计算量小的多变量系统递阶辨识方法; 3) 利用鞅收敛理论建立非线性多变量系统辨识方法的收敛理论; 4) 利用并行计算与递阶计算技术提高辨识算法的计算效率, 以解决一类大规模非线性多变量系统的模型化问题.

     

Multilevel discrete time system identification in large scale systems†

Hierarchical decomposition is considered to be one of the most powerful and offective tools to deal with complexity. Hierarchical system theory, which deals with system decomposition and coordination, can be used to decentralize and reduce the computational efforts requirements for many large-scale problems. This is achieved by decomposing the original system problem into several lower order easier to handle sub-problems, which are then coordinated such that the overall system objectives are met. In this work a hierarchical system theory approach to the discrete-time system identification problem is considered for stochastic large-scale system applications. A set of sequential discrete-time hierarchical identification algorithms, suitable for known and unknown system noise moments, are first obtained using a maximum a posteriori (MAP) approach with covariance matching and maximum likelihood (ML) methods. This is conducted in a two level hierarchical structure with two principles of coordination. Next, the hierarchical system identification algorithms are extended to multilevel hierarchical structures based on system characteristics of priority of action, spatial structure and time behaviour. This results in multilevel and composite multilevel coordinated system identification procedures, where each subsystem unit can be treated independently in reaching the overall system optimality. Application of these algorithms for the purpose of decentralization and reduction of computational requirements as well as adaptation to structural changes in growth and merger are considered.     

Hierarchical gradient-based identification of multivariable discrete-time systems

In this paper, we use a hierarchical identification principle to study identification problems for multivariable discrete-time systems. We propose a hierarchical gradient iterative algorithm and a hierarchical stochastic gradient algorithm and prove that the parameter estimation errors given by the algorithms converge to zero for any initial values under persistent excitation. The proposed algorithms can be applied to identification of systems involving non-stationary signals and have significant computational advantage over existing identification algorithms. Finally, we test the proposed algorithms by simulation and show their effectiveness.     

System identification in large scale systems with hierarchical structures

Due to its systems control orientation, the theory of multilevel hierarchical control developed by Mesarovic and others appears especially promising for identification and modeling of large scale systems consisting of relatively independent subsystems with strong and weak intersystem coupling.Standard techniques of optimum systems control and estimation theory may be used to resolve system problems described in this format. Determination of system structure and identification of system parameters form an inherent part of this procedure.To achieve advantages by hierarchical system concepts, it is necessary to decompose a large scale system into a number of smaller parts in such a manner that individual subsystem estimation, identification and control is feasible and to coordinate the subsystems in order to obtain the overall system goal. While decomposition is in theory easy, in practice it must be accomplished such that subsystem structure preserves constraints, information structures and acceptable authority structures. The success of coordination will thus, in practice, be affected by the particular system decomposition chosen.This paper presents the results of an investigation of system identification, using the maximum a posteriori criterion, of system parameters within a hierarchical structure. Examples demonstrate the use of the system identification algorithms.     

Decomposition‐based multiinnovation gradient identification algorithms for a special bilinear system based on its input‐output representation

This article considers the parameter estimation for a special bilinear system with colored noise. Its input‐output representation is derived by eliminating the state variables in the bilinear system. Based on the input‐output representation of the bilinear system, a multiinnovation generalized extended stochastic gradient (MI‐GESG) algorithm is proposed by using the multiinnovation identification theory. Furthermore, a decomposition‐based multiinnovation (ie, hierarchical multiinnovation) generalized extended stochastic gradient identification (H‐MI‐GESG) algorithm is derived to enhance the parameter estimation accuracy by using the hierarchical identification principle, and a GESG algorithm is presented for comparison. Compared with the existing identification algorithms for the bilinear system, the proposed MI‐GESG and H‐MI‐GESG algorithms can generate more accurate parameter estimation. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.     

Hierarchical least squares identification methods for multivariable systems

For multivariable discrete-time systems described by transfer matrices, we develop a hierarchical least squares iterative (HLSI) algorithm and a hierarchical least squares (HLS) algorithm based on a hierarchical identification principle. We show that the parameter estimation error given by the HLSI algorithm converges to zero for the deterministic cases, and that the parameter estimates by the HLS algorithm consistently converge to the true parameters for the stochastic cases. The algorithms proposed have significant computational advantage over existing identification algorithms. Finally, we test the proposed algorithms on an example and show their effectiveness.     

