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1.
H∞强镇定问题可解的原始算法是依赖于一个解存在的充分条件.自然的此算法应用起来有一定的局限性.针对此问题,首先给出H∞强镇定问题可解的一个充要条件.并说明该条件在计算上很容易实现的.并由此充要条件出发设计了一个简单且实际可行的算法.该算法实际上没有局限性,而且比较利于计算机编程.最后举例说明新算法与H∞强镇定问题可解的原有算法相比,具有更大的优点.  相似文献   

2.
经典的箱覆盖问题是组合优化中一个著名的问题,并且得到了广泛的研究.本文主要讨论带核元的箱覆盖问题的复杂性和在线条件下的算法.指出了带核的箱覆盖问题是强NP-hard的.给出了在不同的在线条件下可行算法渐近比的上界,指出仅在条件三下才存在渐近比好于0的在线算法,并给出了在此条件下一个渐近比为1/2的最好的在线算法。  相似文献   

3.
计算再生核的卷积方法   总被引:2,自引:0,他引:2  
吴勃英  张钦礼 《数学进展》2003,32(5):635-640
本文利用卷积及H1(R)的再生核给出了一种计算H^n(R)空间再生核的新方法.并用此再生核建立求解n阶常微分方程的数值方法.  相似文献   

4.
利用有理化Haar小波性质和方法,建立了一类非线性微分方程组在任意区间[a,b)的求解算法.基于该算法,运用计算机代数系统Maple,给出了求解非线性微分方程组的程序.并运用此程序给出了一类微分方程组的计算实例,从数值模拟来看可以达到较高的精度,并对方程组的动力学行为给出较好的描述.  相似文献   

5.
本文给出了一种求矩阵到其Jordan标准形的过渡矩阵的新算法,与其它现有的算法相比,此算法最简单有效,且最易于编制程序以利用计算机计算.  相似文献   

6.
文献[4]给出Catmull—Clark细分曲面控制网格的收敛速率和一个误差计算公式.本文在这基础上提出一个新的算法,并借助此新算法得到关于Catmull—Clark细分曲面控制网络的收敛速率的更精确的估计和给出更好的误差计算公式.  相似文献   

7.
本文建立了解二阶双曲型方程的一种新数值方法一再生核函数法.利用再生核函数,直接给出每个离散时间层上近似解的显式表达式.此方法的优点是:计算格式绝对稳定,且可显式求解;利用显式表达式,可实现完全并行计算等文中对近似解的收敛性和稳定性进行了理论分析,并给出数值算例.  相似文献   

8.
针对一类非线性微分代数系统,利用M导数方法,给出了受控不变分布的概念,并讨论了此类微分代数系统受控不变分布的一些性质.给出了一个计算包含在系统输出核(kerE(h))内的最大受控不变分布的算法,同时讨论了该算法的一些性质.最后,给出一个例子说明如何利用给出的算法计算微分代数系统的包含在系统输出核内的最大受控不变分布.  相似文献   

9.
沈小平 《数学研究》2007,40(2):117-131
文[20]引进了Slepian半小波基函数并讨论了这组基在概率度估计核方法中的应用[21],Slepian半小波基函数具有极好的性质.包括多重尺度结构和局部非负性.更值得指出的是.与Gauss核不同,Slepian函数是与无线信号类似的具有平滑谱的有限带宽函数.在所有相同带宽的函数中.Slepian函数在特定的时同区域上具有最大能量.在逼近具有平滑谱的无线信号中.这些特性使得Slepian半小波核与Gauss核以及其他小波基相比具有潜在的优越性.美中不足的是.和其他核密度估计一样.Slepian核密度估计的算法设计具有一定的挑战性.幸运的是.我们注意到Slepian核可以被表示成卷积形式.这一观察具有重要的计算意义.本文主要讨论Slephn核密度估计的应用及其计算.我们首先设计了基于离散卷积的算法并讨论了这一算法的有效性.在文章的结尾,以Slepian核密度估计作为具有平滑谱的远程信号的衰减包络的模型为例.我们考查了Slepian核及其算法的性质.为了尝试数学理论与应用的紧密联系,本文的数值试验不仅采用了模拟数据而且包括了从无线通讯用户的硬件直接采集的实际数据.  相似文献   

