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1.
By means of the real linear operator, we establish an iterative algorithm for solving a class of complex generalized coupled Sylvester matrix equations. The finite termination of the proposed algorithm is proved. By representing a complex matrix as a larger real matrix, we present a new method to prove that the minimum-norm solution or minimum-norm least squares solution of the complex generalized coupled Sylvester matrix equations can be obtained by an appropriate selection for the initial matrices, which has not been found in the existing work. Numerical experiments on some randomly generated data and practical image restoration problem show that the proposed algorithm is feasible and effective.  相似文献   

2.
In this paper, we discuss the properties of the eigenvalues related to the symmetric positive definite matrices. Several new results are established to express the structures and bounds of the eigenvalues. Using these results, a family of iterative algorithms are presented for the matrix equation AX=F and the coupled Sylvester matrix equations. The analysis shows that the iterative solutions given by the least squares based iterative algorithms converge to their true values for any initial conditions. The effectiveness of the proposed iterative algorithm is illustrated by a numerical example.  相似文献   

3.
This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the decomposition technique and the auxiliary model identification idea, we derive a decomposition based auxiliary model recursive generalized least squares algorithm. The key is to divide the system into two fictitious subsystems, the one including a parameter vector and the other including a parameter matrix, and to estimate the two subsystems using the recursive least squares method, respectively. Compared with the auxiliary model based recursive generalized least squares algorithm, the proposed algorithm has less computational burden. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms.  相似文献   

4.
In this paper, a new method is presented to solve the least squares Hermitian problem of the complex matrix equation AXB+CXD=E. The explicit expression of least squares Hermitian solution with the least norm is given. The least squares Hermitian solution with the least norm of complex matrix equation AXB=E is also derived. Numerical algorithms and numerical examples show the feasibility of our method.  相似文献   

5.
沈光星  黄德超 《科技通报》2006,22(3):283-287
利用多项式矩阵理论,给出了循环线性方程组有解的判定并求出各种情况下的解。若方程组有唯一解,求出其唯一解;若方程组有无穷解,求出其极小范数解;若方程组无解,求出其极小范数最小二乘解。  相似文献   

6.
Maximum likelihood methods are significant for parameter estimation and system modeling. This paper gives the input-output representation of a bilinear system through eliminating the state variables in it, and derives a maximum likelihood least squares based iterative for identifying the parameters of bilinear systems with colored noises by using the maximum likelihood principle. A least squares based iterative (LSI) algorithm is presented for comparison. It is proved that the maximum of the likelihood function is equivalent to minimize the least squares cost function. The simulation results indicate that the proposed algorithm is effective for identifying bilinear systems and the maximum likelihood LSI algorithm is more accurate than the LSI algorithm.  相似文献   

7.
This paper develops a decomposition based least squares iterative identification algorithm for two-input single-output (TISO) systems. The basic idea is to decompose a TISO system into two subsystems and then to identify each subsystem, respectively. Compared with the least squares based iterative algorithm, the proposed algorithm has less computational load. The simulation results indicate that the proposed algorithm is effective.  相似文献   

8.
A least squares control algorithm for single-input single-output (SISO) systems is developed. The algorithm allows for a delay with large dead time and uses proportional- integral-derivative actions in their parallel form to achieve steady-state without error. Optimization of the controller parameters is achieved and the parameters of the controller are determined from the solution of a set of linear simultaneous equations. The control strategy is to optimize the controller parameters such that a desired well-behaved trajectory is obtained. The controller is shown to be robust and the algorithm is shown to function as well without or with large dead time, to have low sensitivity to changes in the dead time, and to allow an adaptive estimation of changing system parameters. The application of the developed algorithm to control the glucoregulatory system, based on a 4th-order digital model, is presented in two cases: free time delay and with large dead time.  相似文献   

9.
The paper is dedicated to solving the generalized periodic discrete-time coupled Sylvester matrix equation, which is frequently encountered in control theory and applied mathematics. The solvable condition and a iterative algorithm for this equation are presented. The proposed method is developed from a point of least squares method. The rationality of the method is testified by theoretical analysis, which shows that the algorithm can solve the problem within finite number of iterations. The presented approach is numerically reliable and requires less computation. A numerical example illustrates the effectiveness of the raised result.  相似文献   

10.
In this paper we characterize a symmetrizability property using the theory of output sets. Employing the basic properties of symmetric matrices and an efficient algorithm for systematic generation of output sets, an algorithm for testing the symmetrizability of a matrix is presented and illustrated.  相似文献   

