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1.
In this paper, based on the Smith iteration (Smith, 1968), an inner-outer (IO) iteration algorithm for solving the coupled Lyapunov matrix equations (CLMEs) is presented. First, the IO iteration algorithm for solving the Sylvester matrix equation is proposed, and its convergence is analyzed in detail. Second, the IO iteration algorithm for solving the CLMEs is constructed. By utilizing the latest estimation, a current-estimation-based and two weighted IO iteration algorithms are also given for solving the CLMEs, respectively. Convergence analyses indicate that the iteration solutions generated by these algorithms always converge to the unique solutions to the CLMEs for any initial conditions. Finally, Several numerical examples are provided to show the superiority of the proposed numerical algorithms.  相似文献   

2.
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   

3.
《Journal of The Franklin Institute》2022,359(18):10688-10725
In this paper, we propose the full-rank and reduced-rank relaxed gradient-based iterative algorithms for solving the generalized coupled Sylvester-transpose matrix equations. We provide analytically the necessary and sufficient condition for the convergence of the proposed iterative algorithm and give explicitly the optimal step size such that the convergence rate of the algorithm is maximized. Some numerical examples are examined to confirm the feasibility and efficiency of the proposed algorithms.  相似文献   

4.
At present, gradient iteration methods have been used to solve various Sylvester matrix equations and proved effective. Based on this method, we generalize the factor gradient iterative method (FGI) for solving forward periodic Sylvester matrix equations (FPSME) and backward periodic Sylvester matrix equations (BPSME). To accelerate the convergence of the iterative method, we refer to Gauss-Seidel and Jacobi iterative construction ideas and use the latest matrix information in the FGI iterative method to obtain the modified factor gradient iterative (MFGI) method. Then, the convergence of the proposed methods and the selection of optimal factors are proved. The last numerical examples illustrate the effectiveness and applicability of the iterative methods.  相似文献   

5.
This study proposes an efficient algorithm for the sum-of-absolute-values (SOAV) minimization problem with linear equality and box constraints by exploiting alternating direction method of multipliers (ADMM). In the iteration of ADMM, efficient algorithms for the calculations of proximal points, which are the solutions of sub-problems and have great effects on the computation efficiency, are employed. By focusing on the dynamical structure of the iteration, the linear convergence of the proposed algorithm is proven. Furthermore, a practical application for mechanical system control with discrete-valued control illustrates the advantages of the proposed methods.  相似文献   

6.
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   

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.
Many non-linear programming algorithms employ a univariate subprocedure to determine the step length at each multivariate iteration. In recent years much work has been directed toward the development of algorithms which will exhibit favorable convergence properties on well-behaved functions without requiring that the univariate algorithm perform a sequence of one-dimensional minimizations.In this paper a direct search method (the golden section search) is modified to search for acceptable rather than minimizing step lengths and then used as the univariate subprocedure for a generalized conjugate gradient algorithm. The resulting multivariate minimization method is tested on standard unconstrained test functions and a constrained industrial problem. The new method is found to be relatively insensitive to tuning parameters (insofar as success or failure is concerned).A comparison of the golden section acceptable-point search (GSAP) with other popular acceptable-point methods indicates that GSAP is a superior strategy for use with the conjugate directions-type algorithms and is also suitable for use with the quasi-Newton methods. The comparison are based on equivalent function evaluations required to minimize multivariate test functions.  相似文献   

