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Matching Problem (matching + problem)

Distribution by Scientific Domains

Mathematics and Statistics	50%
Engineering	50%

Selected Abstracts

Linear, parameter-varying control and its application to a turbofan engine

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2002
Gary J. BalasArticle first published online: 15 JUL 200
This paper describes application of parameter-dependent control design methods to a turbofan engine. Parameter-dependent systems are linear systems, whose state-space descriptions are known functions of time-varying parameters. The time variation of each of the parameters is not known in advance, but is assumed to be measurable in real-time. Three linear, parameter-varying (LPV) approaches to control design are discussed. The first method is based on linear fractional transformations which relies on the small gain theorem for bounds on performance and robustness. The other methods make use of either a single (SQLF) or parameter-dependent (PDQLF) quadratic Lyapunov function to bound the achievable level of performance. The latter two techniques are used to synthesize controllers for a high-performance turbofan engine. A LPV model of the turbofan engine is constructed from Jacobian linearizations at fixed power codes for control design. The control problem is formulated as a model matching problem in the ,, and LPV framework. The objective is decoupled command response of the closed-loop system to pressure and rotor speed requests. The performance of linear, ,, point designs are compared with the SQLF and PDQLF controllers. Nonlinear simulations indicate that the controller synthesized using the SQLF approach is slightly more conservative than the PDQLF controller. Nonlinear simulations with the SQLF and PDQLF controllers show very robust designs that achieve all desired performance objectives. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A generalization of the weighted set covering problem

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2005
Jian Yang
Abstract We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b -matching problem. In general, we may use a polynomial-time greedy heuristic similar to the one for the classical weighted set covering problem studied by D.S. Johnson [Approximation algorithms for combinatorial problems, J Comput Syst Sci 9 (1974), 256,278], L. Lovasz [On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383,390], and V. Chvatal [A greedy heuristic for the set-covering problem, Math Oper Res 4(3) (1979), 233,235] to get an approximate solution for the problem. We find a worst-case bound for the heuristic similar to that for the classical problem. In addition, we introduce a general type of probability distribution for the population of the problem instances and prove that the greedy heuristic is asymptotically optimal for instances drawn from such a distribution. We also conduct computational studies to compare solutions resulting from running the heuristic and from running the commercial integer programming solver CPLEX on problem instances drawn from a more specific type of distribution. The results clearly exemplify benefits of using the greedy heuristic when problem instances are large. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005 [source]

The ,(2) limit in the random assignment problem

RANDOM STRUCTURES AND ALGORITHMS, Issue 4 2001
David J. Aldous
Abstract The random assignment (or bipartite matching) problem asks about An=min,,,c(i,,,(i)), where (c(i,,j)) is a n×n matrix with i.i.d. entries, say with exponential(1) distribution, and the minimum is over permutations ,. Mézard and Parisi (1987) used the replica method from statistical physics to argue nonrigorously that EAn,,(2)=,2/6. Aldous (1992) identified the limit in terms of a matching problem on a limit infinite tree. Here we construct the optimal matching on the infinite tree. This yields a rigorous proof of the ,(2) limit and of the conjectured limit distribution of edge-costs and their rank-orders in the optimal matching. It also yields the asymptotic essential uniqueness property: every almost-optimal matching coincides with the optimal matching except on a small proportion of edges. ©2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 381,418, 2001 [source]

A structural optimization method based on the level set method using a new geometry-based re-initialization scheme

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010
Shintaro Yamasaki
Abstract Structural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so-called Hamilton,Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re-initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry-based re-initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd. [source]