In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1‖max-ΣT j and for the problem of maximizing the number of tardy jobs 1‖maxΣU j . In both cases, it is assumed that the processing of the first job starts at time zero and there is no idle time between the jobs. We show that problem 1‖max-ΣT j is polynomially solvable. For several special cases of problem 1‖maxΣT j , we present exact polynomial algorithms. Moreover, we give an exact pseudo-polynomial algorithm for the general case of the latter problem and an alternative exact algorithm.

While the problem of hierarchical menu design is very common in user interface design, existing approaches lack either semantic aspects or optimization techniques. We suggest a semantic-aware mathematical model of hierarchical menu optimization and algorithms developed on the basis of this theory. These algorithms are implemented in the ready-to use design tool. The approach is illustrated by optimization of a banking voice menu. Original Russian Text © A.I. Danilenko, M.V. Goubko, 2012, published in Problemy Upravleniya, 2012, No. 2, pp. 38–44. Первоначальный русский текст опубликован в журнале "Проблемы управления", № 2, 2012, С. 38-44 и доступен по адресу http://www.mtas.ru/search/search_results.php?publication_id=18742

We present, a unified methodology, models, and design methods for optimal modular information control systems for a special class of objects, namely space vehicles. We develop methods arid instruments for creating modular software and dataware for an onboard control unit on a space vehicle.

We consider the problem of ensuring the invariance property for a linear stationary sustem with relay controls. In the case of perfect relays, wide class exogenous disturbances are compensated theoretically on the basis of sliding mode theory. Existing imperfections of relay elements make it impossible to implement a perfect sliding mode; thus, the closed-loop system has dynamics in a zero neighborhood of the given variety. This causes undesirable oscillations in a steady-state mode ("chattering"), leading to missed invariance with respect to exogenous and parametric disturbances. This paper solves the problem of ensuring invariance under imperfect relay elements and involves two approaches. The first one allows for making the relay characterstic close to that of the perfect counterpart; consequently, the chattering problem is eliminated. The second approach proceeds from the high-frequency modulation principle and performs regularization of relay switchings; using the linearization effect for the relay characteristics, the second approach guarantees the invariance property.

Consideration was given to the functional decomposition of the discrete systems which is reducible to the functional decomposition of the discrete functions, where by the decomposition is meant the representation of a function by a formula in the basis of unary and binary operations. The algebraic decomposition in an algebra consisting of two binary operations and functions of two variables was studied. A procedure of formula design on the basis of composition of repetition-free subformulas was substantiated. Both exact and asymptotic complexity estimates of the designed formulas were given.