编号 10 (2023)

The article considers the problem of combinatorial optimization of interception of rectilinearly moving targets as a modification of the traveling salesman problem. New macro characteristics and definitions for this problem are introduced and used to classify the obtained solutions. Vector criteria composed of several important for applications functionals are described. The principles of nowaiting
and maximum velocity are proved for two types of criteria. An intelligent brute-force algorithm with dynamic programming elements for finding optimal plans according to the introduced intercept criteria is proposed and implemented. Statistics of solutions of the developed algorithm is collected for a set of different initial parameters and the proposed macro characteristics are investigated. The conclusions about their applicability as local rules for the greedy algorithm for finding a suboptimal intercept plan are drawn.

This paper conceptualizes the main principles of comprehensive software verification for an onboard spacecraft control system. An optimal comprehensive verification strategy for onboard software
is selected by rigorously stating and solving the corresponding optimization problem. Software verification methods with functional correctness indicators are proposed.

The problem of obtaining three-dimensional radio images of objects with increased resolution based on the use of ultra-wide-band pulse signals and new methods of their digital processing is considered. The inverse problem of reconstructing the image of a signal source with a resolution exceeding the Rayleigh criterion has been solved numerically. Mathematically, the problem is reduced to solving the Fredholm integral equation of the first kind by numerical methods based on the representation of the solution in the form of decomposition into systems of orthogonal functions. The method of selecting the systems of functions used, which increases the stability of solutions, is substantiated. Variational problems of optimizing the shape and duration of ultra-wide-band pulses have been solved, ensuring the maximum possible signal-to-noise ratio during location studies of objects with fully or partially known signal reflection characteristics. The proposed procedures make it possible to increase the range of measuring systems, and also make it possible to increase the stability of solutions to inverse problems. It is shown that the use of the developed methods for achieving super-resolution to process ultra-wideband signals dramatically improves the quality of 3D images of objects in the radio range.

This paper proposes a novel approach to suppressing bounded exogenous disturbances in a linear discrete-time control system by a static state- or output-feedback control law. The approach is based on reducing the original problem to a nonconvex matrix optimization problem with the gain matrix as one variable. The latter problem is solved by the gradient method; its convergence is theoretically
justified for several important special cases. An example is provided to demonstrate the effectiveness of the iterative procedure proposed.

Deterministic continuous finite-dimensional stationary linear dynamic control systems with many inputs and many outputs are considered. Authors assume that the dynamics matrix can be both stable and unstable, but its eigenvalues are different, do not belong to the imaginary axis, and their pairwise sum is not equal to 0. The problems of constructing spectral solutions of the equations of state and matrices of gramian controllability of these systems, as well as the associated energy functionals of the degree of stability and reachability with the aim of optimal placement of sensors and
actuators of multi-connected control systems and complex networks are considered. To solve the listed problems, the article uses various models of the system in state space: a general representation, as well
as a representation in various canonical forms. To calculate the spectral decompositions of controllability gramians, pseudo-Hankel matrices (Xiao matrices) are used. New methods have been proposed
and algorithms have been developed for calculating controllability gramians and energy metrics of linear systems. The research results can be used for the optimal placement of sensors and actuators of
multi-connected control systems or for control with minimal energy in complex networks of various natures

Discrete linear polytopic systems affected by random correlated stationary disturbances are considered. New numerical methods for estimating of the anisotropic norm of a polytopic system using linear matrix inequalities are proposed.