10.
非线性约束条件下一个超线性收敛的可行方法   总被引:3,自引:0,他引:3  
高自友  吴方 《数学学报》1997,40(6):895-900
在本文中,我们对非线性不等式约束条件下的非线性优化问题给出了一个新的SQP类可行方法.此算法不但结构简单、易于计算,并且在适当的假设条件下,我们证明了算法具有全局收敛性及超线性收敛性  相似文献   

11.
Traditional means of studying environmental economics and management problems consist of optimal control and dynamic game models that are solved for optimal or equilibrium strategies. Notwithstanding the possibility of multiple equilibria, the models’ users—managers or planners—will usually be provided with a single optimal or equilibrium strategy no matter how reliable, or unreliable, the underlying models and their parameters are. In this paper we follow an alternative approach to policy making that is based on viability theory. It establishes “satisficing” (in the sense of Simon), or viable, policies that keep the dynamic system in a constraint set and are, generically, multiple and amenable to each manager’s own prioritisation. Moreover, they can depend on fewer parameters than the optimal or equilibrium strategies and hence be more robust. For the determination of these (viable) policies, computation of “viability kernels” is crucial. We introduce a MATLAB application, under the name of VIKAASA, which allows us to compute approximations to viability kernels. We discuss two algorithms implemented in VIKAASA. One approximates the viability kernel by the locus of state space positions for which solutions to an auxiliary cost-minimising optimal control problem can be found. The lack of any solution implies the infinite value function and indicates an evolution which leaves the constraint set in finite time, therefore defining the point from which the evolution originates as belonging to the kernel’s complement. The other algorithm accepts a point as viable if the system’s dynamics can be stabilised from this point. We comment on the pros and cons of each algorithm. We apply viability theory and the VIKAASA software to a problem of by-catch fisheries exploited by one or two fleets and provide rules concerning the proportion of fish biomass and the fishing effort that a sustainable fishery’s exploitation should follow.  相似文献   

12.
Many concepts of viability theory such as viability or invariance kernels and capture or absorption basins under discrete multivalued systems, differential inclusions and dynamical games share algebraic properties that provide simple – yet powerful – characterizations as either largest or smallest fixed points or unique minimax (or bilateral fixed-point) of adequate maps defined on pairs of subsets. Further, important algorithms such as the Saint-Pierre viability kernel algorithm for computing viability kernels under discrete system and the Cardaliaguet algorithm for characterizing discriminating kernels under dynamical games are algebraic in nature. The Matheron Theorem as well as the Galois transform find applications in the field of control and dynamical games allowing us to clarify concepts and simplify proofs.  相似文献   

13.
The aim of the present analysis is to implement a relatively recent computational method, reproducing kernel Hilbert space, for obtaining the solutions of differential algebraic systems for ordinary differential equations. The reproducing kernel Hilbert space is constructed in which the initial conditions of the systems are satisfied. While, two smooth kernel functions are used throughout the evolution of the algorithm in order to obtain the required grid points. An efficient construction is given to obtain the numerical solutions for the systems together with an existence proof of the exact solutions based upon the reproducing kernel theory. In this approach, computational results of some numerical examples are presented to illustrate the viability, simplicity, and applicability of the algorithm developed. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

14.
Aircraft Take-Off in Windshear: A Viability Approach   总被引:1,自引:0,他引:1  
This paper is devoted to the analysis of aircraft dynamics during tage-off in the presence of windshear. We formulate the take-off problem as a differential game against Nature. Here, the first player is the relative angle of attack of the aircraft (considered as the control variable) and the second player is the disturbance caused by a windshear. We impose state constraints on the state variables of the game, which represents aircraft safety constraints (minimum altitude, given altitude rate). By using viability theory, we address the question of existence of an open loop control assuring a viable trajectory (i.e. satisfying the state constraints) no matter the disturbance is, i.e. for all admissible disturbances causeed by the windshear. Through numerical simulations of the viability kernel algorithm, we demonstrate the capabilities of this approach for determining safe flight domains of an aircraft during take-off within windshear.  相似文献   

