The use of unmanned aerial vehicles (UAVs) with a nano communication networks can significantly expand the network’s capabilities. In addition, UAVs can automate the process of data collection and reduce its cost. This article expands the application that uses UAV to collect data from passive nanosensor devices. The article considers the specifics of the THz frequency range for the energy supply of nanodevices, as well as for communication with them. The paper presents a mathematical model of these processes and simulation results.

We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial conditions. The results are applied to the analysis of the accelerated unconstrained optimization method - the Heavy Ball method. We explain non-standard behavior of the method discovered in practical applications. In addition, such non-monotonicity complicates the correct choice of the parameters in optimization methods. We propose to overcome this difficulty by introducing new Lyapunov function which should decrease monotonically. By use of this function convergence of the method is established under less restrictive assumptions (for instance, with the lack of convexity). We also suggest some restart techniques to speed up the method’s convergence.

Abstract: A method for calculating the virtual energy balances of a continuous bilinear system based on the spectral decomposition of its Gramians of controllability and observability is proposed. There were obtained the indicators for the detection of balance anomalies and their expressions through complexvalued quadratic forms. Comparison of the absolute values of these forms makes it possible to identify the balance anomalies and, equally important, point out the specific devices that cause these anomalies. The main contribution of the work can be defined as two main results. Firstly, this is a generalization of the Gramians method developed earlier for discrete bilinear systems to the continuous bilinear systems. Secondly, this is a new method of assembling the Volterra matrix series to calculate the Gramians and energy functionals of the bilinear systems. The elements of the Volterra series are shown to form a geometric progression, the common ratio of which depends on the parameters of two matrices: of the Fadeev matrix in the spectral decomposition of the controllability Grammian of a linear model and the nonlinearity matrices of a bilinear model. Sufficient conditions for the convergence of Volterra series were obtained to guarantee the asymptotic stability of the bilinear system. It is demonstrated that the proposed results can be used in a small signal stability problem analysis for the bilinear representations of power systems.

The mathematical model of cloud computing system based on the queuing system with the splitting of the incoming queries and synchronization of services is considered. The queuing system consists of a single buffer and N servers (N >2), service times are independent and exponentially distributed. The incoming query enters the system as a whole and only before service is divided into subqueries, each subquery is served by its device. The servers with parts of the same query are considered to be employed as long as the query is not serviced as a whole: the query is handled only when the last of it is out and a new query may be served only when there are enough free servers (the response time is the maximum of service times of all parts of this query). Expressions for the stationary performance characteristics of the system are presented.

The article presents a new algorithm for embedding digital watermarks in the data of wireless sensor networks. The algorithm is designed to protect against the substitution of the data source in such networks. An important distinguishing feature of the proposed algorithm is the ability to control the level of distortions introduced as a result of embedding. This allows us to recommend this algorithm for use in wireless sensor networks, including sensor nodes of various types, designed to measure physical quantities of different nature. Computing experiments were carried out by means of simulation modeling in the OMNeT++ framework. The results of the experiments showed that the obtained algorithm provides statistical indistinguishability of sensory data samples before embedding digital watermarks into them and after embedding.