衰减激励条件下递阶最小二乘辨识的均方收敛性

为减少递推辨识的计算量，提出了递阶辨识原理，它是将系统分解为多个维数较小的虚拟子系统进行辨识，从而获得递阶最小二乘辨识方法。在衰减激励条件下，针对时不变系统研究了递阶最小二乘法的收敛性，得到了参数估计误差均方收敛于零时衰减指数应满足的条件。递阶最小二乘具有良好的性能，其计算量比递推量小二乘辨识要小得多，并具有容易实现等优点。     

多变量系统状态空间模型的递阶辨识

研究多变量系统状态空间模型的递阶辨识问题,推广了作者提出的标量系统状态和参数联合辨识算法.当状态可量测时,利用最小二乘原理直接辨识状态空间模型的参数矩阵;当状态不可测时,利用递阶辨识原理提出了状态空间模型递阶辨识方法,使用系统输入输出数据来估计系统的未知状态和参数.状态空间模型递阶辨识方法分为两步:首先假设系统状态是已知的(即参数估计算法中的未知系统状态用其估计代替),基于状态估计和系统输入输出数据递归计算系统参数估计;然后基于系统输入输出数据和获得的参数估计,递归计算系统的状态估计.     

基于神经网络的工业大系统辨识及稳态递阶优化方法

为了对工业大系统进行稳态递阶优化,必须首先获得系统的稳态模型.从神经网络的分 析人手,给出了工业大系统稳态模型的动态辨识方法及基于神经网络模型的推导方法.为了 提高算法的收敛速度,引入Lagrange函数解决大系统优化问题中的各种约束,并用Hopfield 网络实现了大系统稳态递阶优化的网络算法,最后给出了某一大系统辨识及优化的仿真结果.     

Global identification of complex static systems with hierarchical structure: Deterministic problem

The paper deals with a deterministic case of the identification problem of static complex systems with hierarchical structure, in which the globally optimal model of the whole system as a hierarchical configuration of models of individual subsystems is obtained

The considerations are confined to hierarchical complex systems, in which

(a) subsystems belonging to the same levels arc not interconnected

(b) the individual subsystems can be connected through their outputs only with the others from lower levels

Moreover only the hierarchical systems without, external factors (e.g. external controls) affecting particular subsystems (except for the subsystem from the highest level) are examined

It. is shown that for some global identification quality criteria, some structures of interconnections between individual subsystems in the system identified, and for some forms of models assumed for individual subsystems, the problem considered can be reduced to several identification problems of complex systems with cascade structure. The optimal solution of these problems based on the dynamic programming method is discussed.     

Fast multi-order computation of system matrices in subspace-based system identification

Subspace methods have proven to be efficient for the identification of linear time-invariant systems, especially applied to mechanical, civil or aeronautical structures in operation conditions. Therein, system identification results are needed at multiple (over-specified) model orders in order to distinguish the true structural modes from spurious modes using the so-called stabilization diagrams. In this paper, new efficient algorithms are derived for this multi-order system identification with subspace-based identification algorithms and the closely related Eigensystem Realization Algorithm. It is shown that the new algorithms are significantly faster than the conventional algorithms in use. They are demonstrated on the system identification of a large-scale civil structure.     

A sequential method for system identification in hierarchical structure

Implicit in all of hierarchical systems theory is the idea that it is generally easier to deal with several low order systems than with one system of high order. The basic idea of hierarchical systems theory is to decompose a large dimensional system into smaller dimensioned sub-systems in such a way that the overall system objectives can be met.

This paper is concerned with the application of hierarchical system theory to the identification problem. Specifically, the equations associated with a given identification problem are recast such that they may be decomposed into infimal subproblems of system identification which can be coordinated using hierarchical systems theory.

The maximum a posteriori approach to system identification is taken. This leads to a two point boundary value problem solution which determines optimum state and parameter estimates and estimates of any unknown prior statistics. Invariant imbedding is used to resolve this two point boundary value problem such that a recursive or sequential solution to the identification problem is obtained. Several examples indicate the use of the identification algorithms.     

关于递阶控制的几个问题

本文论述了近几年关于递阶控制的几个问题.全文分四节.第一节较详细地介绍了从无限维凸规划出发提出的辅助问题原则和松弛原则,根据这两个原则形成的统一方法可以推导出若干分解-协调算法.第二节介绍了用递阶方法离线地计算线性和非线性系统的闭环控制律,并对稳态系统的在线控制问题作了较详细的介绍.第三节论述了stackelberg策略在递阶控制中的应用.第四节介绍了两种递阶系统状态估计的算法.     

An introduction to hierarchical systems theory

Hierarchical theory is a new and promising area of general systems theory. This theory deals basically with the decomposition of a system into subsystems forming a hierarchical structure and is, therefore, on method of dealing with complexity. These subsystems or infimals are coordinated by a coordinator or supremal in such a way as to obtain original system objectives. Hence, hierarchical theory is applicable to systems with a natural hierarchical structure or whose dimensionality is so high as to present computational difficulties. Thus it would appear to be particularly appropriate for use in public and societal systems problems.This paper presents a tutorial introduction to hierarchical system theory. Optimization theory is used as a vehicle for presenting the hierarchical concepts, although estimation, identification and other systems problems are also amenable to hierarchical structuring. An example is solved to demonstrate the theory and some computational considerations.     

