No 4 (2023)

The efficiency of using the direct Lyapunov method for ensuring the stability of motion in compact invariant sets of finite-dimensional dynamical systems is shown. In the linear model of the restricted three-body problem, the possibility of ensuring the asymptotic stability of the periodic motion of a spacecraft (SC) in the vicinity of the collinear Lagrange point L2 using light pressure forces without the consumption of the working fluid is considered. The required area of control surfaces is estimated depending on the mass of the SC.

In mathematical control theory, a Dubins car is a nonlinear motion model described by differential relations, in which the scalar control determines the instantaneous angular rate of rotation. The value of the linear velocity is assumed to be constant. The phase vector of the system is three-dimensional. It includes two coordinates of the geometric position and one coordinate having the meaning of the angle of inclination of the velocity vector. This model is popular and is used in various control tasks related to the motion of an aircraft in a horizontal plane, with a simplified description of the motion of a car, small surface and underwater vehicles, etc. Scalar control can be constrained either by a symmetric constraint (when the minimum rotation radii to the left and right are the same) or asymmetric constraint (when rotation is possible in both directions, but the minimum rotation radii are not the same). Usually, problems with symmetric and asymmetric constraints are considered separately. It is shown that when constructing the reachability set at the moment, the case of an asymmetric constraint can be reduced to a symmetric case.

The necessary conditions for the implementation of information technology, which ensure the autonomy of operation while improving the accuracy of the ephemerides and clocks of the existing midaltitude segment of GLONASS, are substantiated. The discussed technology includes methods and algorithms for improving the accuracy of forecasting and refining the ephemerides of navigation spacecraft (NSC) in an inertial coordinate system, predicting and refining the evolution of the Earth’s rotation parameters, and precise synchronization of onboard clocks. Attention is paid to creation of the necessary conditions for the implementation of the first of these components of the proposed technology, which provides prediction and refinement of the ephemerides in an inertial coordinate system, including in the autonomous mode of satellite constellations. The component is implemented in the form of a block of special procedures for using equipment for measuring distances between satellites. In this case, a number of technical problems and related limitations arise that prevent the successful use of such equipment in solving the problem of NSC ephemerides refinement. The approaches and methods proposed by the authors, which are designed to overcome some of the problems and limitations and, ultimately, to improve the accuracy of the formed estimates of NSC ephemerides based on processing the intersatellite measurements formed using the onboard hardware, are described.

The well-known problem of synthesizing the optimal on the average and on given time interval of the inertial control law for a continuous stochastic object if only a part of its state variables are accurately measured is considered. Due to the practical unrealizability of its classical infinite-dimensional Stratonovich-Mortensen solution, it is proposed to limit ourselves to optimizing the structure of a finite-dimensional dynamic controller, whose order is chosen by the user. This finiteness allows using a truncated version of the a posteriori probability density that satisfies a deterministic partial differential integrodifferential equation. Using the Krotov extension principle, sufficient optimality conditions for the structural functions of the controller and the Lagrange–Pontryagin equation for finding their extremals are obtained. It is shown that in particular cases of the absence of measurements, complete measurements and taking into account only the values of incomplete measurements, the proposed controller turns out to be static (inertialess), and the relations for its synthesis coincide with the known ones. For a dynamic controller, algorithms for finding each of its structural functions are given.

We consider the problem of the boundary control of one-dimensional oscillations of an effective (averaged) medium corresponding to a two-phase medium consisting of periodically alternating layers of elastic and viscoelastic materials with long-term memory or various viscoelastic materials with Kelvin–Voigt friction and long-term memory. The averaged model is described by a boundary value problem for an integrodifferential equation. It is shown that for this model, it is impossible to bring oscillations to a state of rest in finite time (in contrast to the equation of string oscillations) by a force acting at one end of the band. A hypothesis is formulated on the possibility of bringing the specified object to a state of rest with the help of force effects distributed along the entire length of the object.

The adjacency matrices of extremal 3-uniform hypergraphs occupy a significant amount of computer memory. The solution of two problems is considered: to propose an efficient way of representing and storing such matrices and to find fast algorithms that allow us to operate just with vectors of the vertex degrees and signatures (characteristics of adjacency matrices), without using adjacency matrices in memory. As part of the first task, a second-order signature that uniquely defines an extremal 3-uniform hypergraph without using its adjacency matrix is described. A mechanism for compressing the second-order signature is also proposed, which contributes to greater storage efficiency. For the second problem, a number of algorithms are presented to describe the relationship between the vector of the vertex degrees and signatures of both the first and second orders. In addition, it is shown that an arbitrary second-order signature constructed under a number of constraints always has an extremal 3-uniform hypergraph corresponding to it.

The problem of technical debt arises when part of software source code is upgrading not directly, but is fixed in the second place as outdated. Three corresponding models are presented. Machine learning is used to find code smells. The effectiveness of the approach for specific data is established and the prospect of expanding to a greater number of different cases is outlined.

The problem of evaluating a person’s posture from video data is solved. Various key points of the human body are analyzed. We study the change in the accuracy of a fixed model when using different proportions in the regularization term of the loss function. It is shown that for a fixed number of training epochs, the accuracy of the model differs depending on the selected proportions. In addition, it is shown that the linear correlation between the trajectories of the key points that are part of the regularization term is not the main criterion for predicting the effectiveness of applying the regularization term of the loss function.

The problem of the optimal program control of the angular motion of a spacecraft (SC) as a rigid body with a quadratic functional of the energy spent on the maneuver of the SC and a fixed time of the transition process is investigated. The dynamic configuration of the SC and the boundary conditions are arbitrary and the control vector function is not limited. In the Poinsot concept, using the Pontryagin maximum principle, a quasi-optimal analytical solution of the problem is obtained, which is developed into an algorithm. Confirming numerical examples are given, showing the proximity of the quasi-optimal solution to the optimal solution of the problem.

The problem of the stabilization of programmed trajectories of mechanical systems, taking the constraints on the values of generalized coordinates, velocities, and accelerations into account, is considered. The control is built using the backstepping method in combination with the use of logarithmic Lyapunov barrier functions. The stabilizing feedbacks obtained in this study, in contrast to similar known results, do not lead to an unlimited increase in the values of the control variables when the state variables of the system approach the boundary values. As an example, the problem of constructing and stabilizing the trajectory of the spatial motion of an underwater vehicle is considered.

The motion of an axisymmetric robot controlled by a flywheel mounted on it is considered. It is assumed that the body of the robot is in contact with the plane at three points, while the force of dry anisotropic friction acts at two points, and at the third point the friction is isotropic. The control of the internal flywheel, which ensures the movement of the object in the given direction, is built. The dependence of the average velocity of the center of mass of the robot on the parameters of the system is studied.