9.
分布式水循环模型的参数优化算法比较及应用   总被引：1，自引：0，他引：1  
孙波扬  张永勇  门宝辉  张士锋 《资源科学》2013,35(11):2217-2223
分布式水文模型的优势在于还原水文过程的时空变异性,可以很好地模拟和反映各种水文要素和下垫面因素的时空分布不均匀性。由此也导致模型参数过多,在子流域过多的情况下,人工调节参数繁琐复杂,应用优化算法实现参数自动调节成为首选。本文选取石羊河流域九条岭站1988-2005年实测径流资料,分别应用SCE-UA算法、遗传算法(GA)和粒子群算法(PSO)对分布式水循环模型(时变增益模型)进行参数率定,对比3种算法的收敛速度、所需迭代次数和算法稳定性。结果表明:通过SCE-UA、GA和PSO的优化,模型水平衡系数都控制在0.0左右,而相关系数和效率系数分别能达到0.90和0.84以上,模拟精度较好。但粒子群算法的全局搜索能力和收敛速度优于SCE-UA和遗传算法,所需迭代次数最少,初值敏感性小,更适合时变增益模型的参数寻优,有很高的扩展性和改进潜力。  相似文献   

10.
《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   

11.
《Journal of The Franklin Institute》2023,360(14):10564-10581
In this work, we investigate consensus issues of discrete-time (DT) multi-agent systems (MASs) with completely unknown dynamic by using reinforcement learning (RL) technique. Different from policy iteration (PI) based algorithms that require admissible initial control policies, this work proposes a value iteration (VI) based model-free algorithm for consensus of DTMASs with optimal performance and no requirement of admissible initial control policy. Firstly, in order to utilize RL method, the consensus problem is modeled as an optimal control problem of tracking error system for each agent. Then, we introduce a VI algorithm for consensus of DTMASs and give a novel convergence analysis for this algorithm, which does not require admissible initial control input. To implement the proposed VI algorithm to achieve consensus of DTMASs without information of dynamics, we construct actor-critic networks to online estimate the value functions and optimal control inputs in real time. At last, we give some simulation results to show the validity of the proposed algorithm.  相似文献   

12.
This work presents an iterative concept of the State-space Realization Algorithm with Data Correlation (SSRA-DC) to identify MIMO systems with measurement noise and subjected to a reduced number of samples acquired from the process. The measurement noise is characterized as a random signal with properties of white noise and having up to 1% of the output signal amplitude. The proposed technique is based on the Markov parameters matrix’s feedback in an iterative algorithm supported by the SSRA-DC method. A gain factor takes part in the closed-loop to update the Markov parameters matrix, reducing their residues at each iteration. A fixed value for the gain is applied all over the iterations. The Gaussian White Noise (GWN) is employed as the input excitation signal in simulated experiments of mass-damper-springer models with 50 and 100 degrees of freedom. For some algorithm settings, one hundred simulations, each holding more than 100 iterations, are performed to statistically demonstrate the iterative algorithm’s effectiveness compared to the conventional SSRA-DC. Further comparative analysis is accomplished between the iterative method with the ARMAX and N4SID algorithms.  相似文献   

13.
In this paper, He's variational iteration method (VIM) is applied to solve the Emden–Fowler type equations in the second-order ordinary differential equations (ODEs). In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The Lagrange multipliers in the functionals can be identified optimally via variational theory. This technique provides a sequence of functions which convergence to the exact solutions of the Emden–Fowler equations. Comparison with the exact solutions and the solutions by the Adomian decomposition method (ADM) show efficiency of VIM in solving equations with singularity.  相似文献   

14.
混合遗传蚁群算法的改进及在TSP问题中的应用研究   总被引：1，自引：0，他引：1  
蚁群算法(ACA)与遗传算法(GA)都属于仿生型优化算法,是解决组合优化问题的强有力工具,并都分别成功应用于旅行商问题(TSP)中.本文将两种算法进行融合,并给出了新的融合方式.实验结果表明,新的遗传蚁群混合算法有效地改进了算法的全局收敛性,并加快了收敛速度.  相似文献   

