共查询到20条相似文献,搜索用时 31 毫秒
1.
《Applied Mathematical Modelling》2005,29(11):1135-1148
We treat the sliding mode control problem by formulating it as a two phase problem consisting of reaching and sliding phases. We show that such a problem can be formulated as bicriteria nonlinear programming problem by associating each of these phases with an appropriate objective function and constraints. We then scalarize this problem by taking weighted sum of these objective functions. We show that by solving a sequence of such formulated nonlinear programming problems it is possible to obtain sliding mode controller feedback coefficients which yield a competitive performance throughout the control. We solve the nonlinear programming problems so constructed by using the modified subgradient method which does not require any convexity and differentiability assumptions. We illustrate validity of our approach by generating a sliding mode control input function for stabilization of an inverted pendulum. 相似文献
2.
A. G. Khovanskii 《Proceedings of the Steklov Institute of Mathematics》2007,259(1):82-100
We discuss the problem of representability and nonrepresentability of algebraic functions by radicals. We show that the Riemann
surfaces of functions that are the inverses of Chebyshev polynomials are determined by their local behavior near branch points.
We find lower bounds on the degrees of equations to which sufficiently general algebraic functions can be reduced by radicals.
We also begin to classify rational functions of prime degree whose inverses are representable by radicals. 相似文献
3.
We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class
queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear
program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained.
We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between
the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues.
We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically
optimal when the number of items that is processed and the processing speed increase. We illustrate these results through
a simple example of a three stage re-entrant line.
Research supported in part by Israel Science Foundation Grant 249/02 and 454/05 and by European Network of Excellence Euro-NGI. 相似文献
4.
We consider the linear regression model with Gaussian error. We estimate the unknown parameters by a procedure inspired by
the Group Lasso estimator introduced in [22]. We show that this estimator satisfies a sparsity inequality, i.e., a bound in
terms of the number of non-zero components of the oracle regression vector. We prove that this bound is better, in some cases,
than the one achieved by the Lasso and the Dantzig selector.
相似文献
5.
We study the operad of finite labeled tournaments. We describe the structure of suboperads of this operad generated by simple tournaments. We prove that a suboperad generated by a tournament with two vertices (i.e., the operad of finite linearly ordered sets) is isomorphic to the operad of symmetric groups, and a suboperad generated by a simple tournament with more that two vertices is isomorphic to the quotient operad of the free operad with respect to a certain congruence. We obtain this congruence explicitly. 相似文献
6.
We consider the linear parabolic equation describing the transport of a contaminant in a porous media crossed by a net of infinitely thin fractures. The permeability is very high in the fractures but very low in the porous blocks. We derive the homogenized model corresponding to a net of infinitely thin fractures, by means of the singular measures technique. We assume that these singular measures are supported by hyperplanes of codimension one. We prove in a second step that this homogenized model could be obtained indistinctly either by letting the fracture thickness, in the standard double porosity model, tend to zero, or by homogenizing a model with infinitely thin fractures. 相似文献
7.
We study various methods of aggregating individual judgments and individual priorities in group decision making with the AHP. The focus is on the empirical properties of the various methods, mainly on the extent to which the various aggregation methods represent an accurate approximation of the priority vector of interest. We identify five main classes of aggregation procedures which provide identical or very similar empirical expressions for the vectors of interest. We also propose a method to decompose in the AHP response matrix distortions due to random errors and perturbations caused by cognitive biases predicted by the mathematical psychology literature. We test the decomposition with experimental data and find that perturbations in group decision making caused by cognitive distortions are more important than those caused by random errors. We propose methods to correct the systematic distortions. 相似文献
8.
M. Stojanović 《分析论及其应用》1996,12(2):86-98
We perform analysis for a finite elements method applied to the singular self-adjoint problem. This method uses continuous
piecewise polynomial spaces for the trial and the test spaces. We fit the trial polynomial space by piecewise exponentials
and we apply so exponentially fitted Galerkin method to singular self-adjoint problem by approximating driving terms by Lagrange
piecewise polynomials, linear, quadratic and cubic. We measure the erroe in max norm. We show that method is optimal of the
first order in the error estimate. We also give numerical results for the Galerkin approximation. 相似文献
9.
《Journal of Algorithms in Cognition, Informatics and Logic》1995,19(3):402-431
We examine the probability distribution of the number of comparisons needed by the Quicksort sorting algorithm, where probability arises due to the items being in random order. We develop a general class of distributions for the permutation of the items to be sorted which includes the uniform distribution on permutations as a special case. For this general class, the distribution of the number of comparisons is given by the solution of a simple recurrence relation. We provide an exact solution of the recurrence for very small n. We show that the solution can be approximated asymptotically by the solution of a "quadratic" operator equation. We exhibit three numerical solutions to the operator equation for two different distributions on permutations from the general class. We also exhibit numerical solutions for the case in which the algorithm is modified so that arrays are partitioned by the median-of-three selected items rather than by a single selected item. 相似文献
10.
