На плоскости рассматривается задача типа преследователь-цель-защитник, в которой подвижная цель, имеющая ограничение на минимальный радиус разворота, уклоняется от равномерно и прямолинейно движущегося преследователя (ракеты или торпеды). Для перехвата преследователя цель использует мобильного защитника-перехватчика (подвижную ложную цель, ударный БПЛА и т.п.). Проблема осложняется тем, что в момент запуска перехватчика цель знает только азимут преследователя и его скорость, в то время как информация о расстоянии до преследователя и векторе его скорости недоступна. В данной работе построена оптимальная программа для траектории защитника, которая перехватывает все опасные (с точки зрения цели) направления возможного движения преследователя.

This paper presents a discrete model of non-synaptic interactions between neurons, which are performed by special chemical agents, neurotransmitters. In this model, all signals are broadcast: each neuron’s activity can be perceived by all other neurons that are sensitive to its neurotransmitter. The purpose of leaving synapses out is to demonstrate the importance of heterochemical1 interactions in the nervous system. Transmitter- specific neurons are described as finite automatons, which are a generalization of the traditional formal neuron. In a network consisting of such neurons, all connections are functional and not structural. This feature makes it possible to explain rapid reconfigurations of activity patterns in the generation of different rhythms by neuron ensembles, which are observed in living systems. We discuss and justify the choice of a discrete mathematical framework for simulation of heterochemical interactions.

We formulate the control design problem for systems with structured uncertainty. The source of disturbances that affect both the input and the output of the system is represented by the same vector-valued signal. The method proposed for the solution of this problem is based on the concept of invariant ellipsoids. The efficiency of the approach is exemplified via application to a model of a fighter aircraft.

Despite the positive dynamics in the growth of RES-based power production in electric power systems of many countries, the further development of commercially mature technologies of wind and solar generation is often constrained by the existing grid infrastructure and conventional energy supply practices. The integration of large wind and solar power plants into a single power grid and the development of microgeneration require the widespread introduction of a new smart grid technology cluster (smart power grids), whose technical advantages over the conventional ones have been fairly well studied, while issues of their economic effectiveness remain open. Estimation and forecasting potential economic effects from the introduction of innovative technologies in the power sector during the stage preceding commercial development is a methodologically difficult task that requires the use of knowledge from different sciences. This paper contains the analysis of smart grid project implementation in Europe and the United States. Interval estimates are obtained for their basic economic parameters. It was revealed that the majority of smart grid implemented projects are not yet commercially effective, since their positive externalities are usually not recognized on the revenue side due to the lack of universal methods for public benefits monetization. The results of the research can be used in modernization and development planning for the existing grid infrastructure both at the federal level and at the level of certain regions and territories.

Using the example of Mlodzievsky's pendulum os-cillations of a heavy rigid body with one fixed point, we show how nonlinear dissipation is introduced in the vicinity of the oscillation of a mechanical system in the case when the motion belongs to a two-dimensional integral manifold. In this case, a new characteristic function of the oscillation family is used, an explicit form of dissipation is found and the problem of stabilizing the oscillation of the “adjusted” body is solved.