15.
In this paper, a novel iterative approximate dynamic programming scheme is proposed by introducing the learning mechanism of value iteration (VI) to solve the constrained optimal control problem for CT affine nonlinear systems with utilizing only one neural network. The idea is to show the feasibility of introducing the VI learning mechanism to solve for the constrained optimal control problem from a theoretical point of view, and thus the initial admissible control can be avoided compared with most existing works based on policy iteration (PI). Meanwhile, the initial condition of the proposed VI based method can be more general than the traditional VI method which requires the initial value function to be a zero function. A general analytical method is proposed to demonstrate the convergence property. To simplify the architecture, only one critic neural network is adopted to approximate the iterative value function while implementing the proposed method. At last, two simulation examples are proposed to validate the theoretical results.  相似文献   

16.
结合模松弛SQP算法和强次可行方向算法思想,给出了初始点任意选取的新的拟强次可行方向算法。每步迭代,只需求解一个总有最优解的二次规划子问题来产生主搜索方向,引入一种新的非单调曲线搜索来产生步长,在较弱的条件下,可以得到算法的全局收敛性。  相似文献   

17.
This paper presents a novel switching predefined-time parameter identification algorithm with a relaxed excitation condition based on the dynamic regressor extension and mixing (DREM) method. DREM often requires the persistent excitation (PE) of the extended square regressor's determinant to ensure exponential parameter convergence. Unlike the classical DREM method, a new parameter identification algorithm configured with a two-layer filter technique is proposed under a relaxed initial excitation (IE) condition, rather than strict PE. A key point in choosing IE instead of PE is the introduction of a smooth switching function that dominates the pure integral action and filter behavior of the extended square regressor. The proposed algorithm relies on the predefined-time stability theorem and the settling-time of the identification algorithm is set a priori as a system parameter. The contributions of this paper are a novel switching predefined-time parameter estimation algorithm that 1) relaxes the stringent PE condition, 2) achieves predefined-time convergence, and 3) guarantees the monotonicity of each element of the parameter error inherited from the classical DREM method. Comparative simulation results are presented to illustrate the effectiveness of the proposed algorithm.  相似文献   

18.
Most existing consensus control in multi-agent systems (MASs) require agents to update their state synchronously, which means that some agents need to wait for all individuals to complete the iteration before starting the next iteration. To overcome this bottleneck, this paper studied asynchronous consensus problems of second-order MASs (SOMASs) with aperiodic communication. An asynchronous pulse-modulated intermittent control (APIMC) with heterogeneous pulse-modulated function and time-varying control period, which can unify impulsive control and sampled-data control, is proposed for the consensus of SOMASs. A time-varying discrete system is constructed to describe the evolution of the sample values of position and velocity of the SOMAS. Then, by the analysis tools from the stochastic matrix and the properties of the Laplace matrix of graph, some effective conditions are obtained to show the relationship between the convergence of the controlled SOMASs and the control parameters. Finally, a 300-node SOMAS whose topology is a random geographic network is included to verify the feasibility of the proposed control and the correctness of the theoretical analysis.  相似文献   

19.
This paper investigates the safe-circumnavigation problem of a single agent along a group of static targets. We assume in this paper that the distance information cannot be measured directly and only bearing measurements are available. In order to localize the targets, we design the positional estimator where the bearing measurements of the targets are used to construct the system matrix of the state equation of the estimator. To guarantee that the bearing angles are meaningful and with enough precision, we build the condition keeping safe distance between the agent and the targets. Furthermore, a gradual relaxed method is provided to reduce the limitations brought by the mutual restraint between the accuracy of the initial estimation and the desired encircling radius, so as to make the proposed method easy to apply. The performance of the proposed algorithms is verified through an experiment based on a wheeled robot platform.  相似文献   

20.
This paper proposes a robust version of the unscented transform (UT) for one-dimensional random variables. It is assumed that the moments are not exactly known, but are known to lie in intervals. In this scenario, the moment matching equations are reformulated as a system of polynomial equations and inequalities, and it is proposed to use the Chebychev center of the solution set as a robust UT. This method yields a parametrized polynomial optimization problem, which in spite of being NP-Hard, can be relaxed by some algorithms that are proposed in this paper.  相似文献   

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