Classifying Integrable Egoroff Hydrodynamic Chains 总被引:1,自引:0,他引:1
We introduce the notion of Egoroff hydrodynamic chains. We show how they are related to integrable (2+1)-dimensional equations of hydrodynamic type. We classify these equations in the simplest case. We find (2+1)-dimensional equations that are not just generalizations of the already known Khokhlov–Zabolotskaya and Boyer–Finley equations but are much more involved. These equations are parameterized by theta functions and by solutions of the Chazy equations. We obtain analogues of the dispersionless Hirota equations. 相似文献
11.
V. I. Grunskaya 《Russian Mathematics (Iz VUZ)》2009,53(8):15-19
In this paper we study mosaic labyrinths with the help of words generated by them in the alphabet of labels attached to arcs and vertices of a labyrinth. We consider the problem of the characterization of words generated by a labyrinth. We propose a constructive recognition criterion, it defines whether a word is generated by a labyrinth or not. We establish conditions under which a word can be generated by a unique labyrinth, by a finite number of labyrinths, or by infinitely many labyrinths. 相似文献
12.
We develop an interactive approach for multiobjective decision-making problems, where the solution space is defined by a set of constraints. We first reduce the solution space by eliminating some undesirable regions. We generate solutions (partition ideals) that dominate portions of the efficient frontier and the decision maker (DM) compares these with feasible solutions. Whenever the decision maker prefers a feasible solution, we eliminate the region dominated by the partition ideal. We then employ an interactive search method on the reduced solution space to help the DM further converge toward a highly preferred solution. We demonstrate our approach and discuss some variations. 相似文献
13.
《Optimization》2012,61(1-2):95-114
We solve an optimal control problem for controlled parabolic Ito equations by a stochastic quasigradient method. Because of high amounts of computation time required by numerical solution of such problems we investigate the parallelization of the algorithm. We distribute the computations of space stages over several processor nodes of a parallel computer. We obtain an efficient algorithm with low communication cost by using a ring topology 相似文献
14.
Securitizing and tranching longevity exposures 总被引:1,自引:0,他引:1
We consider the problem of optimally designing longevity risk transfers under asymmetric information. We focus on holders of longevity exposures that have superior knowledge of the underlying demographic risks, but are willing to take them off their balance sheets because of capital requirements. In equilibrium, they transfer longevity risk to uninformed agents at a cost, where the cost is represented by retention of part of the exposure and/or by a risk premium. We use a signalling model to quantify the effects of asymmetric information and emphasize how they compound with parameter uncertainty. We show how the cost of private information can be minimized by suitably tranching securitized cashflows, or, equivalently, by securitizing the exposure in exchange for an option on mortality rates. We also investigate the benefits of pooling several longevity exposures and the impact on tranching levels. 相似文献
15.
We study the interpolation procedure of Gomory and Johnson (1972), which generates cutting planes for general integer programs
from facets of cyclic group polyhedra. This idea has recently been re-considered by Evans (2002) and Gomory, Johnson and Evans
(2003). We compare inequalities generated by this procedure with mixed-integer rounding (MIR) based inequalities discussed
in Dash and Gunluk (2003). We first analyze and extend the shooting experiment described in Gomory, Johnson and Evans. We
show that MIR based inequalities dominate inequalities generated by the interpolation procedure in some important cases. We
also show that the Gomory mixed-integer cut is likely to dominate any inequality generated by the interpolation procedure
in a certain probabilistic sense. We also generalize a result of Cornuéjols, Li and Vandenbussche (2003) on comparing the
strength of the Gomory mixed-integer cut with related inequalities. 相似文献
16.
Frank Natterer Olga Klyubina 《计算数学(英文版)》2007,25(3):368-373
We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging. 相似文献
17.
A. Anthony Eldred P. Veeramani 《Journal of Mathematical Analysis and Applications》2007,336(2):751-757
We consider two generalizations of Nadler's theorem, one proved by Mizoguchi and Takahashi in response to the Reich conjecture and another theorem proved by Kaneko. We show that due to the additional conditions of these theorems the given multi-valued map reduces to a multi-valued contraction map. We prove this result by showing that the orbit of the multi-valued map is bounded under the contractive conditions of the two generalizations. 相似文献
18.
A. Luisa Elgueta Melitta Fiebig-Wittmaack Maria Teresa Villacran 《Applicable analysis》2013,92(3-4):359-367
We approximate a Duffing equation by an averaged system. We solve the system explicitely and draw bifurcation diagrams in dependence of the forcing term. We discuss the goodness of the averaging method, relative to the behavior of the solutions in dependence of involved parameters, by comparing with results obtained in [6,10] for the original Duffing equation. 相似文献
19.
We solve by finite difference method an optimal control problem of a system governed by a linear elliptic equation with pointwise control constraints and non-local state constraints. A discrete optimal control problem is approximated by a minimization problem with penalized state equation. We derive the error estimates for the distance between the exact and regularized solutions. We also prove the rate of convergence of block Gauss–Seidel iterative solution method for the penalized problem. We present and analyze the results of the numerical experiments. 相似文献
20.
Guo-jingWang Su-pingQian RongWu 《应用数学学报(英文版)》2003,19(3):521-528
In this paper we consider the risk process described by a piecewise deterministic Markov processes(PDMP). We mainly discuss the distribution of the deficit at ruin for the risk process. We derive the integrodifferential equation satisfied by this distribution. We obtain the explicit expressions for it for certain choices of the claim amount distribution. 相似文献