Discrete Points In Space Research Articles

Modelling techniques for optimal control of distributed parameter systems

A direct method for solving optimal control problems by parameterizing control variables is considered. This control parameterization technique is formulated for controlling a class of self-adjoint distributed parameter systems using open-closed loop forces applied at discrete points in space. In particular, optimal control of flexible continuous structures is studied with the objective of minimizing a given performance index over a prescribed time interval. The performance index of the problem is taken as a combination of the total energy of the structure and the penalty terms on the expenditure of the open-closed loop forces used in the control process. The control is to be implemented by discrete sets of displacement sensors (closed-loop forces) and force actuators (open-loop forces) that monitor the response of the structure. In contrast to variational methods, a direct application of control parameterization is used in this study. The method is based on polynomial (or trigonometric function) approximation of each open-loop control variable that converts the linear quadratic problem into a mathematical programming problem, where the necessary condition of optimality is derived as a system of linear algebraic equations. Furthermore, the optimal feedback parameters of the closed-loop control forces are numerically determined from the solution of the total energy minimization problem. The effectiveness of the method is demonstrated by applying it to an example of a simply supported beam subject to initial disturbances.

How to Eliminate Certain Defects of the Potential Formula

The potential formula, defined as a sum of regional ‘masses’ weighted by a decreasing function of distance, is a conventional indicator of accessibility in spatial econometrics. If applied to a system of discrete points in space, however, the standard potential formula with an exponential distance-friction does not convey the desired information in the case of sufficiently large distance-friction parameters. The reason for this defect is that the so-called eigenpotential is inappropriately defined by the standard formula. After reviewing the theoretical foundations of the potential index and advocating its derivation from stochastic choice theory, this paper proposes a modification of the potential formula. The basic idea is to handle the region to which the potential refers as a continuous space with equally distributed density of mass. This leads to an index with desirable limiting properties with respect to the distance-friction parameter.

WHEN A RESIDENCE IS NOT A HOUSE: EXAMINING RESIDENCE-BASED MIGRATION DEFINITIONS

Traditional definitions of migration contain implicit assumptions: origin and destination places are fixed residences, households inhabit one residence at any given time, and dwelling units form the center of individual activity spaces. Though these assumptions hold for certain movers, they restrict migration studies to a narrow range of movement. It is argued here that such assumptions bias present notions of migrant behavior and selectivity. A more realistic appraisal might consider integration in sets of spatial networks rather than movement between two discrete points in space.