This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by the search vehicle exceeds a certain threshold value. Interception was carried out by a controlled vehicle (defender) protecting the target. An analytical estimation of this detection probability is proposed. The interception problem was formulated as an optimal stochastic control problem, which was transformed to a deterministic optimization problem. As a result, the optimal control law of the defender was found, and the optimal interception time was estimated. The deterministic problem is a simplified version of the problem whose optimal solution provides a suboptimal solution to the stochastic problem. The obtained control law was compared with classic guidance methods. All the results were obtained analytically and validated with a computer simulation.

The actual modern problem of developing and improving measurement and observation systems (including robotic ones) is to increase the volume and quality of the information received. Increasing the angle resolution to values significantly exceeding the Rayleigh criterion, i.e. achieving super-resolution is one of important ways to solve the problem. Angular super-resolution which makes it possible to detail images of research objects and their individual fragments, improves the quality of solutions to detection, recognition and identification problems, increases the range of such systems. In many papers methods developed by authors to achieve a super-resolution based on approximate solutions of inverse problems in the form of Fredholm integral equation of the first kind of convolution type called algebraic are presented. The methods used, as well as their varieties, make it possible to reduce solutions of inverse problems posed to solving sets of linear algebraic equations (SLAE). This paper presents results of further improvement of algebraic methods based on intelligent analysis of received signals. It is shown that their use in systems based on digital antenna arrays makes it possible to increase the achieved degree of exceeding the Rayleigh criterion. In the course of numerical experiments with a mathematical model, the stability of the solutions obtained and their adequacy were confirmed. The numerical results obtained open the following possibilities: (1) obtaining images of studied objects with a resolution exceeding the Rayleigh criterion by 4 to 10 times, (2) determining the angular coordinates of individual small-sized objects as part of multi-element complex objects (group targets), (3) clarifying boundaries of extended objects and their individual elements, (4) localizing individual bright objects on a smoothly inhomogeneous reflective background. Applying presented new methods does not require a significant computing power, what allows you to work in a real time mode using relatively simple and inexpensive computing devices. The ways of further improvement of presented algebraic methods for solving applied inverse problems are described.