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在求解一维连续型动态规划问题的自创算法一离散近似迭代法的基础上,结合双收敛方法,对多维连续型动态规划问题进行计算.该算法的基本思路为:在给定其他状态向量序列的基础上,每次对一个状态变量序列进行离散近似迭代,并找出该状态变量的最优序列,直到所有状态向量序列都检查完,当模型为非凸非凹动态规划时,证明了该算法的收敛性;当模型为凸动态规划时,证明了该算法的线性收敛性,最后,通过具体算例验证了该模型和算法的有效性. 相似文献
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离散状态马尔科夫链理论已经广泛应用于进化算法的收敛性和时间复杂度分析中,而连续状态马尔科夫过程理论由于需要用到比较高深的数学工具,应用还不多.引入连续状态马尔科夫过程理论,以测度论为工具,借助公理化的条件数学期望理论推导出关键的转移概率的计算公式,分析了以(1+1)ES为代表的连续型进化算法的收敛性,从理论上证明若采用常变异算子,包括正态分布、柯西分布在内的一大类常用变异分布可使(1+1)ES依概率收敛到全局最优解的ε-邻域;构造了一个带适应值平台的函数,从理论上证明某些自适应变异算子即使以正态分布、柯西分布为变异分布也会导致(1+1)ES陷入早熟收敛.通过仿真实验验证了理论分析.结果表明自适应调整机制并非总是有效的. 相似文献
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针对离散线性时滞系统,设计了最优滑模面和最优离散变结构控制律.在设计最优滑模面的过程中,利用逐次逼近算法,将既含有时滞项又含有超前项的两点边值问题转化为不含时滞项和超前项的线性两点边值问题,并证明了其解序列一致收敛于原系统的最优滑模.进一步给出了原系统的变结构控制律. 相似文献
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针对二阶多智能体系统中的分布式资源分配问题, 本文设计两种连续时间算法. 基于KKT (Karush?Kuhn?Tucker, 卡罗需?库恩?塔克)优化条件, 第一种控制算法利用节点局部不等式及其梯度信息来约束节点状态. 与上述梯度方法不同, 第二种控制算法包括一致性梯度下降法和固定时间收敛映射算子, 其中固定时间收敛映射算子确保算法的节点状态在固定时间收敛到局部约束集, 一致性梯度下降法目的是确保节点迭代到资源分配问题最优解. 两种控制算法都对状态无初始值约束, 且控制参数都是常数. 利用凸优化理论和固定时间李雅普诺夫方法, 分别分析了上述控制策略在有向平衡网络条件下的渐近和指数收敛性. 最后通过数值仿真验证了所设计算法在一维和高维资源分配问题的有效性. 相似文献
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图像边缘检测是数字图像处理领域的关键技术,边缘检测的结果决定了图像后续处理的质量。模糊推理规则边缘检测算法具有较强的边缘检测能力,并且具备一定的抗噪效果。但是,这种算法只在高斯噪声较小时有效,当高斯噪声较大时它的边缘检测效果甚至比Canny等算子的效果还差。针对模糊推理规则算法在强高斯噪声时效果较差的问题,提出一种改进的模糊边缘检测算法。该算法能够根据图像含噪情况调整边缘检测方案:当噪声较弱时,使用模糊推理规则边缘检测算法;当噪声较强时,为提高算法抑制噪声的能力,使用改进的模糊推理规则边缘检测算法。实验结果表明,该方法具有更好的抗噪性能和边缘检测能力。 相似文献
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基于Priwitt算子的偏微分方程图像去噪模型 总被引:1,自引:0,他引:1
利用归一化的Priwitt微分算子作为权重,提出了两种融合Gauss曲率和平均曲率扩散的偏微分方程去噪模型,使得它们在去除噪声的同时能保持图像的重要特征。首先,对噪声图像进行Gauss滤波并计算滤波后图像的Priwitt微分算子;然后,新模型根据归一化的Priwitt微分算子自适应地平衡于高斯曲率扩散去噪与平均曲率扩散去噪之间,从而去除图像的噪声。利用偏微分方程有限差分法给出了新模型的离散迭代格式,并进行了数值实验。实验结果表明,新模型不仅迭代收敛的速度快,而且在均方误差和峰值信噪比两个评价指标上均优于单一曲率扩散去噪模型,并更好地保持了图像的细节特征。 相似文献
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In this paper, we consider coupled semi-infinite diffusion problems of the form ut(x, t)− A2 uxx(x,t) = 0, x> 0, t> 0, subject to u(0,t)=B and u(x,0)=0, where A is a matrix in
, and u(x,t), and B are vectors in
. Using the Fourier sine transform, an explicit exact solution of the problem is proposed. Given an admissible error and a domain D(x0,t0)={(x,t);0≤x≤x0, t≥t0 > 0, an analytic approximate solution is constructed so that the error with respect to the exact solution is uniformly upper bounded by in D(x0, t0). 相似文献
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Bertina Ho-Mock-Qai 《Systems & Control Letters》2002,45(5):331-338
We show that given any family of asymptotically stabilizable LTI systems depending continuously on a parameter that lies in some subset [a1,b1]××[ap,bp] of
, there exists a C0 time-varying state feedback law v(t,x) (resp. a C0 time-invariant feedback law v(x)) which robustly globally exponentially stabilizes (resp. which robustly stabilizes, not asymptotically) the family. Further, if these systems are obtained by linearizing some nonlinear systems, then v(t,x) locally exponentially stabilizes these nonlinear systems. Finally, v(t,x) globally exponentially stabilizes any time-varying system which switches “slowly enough” between the given LTI systems. 相似文献
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在模糊近似空间中,结合直觉模糊集的隶属度、非隶属度与模糊蕴涵算子,提出基于θ算子和θ算子的直觉模糊集及其隶属度和非隶属度的概念,并证明它们一系列性质.然后,结合直觉模糊集与变精度粗糙集,定义基于θ算子的变精度直觉模糊粗糙集,提出求解变精度粗糙集阈值参数β的方法,使用算例分析该方法. 相似文献
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The aim of this paper is double. First, we point out that the hypothesis D(t1)D(t2) = D(t2)D(t1) imposed in [1] can be removed. Second, a constructive method for obtaining analytic-numerical solutions with a prefixed accuracy in a bounded domain Ω(t0,t1) = [0,p] × [t0,t1], for mixed problems of the type ut(x,t) − D(t)uxx(x,t) = 0, 0 < x < p, t> 0, subject to u(0,t) = u(p,t) = 0 and u(x,0) = F(x) is proposed. Here, u(x,t) and F(x) are r-component vectors, D(t) is a Cr × r valued analytic function and there exists a positive number δ such that every eigenvalue z of (1/2) (D(t) + D(t)H) is bigger than δ. An illustrative example is included. 相似文献
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Error feedback control (in the presence of input constraints) is considered for a class of exothermic chemical reactor models. The primary control objective is regulation of a setpoint temperature T* with prescribed accuracy: given λ>0 (arbitrarily small), ensure that, for every admissible system and reference setpoint, the regulation error e=T−T* is ultimately smaller than λ (that is, ||e(t)||<λ for all t sufficiently large). The second objective is guaranteed transient performance: the evolution of the regulation error should be contained in a prescribed performance funnel F around the setpoint temperature T*. A simple error feedback control with input constraints of the form , u* an offset, is introduced which achieves the objective in the presence of disturbances corrupting the measurement. The gain k(t) is a function of the error e(t)=T(t)−T* and its distance to the funnel boundary. The input constraints
