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 421 毫秒
1.
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   

2.
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   

3.
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   

4.
Asymmetric self-excited periodic motions or periodic solutions which are produced by relay feedback systems that have symmetric characteristics are studied in the paper. Two different mechanisms of producing an asymmetric oscillation by a system with symmetric properties are noted and analyzed by the locus of a perturbed relay system (LPRS) method. Bifurcation between the ability to excite symmetric and asymmetric oscillation with variation of system parameters is analyzed. An algorithm of finding asymmetric solutions is proposed.  相似文献   

5.
In this paper, we present a functional variable method for finding periodic wave and solitary wave solutions of complex nonlinear evolution equations in mathematical physics and engineering sciences. The proposed technique is tested on the generalized Zakharov equation and higher-order nonlinear Schrödinger equations. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in applied mathematics.  相似文献   

6.
This paper addresses the design of a sliding mode based extremum-seeking controller for a class of single-input–single-output (SISO) uncertain nonlinear systems with unmatched and state-dependent strong nonlinearities. We demonstrate that it is possible to achieve an arbitrarily small neighborhood of the desired optimal point using only output-feedback. The key idea is the combination of a periodic switching function with a norm state observer. As an important advantage, we show that the proposed scheme achieves extremum-seeking for all initial conditions, i.e., the real-time optimization algorithm has global convergence properties. An application to a simple nonderivative optimizer illustrates the viability of the proposed approach.  相似文献   

7.
Optimal parametrization in numerical construction of curve   总被引：1，自引：0，他引：1  
The application of the optimal parametric continuation method to constructing a solution set curve for a system of nonlinear algebraic or transcendental equations depending on a parameter is considered. There are discussed two approaches to solving this problem—the use of iterative methods and reduction to an initial value problem for a system of ordinary differential equations. The algorithm suggested in this paper can also be used for finding an appropriate initial approximation when solving a system of nonlinear algebraic or transcendental equations not depending on a parameter by an iterative method.  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.
本文考虑一个二阶非线性微分方程，它是作为卫星绕着椭圆轨道作周期运动的模型而提出的。我们用初等方法证明了奇周期解的存在性，并且扩大了过去文献中给出的参数范围。  相似文献   

10.
Earth surface vibrations generated by passing vehicles, excavation equipment, footsteps, etc., attract increasing attentions in the research community due to their wide applications. In this paper, we investigate the periodic vibration source localization problem, which has recently shown significance in excavation device detection and localization for urban underground pipeline network protection. An intelligent propagation distance estimation algorithm based on a novel fundamental frequency energy distribution (FBED) feature is developed for periodic vibration signal localization. Contributions of the paper lie in three aspects: 1) a novel frequency band energy distribution (FBED) feature is developed to characterize the property of vibrations at different propagation distances; 2) an intelligent propagation distance estimation model built on the FBED feature with machine learning algorithms is proposed, where for comparisons, the support vector machine (SVM) for regression and regularized extreme learning machine (RELM) are used; 3) a localization algorithm based on the distance-of-arrival (DisOA) estimation using three piezoelectric transducer sensors is given for source position estimation. To testify the effectiveness of the proposed algorithms, case studies on real collected periodic vibration signals generated by two electric hammers with different fundamental frequencies are presented in the paper. The transmission medium is the cement road and experiments on vibration signals recorded at different propagation distances are conducted.  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 smooth periodic delayed feedback (SPDF) control scheme is proposed for the fixed-time stabilization problem of linear periodic systems subject to input delay. By investigating the monodromy matrix of the periodic system, it is proved that the SPDF controller can achieve the fixed-time stabilization of linear periodic systems with arbitrarily long yet bounded input delays under the condition that the original system is uniformly completely controllable. The proposed controller is continuously differentiable and smooth. The SPDF control scheme is then applied to the elliptical spacecraft rendezvous problem. The effectiveness of the established method is verified on numerical simulations.  相似文献   

13.
An impulsive reaction-diffusion periodic food-chain system with Holling type III functional response is presented and studied in this paper. Sufficient conditions for the ultimate boundedness and permanence of the food-chain system are established based on the upper and lower solution method and comparison theory of differential equation. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are shown to illustrate our results. A discussion is given in the end of the paper.  相似文献   

