Energy-optimal program control for the spatial motion (maneuvering) of a spacecraft taken as a free rigid body of arbitrary dynamic configuration is analyzed under arbitrary boundary conditions for angular and linear positions and velocity. The Pontryagin maximum principle and Clifford biquaternions are used to obtain a numerically optimal solution to the problem. The integral cost functional is minimized in terms of a weighted sum of the squares of the projections of the spacecraft’s angular and linear acceleration vectors, characterizing the energy consumption required to achieve the terminal state. In addition, a biquaternion-based analytical solution that is energy-optimal in the class of generalized helical conical motions is presented. This solution is derived using Chasles’ theorem on the displacement of a free rigid body and the Kotelnikov–Study transfer principle, and is developed into an algorithm. Numerical examples are given to illustrate the characteristics of the optimal solution to the original problem and the features of the proposed analytical biquaternion algorithm of program control.
An important applied problem in graph processing is the classification of vertices and edges. For this purpose, the neighborhood of the object in question is used. Vertices and edges in a dynamic graph can appear, disappear, or change their properties. This creates difficulties in describing the neighborhood, especially in cases of short lifetimes or rapidly changing edge parameters. Most existing approaches represent a dynamic graph as successive snapshots, which are static graphs that approximate the dynamic graph over a given time interval. Aggregating over large intervals loses important information about the sequence of graph modifications, while using small intervals leads to the loss of edges whose beginning and end points have different timestamps, resulting in uninformative snapshots. We propose an approach based on adding imaginary vertices to the snapshot, which are copies of vertices present in the history of the dynamic graph but absent from the snapshot’s time interval. Imaginary edges are constructed similarly. This allows the features of the dynamic graph to be preserved in the snapshot and the methods of static graph processing efficiently used. The proposed approach is versatile, can be applied to various problems involving dynamic graphs, and can be generalized to hypergraphs.
A hierarchical structure for quadcopter control is proposed for maritime search and rescue missions under strong winds and prolonged disturbances. Adaptive integral sliding mode control with an extended state observer is used in the outer position control loop to compensate for control errors under the influence of cumulative disturbances. Sliding control with an extended state observer is used in the inner attitude control loop to ensure high performance and stability. Cumulative disturbances are directly estimated using the extended state observer and compensated in the control law, which improves the noise immunity of the system. The 3S Optimizer metaheuristic algorithm is used to develop a technique for selecting controller parameters, taking into account Lyapunov stability conditions and the physical constraints of the quadcopter. Simulation results showed that the proposed structure provides higher trajectory tracking accuracy and better disturbance tolerance compared to the control structures considered under identical operating conditions.
Adaptive filtering of the state of an underwater object is considered on the basis of acoustic observations with random time delays. Delays are caused by a finite rate of acoustic signal propagation in water and have a significant effect on positioning accuracy. An extended Kalman filter based on the method of linear pseudo-measurements for systems with delays is used as the baseline scheme. Adaptive modifications of the filter are proposed for the case of unknown covariances of dynamic disturbances and measurement errors. The covariance of dynamic disturbances is estimated by using a robust variant that avoids unstable subtraction in the Sage–Husa scheme. The covariance of measurement errors is estimated by using a modification that takes into account the block-diagonal structure of the covariance matrix arising in the construction of pseudo-observations. Numerical simulation results show that the standard adaptive scheme may cause filter to operate unstably, whereas the proposed robust and structured estimates provide more stable and accurate positioning of the underwater object.
This paper focuses on the improvement of GLONASS performance, specifically the development of information technology for the use of multi-frequency GLONASS ground segment stations equipped with highly directional antenna systems. This type of antenna system potentially allows for a reduction in the equivalent error in determining the pseudorange between the satellite and the user. A technology for calibrating and geodetically referencing highly directional antenna systems in several frequency bands is presented as well as mathematical models used to develop a mathematical apparatus enabling the use of these stations to obtain improved, in terms of accuracy, ephemeris–time support for GLONASS are described. The impact of delays determined by the offsets of the ground station antenna phase centers and delays in the receiving and transmitting paths on the accuracy of unsolicited navigation measurements is analyzed. The solutions of the user’s navigation problem with direct and differential measurements are given. The results obtained by us can be used in the implementation of the promising technology being developed for ephemeris–time support of GLONASS and its introduction into the standard technological cycles of space constellation operation.