15.
一种改进的密度核估计算法   总被引:1,自引:0,他引:1  
密度核估计是解决统计问题中样本分布密度函数拟合的一类非参数统计方法,在经济、金融等领域有着重要的应用价值.密度核估计重点在于研究它的算法,使其估计值相对精确.本文提出了一种密度核估计的迭代方法,并通过算例与原有的密度核估计方法进行统计模拟比较,得出迭代后的值具有较好的拟合程度,充分验证了迭代方法的可行性与优越性.  相似文献   

16.
Computing a viability kernel consumes time and memory resources which increase exponentially with the dimension of the problem. This curse of dimensionality strongly limits the applicability of this approach, otherwise promising. We report here an attempt to tackle this problem with Graphics Processing Units (GPU). We design and implement a version of the viability kernel algorithm suitable for General Purpose GPU (GPGPU) computing using Nvidia’s architecture, CUDA (Computing Unified Device Architecture). Different parts of the algorithm are parallelized on the GPU device and we test the algorithm on a dynamical system of theoretical population growth. We study computing time gains as a function of the number of dimensions and the accuracy of the grid covering the state space. The speed factor reaches up to 20 with the GPU version compared to the Central Processing Unit (CPU) version, making the approach more applicable to problems in 4 to 7 dimensions. We use the GPU version of the algorithm to compute viability kernel of bycatch fishery management problems up to 6 dimensions.  相似文献   

17.
This paper deals with output feedback control of uncertain nonlinear dynamic systems in the presence of state and control constraints. We provide necessary and sufficient conditions for the guaranteed viability property defined by the existence of a Lipschitz closed-loop that maintains exactly the state of the system in a given closed domain of constraints despite some bounded disturbances acting both on the dynamics and on the output. Using the notion of Lipschitz kernel of a closed set-valued map, we obtain some equivalent geometric and Hamilton–Jacobi–Isaac conditions for the guaranteed viability property. We derive an algorithm to build a guaranteed viable output feedback.  相似文献   

18.
In our previous works, we proposed a reproducing kernel method for solving singular and nonsingular boundary value problems of integer order based on the reproducing kernel theory. In this letter, we shall expand the application of reproducing kernel theory to fractional differential equations and present an algorithm for solving nonlocal fractional boundary value problems. The results from numerical examples show that the present method is simple and effective.  相似文献   

19.
ABSTRACT. An attempt to use viability models for studying marine ecosystems is proposed as a possible alternative to classical ecosystem modeling. Viability models do not consider optimal solutions but instead define all possible evolutions of a dynamical system under given constraints. Applied to marine ecosystems, a viability model is formulated based on the trophic coefficients of a mass‐balanced model. This requires relatively few assumptions about the processes involved and can integrate uncertainty associated with the required estimates of input parameters. An iterative algorithm is proposed to calculate the viability kernel, i.e., the envelope of all viable trajectories of the ecosystem. An application to the Benguela ecosystem is presented, considering interactions between detritus, phytoplankton, zooplankton, pelagic fish, demersal fish and fisheries. Results show how a viability kernel could be used to better define the healthy states of a marine ecosystem, by defining what states should be avoided. The paper discusses how viability models of trophic interactions could help to define a new ecosystem‐based indicator for fisheries management. It then discusses how this approach can potentially contribute to a paradigm shift that is emerging in the management of renewable resources.  相似文献   

20.
We consider the problem of open-loop viable control of a nonlinear system in Rn in the case of a nonexactly known initial state. We characterize the family of those initial sets for which the problem is solvable. The characterization employs the notion of a contingent field to a given collection of sets introduced in the paper. It also involves an appropriate set-dynamic equation that describes the evolution of the state estimation within a prescribed collection of sets. An extension of the classical concept of viability kernel with respect to this set-dynamic equation is the key tool. We present an approximation scheme for the viability kernel which is numerically realizable in the case of low dimension and simple collections of sets chosen for state estimation (balls, ellipsoids, polyhedrons, etc.). As an application, we consider a viability differential game, where the uncertainty may enter also in the dynamics of the system as an input which is not known in advance. The control is then sought as a nonanticipative strategy depending on the uncertain input.  相似文献   

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