14.
在二阶系统一系列定理基础上,建立一个直接根据系统Lyapunov函数性质判定系统周期解存在性的定理,针对一类二阶非自治非线性系统构造了适当的Lyapunov函数,并研究了这类系统周期解的存在性。  相似文献   

15.
This paper presents the analysis and control of active magnetic bearing (AMB) systems with a flexible rotor. A sliding mode controller design scheme is proposed to compensate for the nonlinear effects of the AMB system. A nonlinear model of the AMB system with an electromagnetic actuator and a flexible rotor is proposed to facilitate the present system analysis and controller design. This nonlinear model takes into account the dynamics of the flexible rotor, the characteristics of the nonlinear electromagnetic suspended system, and the contact force between the auxiliary bearing and the shaft. This study also considers the auto-centering control of the AMB system when subjected to disturbances and variations in the system parameters. The numerical results show that the system exhibits a periodic motion and demonstrates high accuracy and robustness when operating under sliding mode control.  相似文献   

16.
This paper is mainly focused on the stabilization problem of uncertain delayed periodic piecewise time-varying systems inclusive of disturbances and faults in actuators. More specifically, the considered system is encompassed of periodic dynamics, which exhibits the nature of switched systems with fixed switching sequence and dwell time. The control protocol is configured in the form of both the present and past state information of the addressed system with passive performance. Moreover, the proposed control approach discloses the stabilization issue mainly by resolving the effect of faults in actuator components. Precisely, the desired periodic gain matrices of the developed controller are calculated by way of solving some matrix inequalities which are derived by making use of Lyapunov stability theory and matrix polynomial approach. As a result, the asymptotic stability of the considered system is ensured in conjunction with satisfied disturbance attenuation index. Conclusively, the simulation results of two numerical examples including mass-spring damping system are presented for validating the theoretical result.  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.
In this paper, we considered a time-optimal control problem for a new type of linear parameter varying (LPV) system which is obtained through data identification in the process of dealing with actual problems. The addition of non-linear terms is compensation for the method that does not require linear expansion at the equilibrium point. Since the objective function is the terminal time which is an implicit function concerning decision variables, it is a non-standard optimal control problem with uncertain terminal time. To find the global optimal solution to this problem, firstly, the control parameterization method is used to transform it into a nonlinear optimization problem of parameter selection, and then the modifed particle swarm optimization (PSO) algorithm is combined to solve the equivalent nonlinear programming problem. Numerical examples are used to illustrate the effectiveness of the proposed algorithm.  相似文献   

19.
Transient delayed feedback control is proposed by applying the transient control technique to the original delayed feedback control, with the aim of enlarging the stable region of the stabilized periodic oscillation, where the stable region is a subset of the parameter space of feedback gains for which the periodic oscillation is stabilized. The control signal is activated when the system is in a certain subset (the controlling area) of the state space, and inactivated otherwise, which is different from the standard control signal of the original delayed feedback control. The specific control performances of the transient delayed feedback control are investigated through case studies. The relationship between the stable region of the stabilized periodic oscillation and the controlling area is obtained by calculating the maximum Lyapunov exponent, which is a function of the feedback gain. It is shown that the stable region varies non-smoothly with the change of the controlling area. When the controlling area is properly chosen, the stable region with transient delayed feedback control is much larger than the stable region with original delayed feedback control.  相似文献   

20.
This paper tackles in the stabilization of periodic orbits of nonlinear discrete-time dynamical systems with chaotic sets. The problem is approximated locally to the stabilization of linear time-periodic systems and the theory of modern control is applied to the Prediction-Based Control, resulting in a new control law. This control law sets all the Floquet multipliers of the stabilized orbit to zero, resulting in fast convergence of trajectories in its vicinity. Another important characteristic of the control law is that no previous knowledge about the periodic orbit is required for stabilization. Using numerical simulations, this control law was analysed and compared to an optimal Delayed Feedback Control evidencing its advantages in theoretical and practical aspects.  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