The paper is devoted to the problem of state variables observers synthesis for linear stationary system operating under condition of noise or disturbances in the measurement channel. The paper considers a completely observable linear stationary system with known parameters. It is assumed that the state variables are not measured, and the measured output variable contains a small amplitude (in general, modulo less than one) additive noise or disturbance. It is also assumed that there is no a priori information about the disturbance or noise in the measurement channel (for example, frequency spectrum, covariance, etc.). It is well known that many observer synthesis methods have been obtained for this type of systems, including the Kalman filter, which has proven itself in practice. Under the condition of complete observability and the presence of some a priori information about a random process (which is typical for the case when a disturbance in the measurement channel can be represented as white noise), approaches based on Kalman filtering demonstrate the highest quality estimates of state variables convergence to true values. Without disputing the numerous results obtained using the application of the Kalman filter, an alternative idea of the state variables observer constructing is considered in this paper. The alternative of the new approach is primarily due to the fact that there is no need to use the usual approaches based on the Luenberger observer. The paper proposes an approach based on the estimation of unknown parameters (in this case, an unknown vector of initial conditions of the plant state variables) of a linear regression model. Within the framework of the proposed method, after a simple transformation, a transition is made from a dynamic system to a linear regression model with unknown constant parameters containing noise or disturbing effects. After that, a new nonlinear parametrization of the original regression model and an algorithm for identifying unknown constant parameters using the procedure of dynamic expansion of the regressor and mixing are proposed which ensure reduction the influence of noise. The article presents the results of computer simulations verifying the stated theoretical results.

The paper is devoted to the problem of parameter identification of two FitzHugh-Nagumo neuron models. The FitzHugh-Nagumo model is a simplification of the Hodgkin-Huxley model and it is very valuable for using on practice thanks to its simplicity. However, within an experiment only one variable of the FitzHugh-Nagumo model, the membrane potential, is measured, while another variable of cumulative effects of all slow ion currents responsible for restoring the resting potential of the membranes and both variables’ derivatives cannot be measured. This circumstance brings additional difficulties to the parameters estimation problem and, therefore, this case needs special attention. Firstly, the model was transformed to more simple form without unmeasured variables. Variables obtained from applying second-order real filter-differentiator were used instead of unmeasured derivatives in model’s equations. As a result, a linear equation was gotten and for this equation the identification goal, which guarantees correct parameters’ adjustment, was formulated and an adaptive system, parameters of which are estimations of original system’s parameters and an output of which estimates the output of the linear equation, was constructed. Then, the integral objective function was defined and the algorithm for the original model parameters identification was designed with the speed-gradient method. The results of computer simulation in the Simulink environment are presented. These results demonstrate that estimates of the model’s state and parameters converge to their true values rather fast. Unlike existing solutions of the FitzHugh-Nagumo identification problem, we propose a much easier deterministic algorithm. Moreover, the parameters are estimated for a system collected from two FitzHugh-Nagumo models, which opens perspectives for using the proposed method in modeling neuron population activity.

A review of models and algorithms for control of a stepper motor (SM) is presented. Due to high accuracy, improved power density, economy and reliability compared to other synchronous motors, stepper motors are widely used in various practical applications and scientific equipment. In aviation and space technology, step motors are actively used in actuating systems, such as drives for the movement of elements of large-sized structures, guidance, and stabilization systems, etc. The article describes some existing stepper motor control algorithms, which are both based on the knowledge of the parameters of the stepper motor model, and on the absence of this or that information. Of the many described algorithms, four were selected (PID controller, exact feedback linearization algorithm, adaptive control with partially unknown parameters and adaptive control with completely unknown parameters), which showed the best results of transient processes in tracking the angle of the rotor of the SM behind the reference value. A comparative numerical analysis among these four algorithms is also given, which showed that the best results of transients are demonstrated by adaptive controllers (in the sense of the smallest error in steady state), while the worst results are demonstrated by the PID controller. It is noted that the studied PID controller contains much fewer feedback loops compared to other algorithms, which simplifies the choice of adjustable parameters and reduces the dynamic order of the closed system, however, the design is based on knowing the exact parameters of the drive and is also sensitive to external disturbances. On the contrary, adaptive approaches successfully solve the problem of estimating parametric and functional perturbations, but their implementation is associated with significant difficulties.