have to satisfy certain feasibility assumptions in terms of the model data and the operating point T*. 相似文献
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J. M. Trojan 《Computers & Mathematics with Applications》1980,6(4):433-441
We study the minimal complexity index of one-point iterations without memory for the solution of a system of N nonlinear equations F(x)=0. We present an iteration * with maximal order of convergence and with linear combinatory complexity. We show the complexity index of * is close to the lower bound on the minimal complexity index. 相似文献
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V.Y. Pan 《Computers & Mathematics with Applications》1996,31(12):97-138
We substantially improve the known algorithms for approximating all the complex zeros of an nth degree polynomial p(x). Our new algorithms save both Boolean and arithmetic sequential time, versus the previous best algorithms of Schönhage [1], Pan [2], and Neff and Reif [3]. In parallel (NC) implementation, we dramatically decrease the number of processors, versus the parallel algorithm of Neff [4], which was the only NC algorithm known for this problem so far. Specifically, under the simple normalization assumption that the variable x has been scaled so as to confine the zeros of p(x) to the unit disc x : |x| ≤ 1, our algorithms (which promise to be practically effective) approximate all the zeros of p(x) within the absolute error bound 2−b, by using order of n arithmetic operations and order of (b + n)n2 Boolean (bitwise) operations (in both cases up to within polylogarithmic factors). The algorithms allow their optimal (work preserving) NC parallelization, so that they can be implemented by using polylogarithmic time and the orders of n arithmetic processors or (b + n)n2 Boolean processors. All the cited bounds on the computational complexity are within polylogarithmic factors from the optimum (in terms of n and b) under both arithmetic and Boolean models of computation (in the Boolean case, under the additional (realistic) assumption that n = O(b)). 相似文献
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The paper presents sufficient conditions for the existence of positive solutions of the equation x″(t) + q(t)f(t,x(t),x′(t)) = 0 with the Dirichlet conditions x(0) = 0, x(1) = 0 and of the equation (p(t)x′(t))′ + p(t)q(t)f(t,x(t),p(t)x′(t)) = 0 with the boundary conditions limt→o+ p(t)x′(t) = 0, x(1) = 0. Our nonlinearity f is allowed to change sign and f may be singular at x = 0. The proofs are based on a combination of the regularity and sequential techniques and the method of lower and upper functions. 相似文献
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L. Guo 《Systems & Control Letters》1988,11(5):351-356
When the noise process in adaptive identification of linear stochastic systems is correlated, and can be represented by a moving average model, extended least squares algorithms are commonly used, and converge under a strictly positive real (SPR) condition on the noise model. In this paper, we present an adaptive algorithm for the estimation of autoregressive moving average (ARMA) processes, and show that it is convergent without any SPR condition, and has a convergence rate of O({loglog t)/t}1/2). 相似文献
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We consider the problem of inferring the evolutionary tree of a set of n species. We propose a quartet reconstruction method which specifically produces trees whose edges have strong combinatorial evidence. Let Q be a set of resolved quartets defined on the studied species, the method computes the unique maximum subset Q* of Q which is equivalent to a tree and outputs the corresponding tree as an estimate of the species’ phylogeny. We use a characterization of the subset Q* due to Bandelt and Dress (Adv. Appl. Math. 7 (1986) 309–343) to provide an O(n4) incremental algorithm for this variant of the NP-hard quartet consistency problem. Moreover, when chosing the resolution of the quartets by the four-point method (FPM) and considering the Cavender–Farris model of evolution, we show that the convergence rate of the Q* method is at worst polynomial when the maximum evolutive distance between two species is bounded. We complete these theoretical results by an experimental study on real and simulated data sets. The results show that (i) as expected, the strong combinatorial constraints it imposes on each edge leads the Q* method to propose very few incorrect edges; (ii) more surprisingly; the method infers trees with a relatively high degree of resolution. 相似文献