首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 31 毫秒
1.
This paper focuses on constructing a conjugate gradient-based (CGB) method to solve the generalized periodic coupled Sylvester matrix equations in complex space. The presented method is developed from a point of conjugate gradient methods. It is proved that the presented method can find the solution of the considered matrix equations within finite iteration steps in the absence of round-off errors by theoretical derivation. Some numerical examples are provided to verify the convergence performance of the presented method, which is superior to some existing numerical algorithms both in iteration steps and computation time.  相似文献   

2.
The purpose of this paper is to present an iterative algorithm for solving the general discrete-time periodic Sylvester matrix equations. It is proved by theoretical analysis that this algorithm can get the exact solutions of the periodic Sylvester matrix equations in a finite number of steps in the absence of round-off errors. Furthermore, when the discrete-time periodic Sylvester matrix equations are consistent, we can obtain its unique minimal Frobenius norm solution by choosing appropriate initial periodic matrices. Finally, we use some numerical examples to illustrate the effectiveness of the proposed algorithm.  相似文献   

3.
The paper studies the iterative solutions of the generalized coupled Sylvester transpose matrix equations over the reflexive (anti-reflexive) matrix group by the generalized conjugate direction algorithm. The convergence analysis shows that the solution group can be obtained within finite iterative steps in the absence of round-off errors for any initial given reflexive (anti-reflexive) matrix group. Furthermore, we can get the minimum-norm solution group by choosing special kinds of initial matrix group. Finally, some numerical examples are given to demonstrate the algorithm considered is quite effective in actual computation.  相似文献   

4.
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   

5.
Sylvester quaternion tensor equations have a wide range of applications in image processing and system and control theory. In this paper, by the Kronecker product and vectorization operator and the properties of quaternion tensors, we focus mainly on proposing the tensor form of the generalized product-type biconjugate gradient method for solving generalized Sylvester quaternion tensor equations. As an application, we apply the proposed method to restore a blurred and noisy-free color video. The obtained numerical results illustrate the effectiveness of our method compared with some existing methods.  相似文献   

6.
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   

7.
This paper focuses on the numerical solution of a class of generalized coupled Sylvester-conjugate matrix equations, which are general and contain many significance matrix equations as special cases, such as coupled discrete-time/continuous-time Markovian jump Lyapunov matrix equations, stochastic Lyapunov matrix equation, etc. By introducing the modular operator, a cyclic gradient based iterative (CGI) algorithm is provided. Different from some previous iterative algorithms, the most significant improvement of the proposed algorithm is that less information is used during each iteration update, which is conducive to saving memory and improving efficiency. The convergence of the proposed algorithm is discussed, and it is verified that the algorithm converges for any initial matrices under certain assumptions. Finally, the effectiveness and superiority of the proposed algorithm are verified with some numerical examples.  相似文献   

8.
《Journal of The Franklin Institute》2022,359(18):10849-10866
This paper considers neural network solutions of a category of matrix equation called periodic Sylvester matrix equation (PSME), which appear in the process of periodic system analysis and design. A linear gradient-based neural network (GNN) model aimed at solving the PSME is constructed, whose state is able to converge to the unknown matrix of the equation. In order to obtain a better convergence effect, the linear GNN model is extended to a nonlinear form through the intervention of appropriate activation functions, and its convergence is proved through theoretical derivation. Furthermore, the different convergence effects presented by the model with various activation functions are also explored and analyzed, for instance, the global exponential convergence and the global finite time convergence can be realized. Finally, the numerical examples are used to confirm the validity of the proposed GNN model for solving the PSME considered in this paper as well as the superiority in terms of the convergence effect presented by the model with different activation functions.  相似文献   

9.
In this paper, the optimal consensus control problem of nonlinear multi-agent systems(MASs) with completely unknown dynamics is considered. The problem is formulated in a differential graphical game approach which can be solved by Hamilton-Jacobi (HJ) equations. The main difficulty in solving the HJ equations lies in the nonlinear coupling between equations. Based on the Adaptive Dynamic Programming (ADP) technique, an VI-PI mixed HDP algorithm is proposed to solve the HJ equations distributedly. With the PI step, a suitable iterative initial value can be obtained according to the initial policies. Then, VI steps are run to get the optimal solution with exponential convergence rate. Neural networks (NNs) are applied to approximate the value functions, which makes the data-driven end-to-end learning possible. A numerical simulation is conducted to show the effectiveness of the proposed algorithm.  相似文献   

10.
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   

11.
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   

12.
A matrix-based framework for the modeling, analysis and dynamics of Bayesian games are presented using the semi-tensor product of matrices. Static Bayesian games are considered first. A new conversion of Bayesian games is proposed, which is called an action-type conversion. Matrix expressions are obtained for Harsanyi, Selten, and action-type conversions, respectively. Certain properties are obtained, including two kinds of Bayesian Nash equilibria. Then the verification of Bayesian potential games is considered, which is proved to test the solvability of corresponding linear equations equivalently. Finally, the dynamics of evolutionary Bayesian games are considered. Two learning rules for Bayesian potential games are proposed, which are type-based myopic best response adjustment and logit response rule, respectively. Markovian dynamic equations are obtained for the proposed strategy updating rules and convergence is proved.  相似文献   

