arXiv subjects

V. N. Tibabishev

Publications and source records attributed to V. N. Tibabishev.

6 recordsLinked to original sources

arXiv2013

Alternative to the Well-known Statistical Dynamics of Linear Systems

The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems is a more effective alternative. Background information is presented in the form of individual implementations nonergodic stochastic processes. Such a realization is deterministic functions. We introduce the concept of systems of sets of signals for the components on the semiring. For the system of sets of linearly dependent and linearly independent of the measured signals of a certain frequency properties. Frequency method is designed to deal with the noise on the set of deterministic functions. Example is the determination of the dynamic characteristics of the aircraft in accordance with the data obtained in one automatic landing.

math.GM↗

arXiv2011

The function space to describe the dynamics of linear systems

Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to contradictions. It is shown that the transition to the Hilbert space of almost periodic functions leads to the elimination of the detected inconsistencies. Multiple signals and interference with discrete spectrum are systems of sets. The properties of these systems lead to a new more effective method to combat noise in this space. The method used to identify the differential equations for the airbus. Baseline data were obtained during automatic landing.

eess.SY↗

arXiv2011

Optimization of frequency quantization

We obtain the functional defining the price and quality of sample readings of the generalized velocities. It is shown that the optimal sampling frequency, in the sense of minimizing the functional quality and price depends on the sampling of the upper cutoff frequency of the analog signal of the order of the generalized velocities measured by the generalized coordinates, the frequency properties of the analog input filter and a maximum sampling rate for analog-digital converter (ADC). An example of calculating the frequency quantization for two-tier ADC with an input RC filter.

math.OC↗

arXiv2011

Suppression of random noise by the separation of frequencies

It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with handicaps is received on the basis of the carried out researches. Method of dealing with noise leads to a new method of identification of dynamic characteristics of control objects in a class of multidimensional linear stationary models. As an example, describe an algorithm for obtaining the differential equation-wire feed control aircraft pitch, taking into account the elastic deformation of the structure of class IL -96 aircraft.

math.ST↗

arXiv2011

Fighting with deterministic disturbances

Consider the problem of interference mitigation in the identification of the dynamics of multidimensional control systems in the class of linear stationary models for single realizations of the observed signals. A concepts uncorrelated processes is not verifiable. Is entered the concept of system components of the signal measured on a semiring. Properties of signals are defined for systems of sets of linearly dependent and linearly independent measured signals. Frequency method is found to deal with noise on the set of deterministic functions. Example is considered to identify the dynamic characteristics of the aircraft on the data obtained in the regime of one automatic landing.

math.DS↗

arXiv2011

The domain of the Fourier integral

We consider the problem of determining the Fourier integral in the Hilbert space of square integrable functions. Fourier integral is the scalar product of two functions belonging to the Hilbert space of square integrable functions and the Hilbert space of almost periodic functions. Scalar product for different Hilbert spaces defined at the intersection of these spaces, which contains only one zero element. Therefore, the Fourier integral is not defined in the Hilbert space of square integrable functions with nonzero norm.

math.GM↗