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一般Henstock积分的支配收敛定理   总被引:1,自引:0,他引:1       下载免费PDF全文
丁传松  李秉彝 《数学学报》1994,37(4):497-506
本文给出划分空间上一般Henstock积分,最一般形式支配收敛定理、推进和概括这一方面的结论.  相似文献
2.
The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.  相似文献
3.
The numerical solution of initial value problems for ordinary differential equations is frequently performed by means of adaptive algorithms with user-input tolerance τ. The time-step is then chosen according to an estimate, based on small time-step heuristics, designed to try and ensure that an approximation to the local error commited is bounded by τ. A question of natural interest is to determine how the global error behaves with respect to the tolerance τ. This has obvious practical interest and also leads to an interesting problem in mathematical analysis. The primary difficulties arising in the analysis are that: (i) the time-step selection mechanisms used in practice are discontinuous as functions of the specified data; (ii) the small time-step heuristics underlying the control of the local error can break down in some cases. In this paper an analysis is presented which incorporates these two difficulties. For a mathematical model of an error per unit step or error per step adaptive Runge–Kutta algorithm, it may be shown that in a certain probabilistic sense, with respect to a measure on the space of initial data, the small time-step heuristics are valid with probability one, leading to a probabilistic convergence result for the global error as τ→0. The probabilistic approach is only valid in dimension m>1 this observation is consistent with recent analysis concerning the existence of spurious steady solutions of software codes which highlights the difference between the cases m=1 and m>1. The breakdown of the small time-step heuristics can be circumvented by making minor modifications to the algorithm, leading to a deterministic convergence proof for the global error of such algorithms as τ→0. An underlying theory is developed and the deterministic and probabilistic convergence results proved as particular applications of this theory. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献
4.
This paper concerns production planning in manufacturing systems with two unreliable machines in tandem. The problem is formulated as a stochastic control problem in which the objective is to minimize the expected total cost of production, inventories, and backlogs. Since the sizes of the internal and external buffers are finite, the problem is one with state constraints. As the optimal solutions to this problem are extremely difficult to obtain due to the uncertainty in machine capacities as well as the presence of state constraints, a deterministic limting problem in which the stochastic machine capacities are replaced by their mean capacities is considered instead. The weak Lipschitz property of the value functions for the original and limiting problems is introduced and proved; a constraint domain approximation approach is developed to show that the value function of the original problem converges to that of the limiting problem as the rate of change in machine states approaches infinity. Asymptotic optimal production policies for the orginal problem are constructed explicity from the near-optimal policies of the limiting problem, and the error estimate for the policies constructed is obtained. Algorithms for constructing these policies are presented.This work was partly supported by CUHK Direct Grant 220500660, RGC Earmarked Grant CUHK 249/94E, and RGC Earmarked Grant CUHK 489/95E.  相似文献
5.
本文根据有限区间上Riemann积分的Arzela控制收敛定理[1],给出无穷限积分的控制收敛定理,并做了相应的推广。  相似文献
6.
In this paper, we consider a class of optimal control problems with control and terminal inequality constraints, where the system dynamics is governed by a linear second-order parabolic partial differential equation with first boundary condition. A feasible direction algorithm for solving this class of optimal control problems has already been obtained in the literature. The aim of this paper is to improve the convergence result by using a topology arising in the study of relaxed controls.  相似文献
7.
A relaxed control problem is solved using the epsilon method of Balakrishnan. The singularity of the problem with respect to one of the controls presents no difficulty. However, solutions are sensitive to the initial guess of the states and controls. For a system with true dynamics, terminal conditions may generally be approximated, but cannot be satisfied exactly.This paper is based on the MS Thesis of K. Shmueli at the Department of Aeronautical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.  相似文献
8.
We study the potential theory of a large class of infinite dimensional Lévy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e., excessive functions with compact level sets. Then many techniques from classical potential theory carry over to this infinite dimensional setting. Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as, e.g., formulated by R. Carmona in 1980. In particular, we prove the analog of the known result, that the Cameron-Martin space is polar, in the Lévy case and apply the technique of controlled convergence to solve the Dirichlet problem with general (not necessarily continuous) boundary data.  相似文献
9.
In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We discuss the relationship between the C-Pettis integral and Pettis integral, and prove a controlled convergence theorem for the C-Pettis integral.  相似文献
10.
本文利用实变函数方法详细证明了Riemann?Lebesgue 定理在开集上成立,并且给出了其应用。  相似文献
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