Simple Localization Problem Research Articles

Can a Skywalker Localize the Midpoint of a Rope?

This article poses a question about a simple localization problem. The question is if an oblivious walker on a line segment can localize the midpoint of the line segment in a finite number of steps observing the direction (i.e., Left or Right) and the distance to the nearest end point. This problem arises from self-stabilizing location problems by autonomous mobile robots with limited visibility , which is an abstract model attracting a wide interest in distributed computing. Contrary to appearances, it is far from trivial whether this simple problem is solvable, and it is not settled yet. This article is concerned with three variants of the problem with a minimal relaxation and presents self-stabilizing algorithms for them. We also show an easy impossibility theorem for bilaterally symmetric algorithms.

An Intelligent Decision Support System Based on Human–Machine Interaction and Dynamic Track of Psychological Evaluation Criterion

ABSTRACT An Intelligent Decision Support System based on man–machine Interaction and Dynamic Track of Psychological Evaluation Criterion is presented in this article. It is shown that a complex decision for a global situation can be disassembled into a series of simple local problems, from which the most satisfactory decision for the local can be found out by individual ways, respectively. At the lower level of total score, the best decision for the local, according to the mathematical interpretation of weight, can be considered as the decision whose distribution of scores is just consistent with the distribution of the psychological weight (or preference) of a decision-maker. At a series of moderate levels, the evaluation criterion is given by human–machine interaction, in which some satisfactory samples are chosen by a decision-maker from a lot of samples, and the barycenter of criterion and the radius of criterion can be estimated by a learning algorithm. In this way the most satisfactory decision for the local made by the decision-maker at each level can be tracked. If we let the collection of satisfactory decisions for the global be the union of the local's most satisfactory decision at all levels, the changing process of psychological criteria, which varies with the change of total score, can be deduced. Finally, a satisfied degree function with which the global consistency of the collection of the local's satisfactory decisions at all levels is given, and a global ranking approach based on the function is presented as well.

Landing system verification based on petri nets and a hybrid approach

One of the most important activities of control system design is its verification. Verification ensures that the controlled system will behave as expected under any circumstances it may operate. In this context, the purpose of this paper is to introduce a new method for the verification of aircraft control systems. The focus of this method is on aircraft systems that are characterized as hybrid, i.e., that merge continuous and discrete dynamics. The method proposed is divided into two main parts: the system modeling and the verification of behavioral properties. In the first part, Petri net, differential equation systems, and object oriented concepts are used concurrently in order to model complex hybrid systems. In the second part, the distributed nature of the model is explored in order to decompose a complex verification problem into series of simple local problems. Linear logic is used as a basis of a theorem-proving approach for the verification from the discrete-event point of view. The verification method has been applied to a number of case studies. Among them is the landing system of a military aircraft, which is described in this paper

Adaptive analysis based on error estimation for nonlocal damage models

An adaptive finite element strategy for nonlocal damage computations is presented. The proposed approach is based on the combination of a residual-type error estimator and quadrilateral h-remeshing. A distinctive feature of the error estimator is that it consists in solving simple local problems over elements and so-called patches. The paper focuses on how the nonlocality of the constitutive model should be accounted for when solving these local problems. It is shown that the nonlocal damage models must be slightly modified. The resulting adaptive strategy is illustrated by means of some numerical examples involving the single-edge notched beam test.

Localization Analysis of Nonlocal Model Based on Crack Interactions

The conventional nonlocal model, often used as a localization limiter for continuum‐based constitutive laws with strain‐softening, has been based on an isotropic averaging function. It has recently been shown that this type of nonlocal averaging leads to a model that cannot satisfactorily reproduce experimental results for very different test geometries without modifying the value of the characteristic length depending on geometry. A micromechanically based enrichment of the nonlocal operator by a term taking into account the directional dependence of crack interactions can be expected to improve the performance of the nonlocal model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one‐dimensional description. Strain localization in an infinite layer under plane stress is studied using both the old and the new nonlocal formulations. The importance of a renormalization of the averaging function in the proximity of a boundary is demonstrated ...

Nonlocal Model Based on Crack Interactions: A Localization Study

A micromechanically based enrichment of the nonlocal operator by a term taking into account the directional dependence of crack interactions (Bazˇant, 1992) can be expected to improve the performance of the nonlocal model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one-dimensional description. Strain localization in an infinite layer under plain stress is studied using both the old and the new nonlocal formulations. The importance of renormalization of the averaging function in the proximity of a boundary is demonstrated and the differences between the localization sensitivity of the old and new model are pointed out.

Economic Development of Groundwater in Arid Zones with Applications to the Negev Desert, Israel

A mixed binary integer linear program is formulated to determine the economic development of marginal groundwater sources at local demand sites in an arid region. These marginal sources are required to augment the supply from an overloaded regional source. The model accounts for variable costs of supply, fixed investment costs, capacity constraints at the regional and local levels, and water quality requirements at the local sites. A Lagrangian relaxation reduces the model to a series of simple local problems, the solution of which provides an optimal sequence for developing the marginal groundwater sources while reducing the demands on the regional source. A heuristic and an exact procedure are also proposed to solve the problem for arbitrary levels of supply from the regional source. The exact procedure uses characteristics of the optimal solution to reduce the model to a series of knapsack-type problems. The theory is applied to a small case study taken from the Negev Desert in southern Israel.