This paper is devoted to two applications of contact geometry to problems arising in the theory of continuous media control: control of the thermodynamic state of a van der Waals gas and control of liquid crystals. The first problem is reduced to constructing vector fields on a two-dimensional Lagrangian manifold, which is determined by the equations of the thermodynamic states of the gas. The second one is devoted to the method of solving the Cauchy problem for the Hunter -Saxton equation, which describes the dynamics of liquid-crystal structures.

The strategic planning system of the Russian Federation widely uses programtarget planning methods to achieve target development indicators for individual sectors and industries of the economy. The report examines the tasks of analyzing and forecasting the degree of achievability of target indicators of development programs under sanctions. We propose an approach to solving this problem, based on the construction of simula-tion models that make it possible to simulate material and financial flows over the periods of the program for various scenarios of sanctions restrictions. This approach allows us to numerically assess the impact of identified risks and changes in scenario conditions on the target indicators of the program. As part of the study, multifactor calculations were carried out to analyze the achievability of the target indicators of the “Com-prehensive Program for the Development of the Air Transport Industry of the Russian Federation until 2030,” which are il-lustrated with numerical examples.

Border activities are aimed at ensuring national security in the border space. They can be treated as a system of preventive measures (border prevention and containment), security and control measures (border service and search), and protective and combat measures (special and combat actions, operational actions). Functions (stages of the activity cycle) are assigned to each type of boundary measure. Border measures can be implemented via operations carried out throughout the country, one or several federal subjects according to a single plan for achieving a specific goal. The problems of border activities are investigated in the science of border activities--the system of knowledge to ensure border security, build state border organizations, prepare and conduct border activities, and provide comprehensive support of border activities. The substantial aspects of the science of border activities are studied. The principles of border activities are systematized as follows: activity, the secrecy and surprise of actions, flexibility, complex use of forces and means, the continuity of actions in place and time, the concentration of main efforts on the key directions and tasks, interaction, international cooperation, the main link, the balance of security and freedom, deterrence, reliance on the local population, the primacy of preventive measures, a combination of traditional and new technologies, and a comprehensive assessment of border security.

The list of research works of Boris Polyak.

Supply chains with dynamical behavior (SCD) are significant in the current industrial management. They can help to reduce inventory, enable flow of materials, maximize profits, and minimize costs. Dynamics of SCD is usually represented by a nonlinear perturbed dynamical system with imprecise parameters and limited state vector. The potential application of SCDs in industrial scenarios requires an effective model representation that can be used in a posterior optimization approach. Differential neural networks (DNN) with continuous-time dynamics can be used to obtain a feasible approximate mathematical model of the SCD that can be further used as a part of the optimization approach. This study develops a DNN identifier to approximate the dynamics of SCD considering the limitations on the states. The differential learning laws for the aforementioned neural network, which take into account restrictions on the states, are presented using the concept of barrier Lyapunov functions. A formal analysis that justifies the existence of the barrier learning laws is presented. The explicit implementation of the identifier is explained in detail, high-lighting how particular SCD can be handled with the proposed continuous neural network. A numerically simulated example of a three level continuous-time model of the nonlinear supply chain is evidenced in this study to illustrate the applicability of the proposed identifier for a supply chain with imprecise mathematical description.