Том 80, № 8 (2019)

We distinguish a subclass of switched linear systems that we call pairwise connected. We show that the dynamics of such systems can be described by Lur’e systems. For pairwise connected systems, we obtain a sufficient frequency-domain condition for the existence of a quadratic Lyapunov function. The well-known Aizerman problem is reformulated for switched linear systems. We show an example of a system with switchings between three linear third order subsystems for which Aizerman’s problem has a positive solution.

We consider the possibilities of using stochastic approximation algorithms with randomization on the input under unknown but bounded interference in studying the clustering of data generated by a mixture of Gaussian distributions. The proposed algorithm, which is robust to external disturbances, allows us to process the data “on the fly” and has a high convergence rate. The operation of the algorithm is illustrated by examples of its use for clustering in various difficult conditions.

We consider a generalization of processes with disorder, namely processes with a vector disorder. For these problems, we consider a class of optimal control problems that do not detect the disorder. We propose a computational method for solving control problems on a finite time interval and with an objective functional defined at the end of the interval, based on the use of the martingale technique. We consider a computational experiment for a model with two barriers and two stopping times.

With the use of quaternions and the maximum principle, we solve the optimal orbit transfer problem for a variable-mass spacecraft to a given plane in a nonlinear setting. The motion control of the spacecraft is carried out with the help of a jet thrust, bounded in absolute value and orthogonal to the plane of the osculating spacecraft orbit. We take into account the change in mass of the spacecraft due to the consumption of the working fluid in the control process. The functional that determines the quality of the control process is a linear convolution with weight factors for two criteria: time and total thrust impulse spent on the control process.

We provide an exposition of the theory of the problem’s solution. We show results of optimal control calculations for cases when both criteria are simultaneously taken into account in the minimized combined quality functional of the control process, and for cases when only the total thrust impulse is minimized. We obtain examples of optimal control with up to 192 passive and active stages. We also establish optimal control laws for the rotation of the spacecraft’s orbital plane.

Based on the global Krotov successive improvement method, we propose a dual computational algorithm for a discrete optimal control problem corresponding to a convex large-scale quadratic programming problem with a separable functional that arises in the prediction of the direct costs (structural) matrix in dynamic input-output models. With decomposition, we are able to use a special form of the constraint matrix to reduce the problem dimension.

The formal problem to estimate the complexity of a scene with numerous obstacles and mobile objects is considered. By assumption there is only limited information on the location of obstacles in a small part of the scene, which is obtained by the sensor systems of one or more objects. Upper and lower bounds for the complexity of the scene are derived for one and two observations of the local domains.

We propose an accelerated gradient-free method with a non-Euclidean proximal operator associated with the p-norm (1 ⩽ p ⩽ 2). We obtain estimates for the rate of convergence of the method under low noise arising in the calculation of the function value. We present the results of computational experiments.

In this paper, asymmetric regular resource networks with several attractor vertices are considered. It is demonstrated that the resource surplus ΔW = W − T above a threshold value W = T has the same allocation in such a network as in the corresponding absorbing network, which is obtained from the asymmetric one by eliminating the outbound edges of attractors. But there exist corrections depending on the capacities of the outbound edges of attractors and also on the initial resource allocation. Upper bounds of these corrections are derived. The initial states that lead to the exact limit states without any adjustments are determined.

This paper considers a cooperative game in which the distance (or similarity) between some objects (players) can be measured numerically. For this game, a characteristic function is defined so that it takes high values for the coalitions consisting of most close (similar) players in comparison with the players from the other coalitions. Such a function does not satisfy superadditivity, and hence it seems reasonable to introduce the model with coalition structure. Therefore, this game can be treated as a clustering procedure for objects (players). Finally, the existence conditions of a stable coalition structure are established, which allow to perform efficient (crisp) clustering.

The specificity of concrete products (CP) plants planning and scheduling is discussed. Design concepts of work schedules for such facilities are examined. Operation principles of scheduling algorithms are described.

Methods are considered of an approximate solution of the static problem of forming the optimal aircraft queue for landing, which do not guarantee an accurate solution but provide an opportunity to obtain an acceptable solution that meets the requirements. It is noted that typically they are a synthesis of a meta-heuristic method of global optimization to obtain the landing sequence of aircraft and a local exact method to find the optimal solution for the sequences obtained. The brief overview of some of them is presented.