13.
The purpose of this paper is deriving the minimal residual (MINIRES) algorithm for finding the symmetric least squares solution on a class of Sylvester matrix equations. We prove that if the system is inconsistent, the symmetric least squares solution can be obtained within finite iterative steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrix to obtain the minimum norm least squares symmetric solution of the problem. Finally, we give some numerical examples to illustrate the performance of MINIRES algorithm.  相似文献   

14.
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   

15.
In this paper, combining the multi-step Smith-inner-outer (MSIO) iteration framework with some tunable parameters, a relaxed MSIO iteration method is proposed for solving the Sylvester matrix equation and coupled Lyapunov matrix equations (CLMEs) in the discrete-time jump linear systems with Markovian transitions. The convergence properties of the relaxed MSIO iteration method are investigated, and the choices of the parameters are also discussed. In order to accelerate the convergence rate of the relaxed MSIO iteration method for solving the CLMEs, a current-estimation-based and a weighted relaxed MSIO iteration algorithms are presented, respectively. Finally, several numerical examples are given to verify the superiorities of the proposed relaxed algorithms.  相似文献   

16.
Recently, Xiao et al. (2021) proposed an efficient noise-tolerant zeroing neural network (NTZNN) model with fixed-time convergence for solving the time-varying Sylvester equation. In this paper, we propose a modified version of their NTZNN model, named the modified noise-tolerant zeroing neural network (MNTZNN) model. It extends the NTZNN model to a more general form and then we prove that, with appropriate parameter selection, our new MNTZNN model can significantly accelerate the convergence of the NTZNN model. Numerical experiments confirm that the MNTZNN model not only maintains fixed-time convergence and noise-tolerance but also has a faster convergence rate than the NTZNN model under certain conditions. In addition, the design strategy of the MNTZNN is also successfully applied to the path tracking of a 6-link planar robot manipulator under noise disturbance, which demonstrates its applicability and practicality.  相似文献   

17.
Riccati differential equations are a class of first-order quadratic ordinary differential equations and have various applications in systems and control theory. In this study, we analyzed a switched Riccati differential equation driven by a Poisson-like stochastic signal. We specifically focused on computing the mean escape time of the switched Riccati differential equation. The contribution of this study is twofold. We first show that, under the assumption that the subsystems described as deterministic Riccati differential equations escape in finite time regardless of their initial state, the mean escape time of the switched Riccati differential equation admits a power series expression. To further expand the applicability of this result, we then present an approximate formula to compute the escape time of deterministic Riccati differential equations. Numerical simulations were performed to illustrate the obtained results.  相似文献   

18.
The present work proposes a relaxed gradient based iterative (RGI) algorithm to find the solutions of coupled Sylvester matrix equations AX+YB=C,DX+YE=F. It is proved that the proposed iterative method can obtain the solutions of the coupled Sylvester matrix equations for any initial matrices X0 and Y0. Next the RGI algorithm is extended to the generalized coupled Sylvester matrix equations of the form Ai1X1Bi1+Ai2X2Bi2+?+AipXpBip=Ci,(i=1,2,…,p). Then, we compare their convergence rate and find RGI is faster than GI, which has maximum convergence rate, under an appropriative positive number ω and the same convergence factor µ1 and µ2. Finally, a numerical example is included to demonstrate that the introduced iterative algorithm is more efficient than the gradient based iterative (GI) algorithm of (Ding and Chen 2006) in speed, elapsed time and iterative steps.  相似文献   

19.
In this study, a robust fractional-order controller design methodology for a type of fractional-order or integer-order model with dead time is proposed using phase and gain margin specifications. The delayed Bode’s ideal transfer function is used as a reference model to design the controller analytically. The delay term in delayed Bode’s ideal transfer function provides the exact determination of these frequency domain specifications when the system owns a dead time. The analytical robust controller design problem is transformed to solving four nonlinear equations with four unknown variables, two of which are the desired specifications; namely, phase and gain margins. The remaining two are the phase and gain cross-over frequencies. Next, some conditions are set based on the desired specifications so that nonlinear equations provide a unique solution. The proposed method is compared with the other existing robust controller methods based on the same frequency domain specifications. The simulation results reveal that the proposed method outperforms the other methods and also gives closer outcomes to the desired specifications.  相似文献   

20.
In this paper, two relaxed gradient-based iterative algorithms for solving a class of generalized coupled Sylvester-conjugate matrix equations are proposed. The proposed algorithm is different from the gradient-based iterative algorithm and the modified gradient-based iterative algorithm that are recently available in the literature. With the real representation of a complex matrix as a tool, the sufficient and necessary condition for the convergence factor is determined to guarantee that the iterative solution given by the proposed algorithms converge to the exact solution for any initial matrices. Moreover, some sufficient convergence conditions for the suggested algorithms are presented. Finally, numerical example is provided to illustrate the effectiveness of the proposed algorithms and testify the conclusions suggested in this paper.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号