Vol 56, No 6 (2017)

For the linear regression model, the data-fitting problem under the interval uncertainty of the data is studied. As an estimate of the linear function parameters, it is proposed to take their values that deliver the maximum for the so-called recognizing functional of the parameter set compatible with the data (the maximum compatibility method). The properties of the recognizing functional, its interpretation, and the properties of the estimates obtained using the maximum compatibility method are investigated. The relationships to other data analysis methods are discussed, and a practical electrochemistry problem is solved.

The optimal control problem for discrete deterministic time-invariant automaton systems under parametric uncertainty is considered. The changes in the state (switching) of the system are described by a recurrence equation. The switching times and their number are not specified in advance—they are found by optimization. The initial state of the system is not known exactly. For this reason, the problems of finding the optimal on the average and the optimal guaranteeing (minimax) controls of bunches of trajectories are formulated. It is proposed to solve these problems using the separation principle, which assumes that the bunch is controlled using the control that is optimal for a specially chosen individual trajectory in the bunch. Generally, this control is suboptimal. Algorithms for the synthesis of suboptimal control of bunches are developed. It is proved that, in the linear-quadratic time-invariant problems, the suboptimal bunch control is optimal on the average or is the optimal minimax control, depending on the problem being solved.

We consider discrete optimization problems with Boolean variables and rarefied matrices of large dimensions. In some cases we manage to extract the quasi-block structure of the initial matrices. In particular, in this paper we have problems with the so-called block-stair and block-tree structures. Blocks in such problems have connecting variables with other blocks. We present the parallelization of such large problems on GRID systems, where problems for separate blocks are solved independently of one another, and the initial problems cannot be directly solved due to the unacceptably large time requirements.

This paper considers a concept for developing and managing professional virtual environments using a software tool. We propose managing the logical model of a virtual environment by a new extended ontology. We also introduce a control technology for 3D scenes based on a virtual environment model representation. Finally, we describe a mechanism to create and manage specific handling functions of virtual environments and also to interpret and launch a virtual environment with integrity checking.

A dynamic network flow model for analyzing aggregated energy supply processes, including the extraction, processing, transport, transformation, and redistribution of the main fuel and energy resources is prorosed. The changes in the functional characteristics of the energy system under large-scale disturbances are analyzed. The model is used to identify control strategies for energy flows in a damaged network. During optimization calculations, the set of problems on a single-product flow of the minimum value is solved. In addition, the software system based on the proposed model is described. The software system has an option to specify the locations of damage and scenarios for the subsequent restoration of network elements with the aim of fulfilling the user demands on the amount of energy supply. The proposed approach can be used to analyze the functional vulnerability of spatially distributed resource supply systems.

In this paper, the theory and methods of solving the vector problem of mathematical programming with equivalent criteria and with a given criterion priority are presented. The question of the dimension of the problem is studied; here, in its solution and geometrical interpretation, methods with a criterion priority are used. The methodology, the problem-solving methods, and optimal decision making are demonstrated by the test example in the MATLAB system.

A method is developed for constructing a three-dimensional digital surface model based on the use of aerial images with multiple overlapping. The specific feature of this study is the use of the multiview matching method instead of stereo matching. The method is based on adapting the energy aggregation algorithm, which was proposed in the semiglobal matching (SGM) method, to the object space, as well as using the one-to-many scheme of cost calculation. The reconstructed scene is represented as a voxel grid. A high-performance implementation of the digital surface model construction at all stages is proposed based on the massive parallelization of computations on a graphics processing unit.

The trajectory planning on a plane is considered as the problem of finding a path in a graph of a special form. Algorithms that are able to solve this problem in the case of geometric constraints, more precisely, under the assumptions that the trajectory is composed of a sequence of straight segments such that the angle between the adjacent segments does not exceed a given threshold, are analyzed. This statement is important for the development of effective navigation methods for unmanned vehicles. A novel algorithm for solving this problem is proposed, and the results of theoretical and experimental studies are presented. The experimental results confirm that the proposed algorithm can be used in practice for planning the trajectory of low-flying unmanned multirotor aerial vehicles in an urban area. They also show that the proposed algorithm significantly exceeds other available algorithms in terms of the number of successfully accomplished tasks.

A mathematical model of the action of water on a raft in the case of nonstationary motion is developed. In the linear approximation, the dynamics and stability of the raft motion in the case of a shifted constant load and disturbed initial data are investigated. The motion enabling the robot to cross a body of water in the simple case when the robot imparts an initial push from the shore to the raft is designed. The proposed algorithm was worked out using computer simulation. Given sufficient data about the robot’s motion, numerical results proving the validity of the algorithm are presented.