On open-loop and feedback attainability of a closed set for nonlinear control systems

In this note, we investigate the existence of controls which allow to reach a given closed set K through trajectories of a nonlinear control system. In the case where the set is sufficiently regular we give a condition allowing to find a feedback control law which ensures the existence of trajectories to reach the set. We also consider the case where all the trajectories reach K. When K is not necessarily attainable but only viable, we build a set-valued feedback for which the set is invariant. Our approach concerns continuous dynamics, possibly not C¹, so our methods do not come from geometric control theory. Furthermore, we do not require any regularity of the set K in order to obtain our results, except when we want to establish the existence of a feedback control law to achieve our goals.     

Evaluating Recruitment Strategies Using Fuzzy Set Theory in Stochastic Manpower Planning

Abstract

One aspect of Manpower Planning is the investigation of wastage and internal transitions for homogeneous groups of employees in a Manpower system. In the relevant literature, the attainability of a desired stock vector was studied under control by recruitment for time-discrete Markov models. These approaches allow choosing a proper recruitment strategy, resulting in an attainable vector most similar to a desired one. In this article, this problem will be discussed under stochastic assumptions for attainability after one step. Based on fuzzy set theory, a procedure is introduced that allows evaluating and comparing recruitment strategies, resulting in the determination of a most preferable strategy.     

Norm Attainability of Elementary Operators and Derivations

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Prospective control in an enhanced manpower planning model

The present paper deals with the exercise of recruitment control to a time dependent, hierarchical system which incorporates training classes as well as two streams of recruitment; one coming from the outside environment and another from an auxiliary external system. The motivation for this model lies in the need to take into account not only the tendency of the employees to attend seminar courses so as to improve their career prospects, but also the organizations’ intention to avoid situations associated with the unavailability of skilled individuals for hiring. For the suggested model, we define its attainable structures and the sets containing these structures, i.e. attainable sets. We examine the geometrical properties of these sets and it is proved that they form convex polytopes. Moreover, by adopting the equivalent approach of describing convex polyhedral sets via inequalities, we specify the attainable sets of the model for every time point t. An illustrative example follows.