1 Applied Mathematics and Mechanics in Aerospace Industry
5
calculations. The results of the calculation show a higher sensitivity of the lower
prosthesis basis to vary the parameters compared to the upper prosthesis basis.
Part IV provides a numerical study of dynamic systems and includes 6 chapters.
Chapter 15 discusses the framework of the restricted three-body problem [25, 26].
A celestial-mechanical model of the steady-state Chandler wobble of the Earth pole
is proposed. The contribution of the astronomical and geophysical disturbances to
the observed Earth pole oscillations is discussed based on the processing of IERS
observations of the Earth pole motion, NCEP/NCAR geophysical data of the atmospheric circulation, and NASA/JPL angular momentum of the ocean. The Earth pole
oscillatory process that is in-phase with the lunar orbit precessional motion is studied,
and the contribution of moving media to this process is discussed.
Chapter 16 reports two multi-agent algorithms for controlling one class of continuous deterministic systems: a hybrid multi-agent method of interpolation search and
a multi-agent method based on the use of linear regulators of agent movement control
[27, 28]. Detailed descriptions of the strategies of these methods are given and stepby-step algorithms for each multi-agent method are described. Two approaches to
the search for optimal open-loop control are considered: when control is sought in
relay form with a certain number of switches, and when control is sought in the form
of expansion in a system of basis functions.
Chapter 17 describes a modification for the continuous-time particle filter algorithm [29, 30]. The developed modification that is based on the well-known strategy
such as modeling trajectories to numerically solve stochastic differential equations
provides the lack of overflow errors during the calculation of particle weights. To
implement such an idea practically particle weights should be expressed in terms
of logarithms with additional customization of exponents. The effectiveness of the
modified algorithm is demonstrated when solving the tracking problem to find
coordinates and velocities of an aircraft executing a maneuver in the horizontal
plane.
Chapter 18 proposes a solution to the problem of determining the contribution of
airport rating criteria for assessing the integral risk of modernization. The purpose
of modernization is to increase the throughput of the Moscow aviation hub [31]. The
method proposed to solve the problem makes it possible to obtain the alternatives’
weights for incomplete pairwise comparisons matrices of large dimension, as well
as, alternative estimates in interval form, which is illustrated by an example. This
method differs from most existing methods for solving the problem of incomplete
pairwise comparisons by the ability to process incomplete pairwise comparisons
matrices without restoring missing data [32]. It can be applied to solve other decision
problems, where most of the known methods based on the pairwise comparisons
method are not applicable.
Chapter 19 introduces the adaptive interpolation algorithm for systems with
interval parameters [33, 34] and approaches directed to reducing the curse of dimensionality. The main assumption on which these approaches are based is that not all
interval parameters make a significant contribution to the solution. The use of tensor
train decomposition and sparse grids make it possible to take into account these
features and expand the scope of the algorithm for the case of a large number of
5
calculations. The results of the calculation show a higher sensitivity of the lower
prosthesis basis to vary the parameters compared to the upper prosthesis basis.
Part IV provides a numerical study of dynamic systems and includes 6 chapters.
Chapter 15 discusses the framework of the restricted three-body problem [25, 26].
A celestial-mechanical model of the steady-state Chandler wobble of the Earth pole
is proposed. The contribution of the astronomical and geophysical disturbances to
the observed Earth pole oscillations is discussed based on the processing of IERS
observations of the Earth pole motion, NCEP/NCAR geophysical data of the atmospheric circulation, and NASA/JPL angular momentum of the ocean. The Earth pole
oscillatory process that is in-phase with the lunar orbit precessional motion is studied,
and the contribution of moving media to this process is discussed.
Chapter 16 reports two multi-agent algorithms for controlling one class of continuous deterministic systems: a hybrid multi-agent method of interpolation search and
a multi-agent method based on the use of linear regulators of agent movement control
[27, 28]. Detailed descriptions of the strategies of these methods are given and stepby-step algorithms for each multi-agent method are described. Two approaches to
the search for optimal open-loop control are considered: when control is sought in
relay form with a certain number of switches, and when control is sought in the form
of expansion in a system of basis functions.
Chapter 17 describes a modification for the continuous-time particle filter algorithm [29, 30]. The developed modification that is based on the well-known strategy
such as modeling trajectories to numerically solve stochastic differential equations
provides the lack of overflow errors during the calculation of particle weights. To
implement such an idea practically particle weights should be expressed in terms
of logarithms with additional customization of exponents. The effectiveness of the
modified algorithm is demonstrated when solving the tracking problem to find
coordinates and velocities of an aircraft executing a maneuver in the horizontal
plane.
Chapter 18 proposes a solution to the problem of determining the contribution of
airport rating criteria for assessing the integral risk of modernization. The purpose
of modernization is to increase the throughput of the Moscow aviation hub [31]. The
method proposed to solve the problem makes it possible to obtain the alternatives’
weights for incomplete pairwise comparisons matrices of large dimension, as well
as, alternative estimates in interval form, which is illustrated by an example. This
method differs from most existing methods for solving the problem of incomplete
pairwise comparisons by the ability to process incomplete pairwise comparisons
matrices without restoring missing data [32]. It can be applied to solve other decision
problems, where most of the known methods based on the pairwise comparisons
method are not applicable.
Chapter 19 introduces the adaptive interpolation algorithm for systems with
interval parameters [33, 34] and approaches directed to reducing the curse of dimensionality. The main assumption on which these approaches are based is that not all
interval parameters make a significant contribution to the solution. The use of tensor
train decomposition and sparse grids make it possible to take into account these
features and expand the scope of the algorithm for the case of a large number of