Multi-agent Unmanned Aerial Vehicle (UAV) systems require stable and high-precision navigation. The existing navigation solutions, such as global navigation satellite systems (GNSS) and inertial navigation systems, may perform inefficiently in some application scenarios. The relative navigation methods can help solve this problem. Relative navigation enables UAVs to precisely estimate their positions relative to each other, as opposed to absolute navigation, which calculates the UAVs’ position relative to the Earth. Despite the abundance of relative navigation articles, there are no systematic reviews of relative navigation methods. Additionally, various articles on relative navigation use a variety of terms for comparable concepts, which makes it more difficult to understand the subject. Therefore, this review comprehensively studies systematizes relative navigation methods, and analyzes their strengths and weaknesses. We categorize relative navigation methods appropriate for multi-UAV systems, compare them, and make conclusions based on our findings. The relative navigation methods discussed in this review include differential GNSS, radio-frequency-based, visual, and their combinations. We evaluate the achievable accuracy and range for each type of method according to related studies. We also describe the limitations and vulnerabilities of each method. As a result, we outline relative navigation’s primary capabilities and assess its condition now.

Currently one of the promising areas of joint use of unmanned aerial vehicles (UAVs) is group air patrolling of large territories. Here the organization of patrolling assumes the solving the planning problem of routes flight of UAV group. The paper considers the problem of optimal planning of flight routes of the same type of UAVs during group patrolling of large territories. The territorial waters or narrow border areas of any State may serve as an example of such territories. It is suggested that the patrolled area has an elongated shape and is divided into a chain of adjacent patrol zones prescribed by a separate UAV. The drone’s flight route passes through adjacent zones. The flight task performed periodically by each drone consists in moving it to a given flight zone, collecting operational data and transmitting this data to a control point (center, station). The optimization aspect of UAV flight route planning is to minimize the maximum time required to complete flight tasks. The considered problem of group patrolling reduced to the multiple traveling salesman problem — one of the classic intractable combinatorial optimization problems. A brief analysis of modern methods for solving the multiple traveling salesman problem is given. Due to the lack of effective exact methods for solving this problem, it is natural to use approximate heuristic and metaheuristic methods focused on solving NP-hard optimization problems, reducing the full search and giving a solution close to the exact one. The multiple traveling salesman problem considered in this paper is reduced to the problem of integer linear programming, for the solution of which a genetic algorithm implemented in MATLAB based on the mathematical package Global Optimization Toolbox is proposed. An illustrative example of patrolling by three UAVs of an extended territory with 11 adjacent zones is considered. Computational experiments confirm the effectiveness of the algorithmic solutions proposed in the work.

The article is devoted to the development and research of a kinematic model of stabilization and orientation control of the suspended equipment of an unmanned aerial vehicle (UAV). The created model is based on the kinematic model of a three-axis gimbal (TAG): the structure of the TAG for the UAV, the mathematical description of the TAG of the UAV and the derivation of kinematic equations for the problems of stabilizing and controlling the orientation of the UAV suspension equipment. In the general case, the derivation of the kinematic equations of the TAG on the UAV is a complex process and is similar to the derivation of a kinematic model of a robotic arm with six degrees of freedom. The TAG is considered as a manipulative mechanism with six degrees of freedom: three degrees of freedom are determined by the UAV rotations around the axes of the coordinate system attached to the UAV, and three degrees of freedom are set by the frames of the TAG along the channels of yaw, roll and pitch during rotational movements of these frames around the corresponding axes of the coordinate systems attached to the frames of the TAG. Such a statement in the general case does not have an unambiguous solution for the tasks of stabilization and orientation control of the suspended equipment of UAV. To eliminate this ambiguity, optimization is used in the process of designing the TAG and installing the TAG in such positions on the UAV that reduce the computational complexity of the tasks being solved. The kinematic model is presented in the article by kinematic equations, the solution of which ensures the stabilization of the suspended equipment of UAV, and kinematic equations, the solution of which allows you to control the equipment (camera) of the UAV when tracking moving objects (moving targets) in space. The simulation of the TAG in the MATLAB Simulink software environment was performed. The simulation results in the MATLAB Simulink software environment prove the adequacy of the developed kinematic model of the TAG and its effectiveness for solving the problems of stabilization and orientation control of the suspended equipment of UAV.