Hierarchical system identification of states and parameters in interconnected power systems†

This paper presents an application of hierarchical identification procedures of the previous paper to the identification of interconnected power system states and parameters from input—output observed data. A three-area interconnected power system model is used to demonstrate the decomposition of the original system based on its particular characteristics and the implementation of hierarchical algorithms for system identification. The adaptivity of these procedures to structural changes are also illustrated. Numerical results are obtained by conducting a digital simulation of the three-area system and using the hierarchical identification and coordination algorithms to estimate the states and unknown system parameters. Computational aspects of the hierarchical system identification solutions are discussed.     

Data filtering based least squares algorithms for multivariable CARAR-like systems

This paper focuses on the identification problem of multivariable controlled autoregressive autoregressive (CARAR-like) systems. The corresponding identification model contains a parameter vector and a parameter matrix, and thus the conventional least squares methods cannot be applied to directly estimate the parameters of the systems. By using the hierarchical identification principle, this paper presents a hierarchical generalized least squares algorithm and a filtering based hierarchical least squares algorithm for the multivariable CARAR-like systems. The simulation results show that the two hierarchical least squares algorithms are effective.     

连续大系统的网络结构最优滤波器

本文提出一种连续大系统状态估计器的设计方法--网络结构最优滤波器.这个方法基 于矩阵最小值原理,其计算结果是满足任意结构约束的最优估计.对于分散和递阶结构而言, 此方法具有容错和设计灵活等特点,特别适宜于用多计算机系统来实现,且不要求信道有很宽 的通频带.     

Distributed and robust parameter estimation of IIR systems using incremental particle swarm optimization

In recent years because of substantial use of wireless sensor network the distributed estimation has attracted the attention of many researchers. Two popular learning algorithms: incremental least mean square (ILMS) and diffusion least mean square (DLMS) have been reported for distributed estimation using the data collected from sensor nodes. But these algorithms, being derivative based, have a tendency of providing local minima solution particularly for minimization of multimodal cost function. Hence for problems like distributed parameters estimation of IIR systems, alternative distributed algorithms are required to be developed. Keeping this in view the present paper proposes two population based incremental particle swarm optimization (IPSO) algorithms for estimation of parameters of noisy IIR systems. But the proposed IPSO algorithms provide poor performance when the measured data is contaminated with outliers in the training samples. To alleviate this problem the paper has proposed a robust distributed algorithm (RDIPSO) for IIR system identification task. The simulation results of benchmark IIR systems demonstrate that the proposed algorithms provide excellent identification performance in all cases even when the training samples are contaminated with outliers.     

Concurrency control in hierarchical multidatabase systems

Over the past decade, significant research has been done towards developing transaction management algorithms for multidatabase systems. Most of this work assumes a monolithic architecture of the multidatabase system with a single software module that follows a single transaction management algorithm to ensure the consistency of data stored in the local databases. This monolithic architecture is not appropriate in a multidatabase environment where the system spans multiple different organizations that are distributed over various geographically distant locations. In this paper, we propose an alternative multidatabase transaction management architecture, where the system is hierarchical in nature. Hierarchical architecture has consequences on the design of transaction management algorithms. An implication of the architecture is that the transaction management algorithms followed by a multidatabase system must be composable– that is, it must be possible to incorporate individual multidatabase systems as elements in a larger multidatabase system. We present a hierarchical architecture for a multidatabase environment and develop techniques for concurrency control in such systems. Edited by R. Sacks-Davis. Received June 27, 1994 / Accepted September 26, 1995     

Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems

This paper is concerned with the joint estimation of states and parameters of a special class of nonlinear systems, ie, bilinear systems. The key is to investigate new estimation methods for interactive state and parameter estimation of the considered system based on the interactive estimation theory. Because the system states are unknown, a bilinear state observer is established based on the Kalman filtering principle. Then, the unavailable states are updated by the state observer outputs recursively. Once the state estimates are obtained, the bilinear state observer–based hierarchical stochastic gradient algorithm is developed by using the gradient search. For the purpose of improving the convergence rate and the parameter estimation accuracy, a bilinear state observer–based hierarchical multi‐innovation stochastic gradient algorithm is proposed by expanding a scalar innovation to an innovation vector. The convergence analysis indicates that the parameter estimates can converge to their true values. The numerical example illustrates the effectiveness of the proposed algorithms.