A non-stationary problem of group pursuit

A linear non-stationary conflict-interaction problem for controlled objects with n pursuers and m evaders with equal dynamical potency of each participant is considered. The objective of the pursuers is to capture all the evaders; the objective of the evaders is to avoid overtaking of at least one of them. Sufficient conditions for the global evasion problem solvability are stated.     

Problems of group pursuit with integral constraints on controls of the players. I

The paper studies problems of group pursuit for linear differential games with integral constraints. The problems are analyzed on the basis of Chikrii’s method of resolving functions. The proposed method substantiates the parallel approach strategy, i.e., the Π-strategy. The new sufficient solvability conditions are obtained for problems of group pursuit. As an example, two classes of problems are considered, namely, the Pontryagin control example and a group pursuit with a simple motion for the case of “l-catch.”     

一类具有资源约束和恶化效应的单机成组排序问题

讨论具有连续资源的单机成组排序问题.这一模型中同一组内的工件不允许分开加工,各工件组的安装时间是所消耗资源的非负减少连续函数.工件的加工时问是开工时问的严格减少函数.针对满足资源消耗总量限制条件下极小化最大完工时问的问题.以及在满足最大完工时间限制条件下极小化资源消耗总量的问题,讨论了最优排序的某些特征,分别给出了求解最优资源分配的方法.最后通过数值例子表明了所提出方法的正确性和有效性.     

On the “soft” capture in one group pursuit problem

For the generalized L.S. Pontryagin example, sufficient conditions for a “soft” capture of one evader by a group of pursuers are obtained.     

Positional group pursuit

A general scheme is proposed deriving different types of sufficient conditions for a group pursuit starting from given initial positions to terminate in a finite time. The results are applied to some examples of group pursuit.Translated from Kibernetika, No. 1, pp. 55–62, January–February, 1989.     

Linear regression with nonstationary variables and constraints on its parameters

The problem of estimating parameters of a linear regression with allowance for inequality constraints on the parameters is considered in the special case when its variables have a trend. A parameter estimation algorithm is described. The consistency of parameter estimates is proved and their asymptotic distribution is found. Consistent estimates are proposed for the mean-square error matrix of estimates of regression parameters and noise dispersion under rather general assumptions on the law of noise distribution. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 50–64, May–June 2009.     

A problem of group pursuit in the class of impulse strategies of pursuers

For the generalized Pontryagin example, sufficient conditions of caption of one evader by a group of pursuers are obtained under the condition that the pursuers use impulse strategies.     

Simple pursuit of one evader by a group

The pursuit of one evader by a group of controlled pursuers is considered for the case of simple motion of the players in nonempty compact sets. Sufficient solvability conditions are derived. These conditions are sometimes also necessary.Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 131–137, May–June, 1992.     

On a parallel machine scheduling problem with precedence constraints

We characterize a nontrivial special case with a polynomial-time algorithm for a well-known parallel machine scheduling problem with precedence constraints, with a fixed number of machines, and with tasks of unit length. The special case is related to instances with given maximum path length and maximum degree of the task precedence graph. The method is based on the observation that the number of tasks is either small and bounded by a constant depending on the maximum path length and maximum degree, or alternatively, the number of tasks is large, giving a “dense” schedule.     

The analytical method to solve nonstationary differential games of pursuit

The game problem of pursuit is studied for dynamic processes evolving under uncertainty and counteraction. The terminal set is supposed to be a cylindrical set-valued mapping. The method of resolving functions is used to establish the sufficient conditions for the game termination in the class of quasi- and stroboscopic strategies for various schemes of the method. The guaranteed times are compared. The results are illustrated using the model with integral control unit and game problems with simple motion.     

On a differential game with integral and phase constraints

Consideration is given to a differential game on the plane when the moves of a pursuer and a running away are described by equations of the simple move, and integral constraints are imposed on control functions. In the process of the game the pursuer moves within the prescribed closed convex subset of the plane and the running away moves along its boundary. In the case when the running away has an advantage of resources, the development is made of the runaway strategy that affords the lower bound for the distance between the players. In the case when the pursuer has an advantage of resources, for any initial positions of the players the optimal time of pursuit is found and optimal strategies of the players are set up.     

Time-optimal control in a single machine problem with resource constraints

The paper deals with time-optimal control of performance of jobs on a single machine. It is assumed that each job is available for processing at the moment which is a positive strictly decreasing continuous function with respect to the amount of a constrained resource (e.g. fuel, raw materials). An algorithm of finding the time-optimal control, i.e. time-optimal permutation of jobs with resource allocation, is presented.     

On the generalized Wolf problem: Preprocessing of nonnegative large-scale linear programming problems with group constraints

Nonnegative large-scale linear programming problems with group constraints are extremely important for different applications in economics, technology, and other spheres. In this paper, we describe a new approach to preprocessing of these problems so that to reduce their dimensions considerably by defining and removing redundant constraints and variables.     

一类资源约束的单机成组调度问题

本文讨论具有连续资源的单机成组调度问题.在这一模型中,工件组的安装时间是所消耗资源的非负严格减少连续函数,工件的加工时间是开工时间的严格增加函数.考虑两个问题,第1个问题是在满足资源消耗总量限制条件下,极小化最大完工时间.第2个问题的目标函数是在满足最大完工时间限制条件下,极小化资源消耗总量.分别对两个问题讨论了最优调度的某些特征,分别给出了求解最优资源分配的方法,并通过数值例子进行说明.