11.
Severely ill-conditioned Hermitian matrices are commonly seen in digital signal processing as well as in other applications where the Galerkin method and the least squares method are employed to seek optimal solutions of linear or nonlinear models. A new treatment for such matrices is proposed in this paper, which is fundamentally different from the well-known conjugate gradient preconditioners, SVD-based methods, and other popular algorithms for solving ill-conditioned systems in the literature. We propose an exact, alternative formula for the inverse of a Hermitian matrix via parametric diagonal perturbation. It reduces the condition number of the original ill-conditioned matrix exponentially. The performance of the proposed algorithm is established via condition analysis and demonstrated over severely ill-conditioned matrix systems from digital filter designs.  相似文献   

12.
自适应滤波算法根据采用优化准则的不同,通常分为两类最基本算法:最小均方误差(LMS)类算法和递归最小二乘(RLS)类算法。本文重点介绍了最小均方误差算法和递归最小二乘算法,并将这两类算法在MATLAB上进行仿真,并对结果作出比较和分析。  相似文献   

13.
This paper studies the numerical solutions of a class of periodic coupled matrix equations. Based on the least square method, a finite iterative algorithm for a class of periodic coupled matrix equations is proposed, and the convergence of the algorithm is proved by theoretical derivation. For any initial value, the algorithm can converge to the solution in finite iterations. Since the equations considered in paper contain many variants, the proposed algorithm has a wide range of applications. Finally some numerical examples in practical systems are given to prove the effectiveness and efficiency of the algorithm.  相似文献   

14.
This paper focuses on parameter estimation problems for non-uniformly sampled Hammerstein nonlinear systems. By combining the lifting technique and state space transformation, we derive a nonlinear regression identification model with different input and output updating rates. Furthermore, the unmeasurable state vector is estimated by Kalman filter, and by using the hierarchical identification principle, we develop a hierarchical recursive least squares algorithm for estimating the unknown parameters of the identification model. Finally, illustrative examples are given to indicate that the proposed algorithm is effective.  相似文献   

15.
The paper is indicated to constructing a modified conjugate gradient iterative (MCG) algorithm to solve the generalized periodic multiple coupled Sylvester matrix equations. It can be proved that the proposed approach can find the solution within finite iteration steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrices to obtain the least Frobenius norm solution of the system. Some numerical examples are illustrated to show the performance of the proposed approach and its superiority over the existing method CG.  相似文献   

16.
This paper focuses on the parameter estimation problems of multivariate equation-error systems. A recursive generalized extended least squares algorithm is presented as a comparison. Based on the maximum likelihood principle and the coupling identification concept, the multivariate equation-error system is decomposed into several regressive identification models, each of which has only a parameter vector, and a coupled subsystem maximum likelihood recursive least squares identification algorithm is developed for estimating the parameter vectors of these submodels. The simulation example shows that the proposed algorithm is effective and has high estimation accuracy.  相似文献   

17.
This paper presents a decomposition based least squares estimation algorithm for a feedback nonlinear system with an output error model for the open-loop part by using the auxiliary model identification idea and the hierarchical identification principle and by decomposing a system into two subsystems. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm has a smaller computational burden. The simulation results indicate that the proposed algorithm can estimate the parameters of feedback nonlinear systems effectively.  相似文献   

18.
This paper uses the filtering technique, transforms a pseudo-linear auto-regressive system into an identification model and presents a new recursive least squares parameter estimation algorithm pseudo-linear auto-regressive systems. The proposed algorithm has a high computational efficiency because the dimensions of its covariance matrices become small compared with the recursive generalized least squares algorithm.  相似文献   

19.
This paper researches parameter estimation problems for an input nonlinear system with state time-delay. Combining the linear transformation and the property of the shift operator, the system is transformed into a bilinear parameter identification model. A gradient based and a least squares based iterative parameter estimation algorithms are presented for identifying the state time-delay system. The simulation results confirm that the proposed two algorithms are effective and the least squares based iterative algorithm has faster convergence rates than the gradient based iterative algorithm.  相似文献   

20.
This paper surveys the identification of observer canonical state space systems affected by colored noise. By means of the filtering technique, a filtering based recursive generalized extended least squares algorithm is proposed for enhancing the parameter identification accuracy. To ease the computational burden, the filtered regressive model is separated into two fictitious sub-models, and then a filtering based two-stage recursive generalized extended least squares algorithm is developed on the basis of the hierarchical identification. The stochastic martingale theory is applied to analyze the convergence of the proposed algorithms. An experimental example is provided to validate the proposed algorithms.  相似文献   

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