Vol 21, No 8 (2015)

Provides an overview on the use of partial differential equations in optimal control problems, it is noted that they are used in the methods of Bellman and Krasovsky Second-order equations are presented in the form of two classes: Elementary and equations whose solutions are represented as different functional series. These equations have different coefficients, which are represented as fuzzy variables. In this connection, is formed and solved one-point boundary value problem on the synthesis of fuzzy optimal control method Bellman.

Next article provides basic definitions and notation of the theory of fuzzy sets, which are used for solving the fuzzy-point problem. These include the notions of membership functions; types of fuzzy numbers; fuzzy function; types of fuzzy derivatives; types of fuzzy initial value problems and algorithms for their solution.

Solved fuzzy partial differential equations of the first order and second-order elementary, then we solve the problem of synthesis of fuzzy optimal linear regulator. In accordance with the types of solutions of the initial problem of fuzzy controllers are synthesized BF (Buckley-Feuring) and S (Seikkala) types.

It is noted that the fuzzy equation of elliptic, hyperbolic and parabolic types are solved by numerical methods. This avoids making the fuzzy representation in the form of various types of rows.

The article ends with conclusions. A reference contains 15 sources. 4 of them are foreign-source.

The article presents a development reasoning for arithmetic units that implement the compensated operations of addition and multiplication to accelerate elementary functions in scientific calculations of gas dynamics and thermodynamics.

Full hardware support for transcendental functions in the microprocessor is allowed in the case of a large calculation errors and the single-precision real arithmetic format. If double-precision result with an error of no more than 0,5 ulp is required, it is advisable to use a hardware-software approach, since the cost for a fully hardware implementation are extremely high.

Despite the fact that the standard 1EEE754 did not declare anything about elementary (transcendental) functions, there are software libraries that provide the calculation of these functions with an error of not more than 0,5 ulp mantissa format double. This ensures the stability of the software results, enabling cross-platform compatibility. Therefore, there is a method for providing hardware accelerated some algorithmic "primitives", involved in a software library, as an alternative to conventional hardware acceleration calculating elementary functions. This is the compensated functions of addition and multiplication, which are the basic building block of libraries with double/triple internal precision (double-double, triple-double).

For example, the library CRLIBM implements the calculation of elementary functions with correct rounding. The library is written in C and it is support the double-double/triple-double accuracy of intermediate calculations, and also provides support for hardware operations FMA (Fused Multiply-Add).

Development of hardware floating-point units that implement the compensated lower-level operations will accelerate the implementation of compensated library functions allowing the use of specialized arithmetic unit instead of standard FPU.

Authors described the proposed improvement of the floating-point addition module to perform the addition of macro compensated CRLIBM.

The benefits of adding the compensated hardware-unit support in the exponent function calculation reached 20 percent, and implementation of compensated hardware multiplier provides the acceleration up to 5 times. Thus, the creation of a specialized coprocessor based on compensated arithmetic units and supported a set of basic transcendental functions operations for scientific calculations in the field of thermodynamics and gas is a promising direction.

Problem of clustering trajectories is pre-conditioned by a need to organize motion of objects under control. The polynomial regression method is the best approach to trajectory cluster selection, which estimates a form of general trajectory of each cluster. For a set of sufficiently heterogeneous trajectories, the defined clusters are heterogeneous also. For the inhomogeneous cluster, its polynomial regression is a too strong abstraction. To demonstrate the cluster heterogeneity (and, thus, non-full clustering trajectories) a method of dimension reducing is in need. So, linear dynamical system models are applied to object multi dimensional trajectory clustering by the polynomial regression method. Extracted components of system state vector give an opportunity to elicit cluster fine structure in accordance with cosine measure. In present paper applying continuous latent profile models is shown for determining a central trajectory in sufficiently homogeneous clusters of multi-dimensional trajectory projections. Continuous profile models are the hidden Markov models with internal states of time and scale. Defining the cluster central trajectory with affinity estimation by cosine measure in use gives an opportunity to determine the cluster outlying trajectories in potential, which represent motions located in a risk zone.

Requirements on GLONASS integrity are analyzed; basic integrity parameters are described. Core GLONASS performance monitoring elements are addressed together with the methods for GNSS integrity indicators generation onboard a navigation satellite through the navigation system ground control facilities, in a user receiver and spaceand ground based augmentation systems. Trade off analysis on basic techniques for receiver autonomous integrity monitoring (RAIM) is conducted. Structure chart of SBAS integrity monitoring algorithm is provided based on correction information analysis ensuring the GNSS integrity. Main distinctive features of RAIM in high precision navigation solutions are described. Conclusions and recommendations are given as to major improvement directions of GLONASS integrity.

The article contains description of mobile device logical structure management process model. This model contains the analytic model of mobile device logical structure, the logical structure of mobile device functional blocks relations, the mobile device security profile management model based on matrix graph grammars.

The essence of mobile device logical structure management process model is the reconfiguration of the logical structure of the interconnections between the mobile device functional blocks such as CPU, RAM, communication modules, for example, GSM, CDMA, LTE, Wi-Fi, Bluetooth, video and audio subsystems, etc. The main objective of this model is providing the required level of information security.

Mobile device logical structure features are presented. These features allow to present informational traffic routes between mobile device functional blocks. So, using these routes the mobile device logical structure can be justified.

The authors show location of this model in the services access control system using access to services with different privacy level. The optimal mobile device logical structure achieve by using the mathematical apparatus of dynamic graphs and optimization iterative algorithms.

Using this model, the authors offer mobile device security profile management model using access to services with different privacy level based on matrix graph grammars.

The article contains the results of the development and use of geographic information system for long-term monitoring of nature use of the territory by the example of the Lake Baikal basin. As an information base used arrays of multi-temporal topographic maps. To assess the suitability of these materials for a long-term monitoring of documents made a comprehensive analysis of the topographic map sheets, scale 1:84,000, created in 1896—1914 years. Described the technique of automating, geometric correction and creation cartographic information resources, based on them serving as a reference document for monitoring territory. Submitted by the experience of creating a multi-temporal Cartographical Data Warehouse. The technique of works with Data Warehouse, is the possibility of forming a plurality of cartographic representations, which changes the way of cartographic images of objects, but the integrity and coherence of the topological data sets does not depend on their combination. Presented the mechanism of interactive works with Data Warehouse through the geoinformation requests. Presented a practical example of qualitative and quantitative assessment of the transformation of the territory.

Approaches to enhance the cognitive capabilities of recurrent neural networks are investigated. In the interests it is proposed to empower such a networks of associative and spatial addressing to memory. The additional spatial addressing to memory of recurrent neural networks allows them to manage the associative interaction of processed signals. The improved model of recurrent neural network with associative and spatial addressing to memory is disclosed. It is shown that a memory addressing can be easily implemented in the electrical models recurrent neural networks. Examples of spatial redistribution of the currents in such networks, depending on the current state of interacting layers are shown. The proposed solutions allow to remove a number of constraints to understanding the processes of cognitive information processing in recurrent neural networks. These solutions can be used to develop advanced cognitive neural machines with high-speed parallel processing of different signals.