№ 2 (2025)

A universal analytical method of static output feedback pole placement for fourth-order linear time-invariant systems with two control inputs and two observe outputs is suggested, regardless the relations between controllability and observability indices. The method does not require decomposing or reducing a system and may be implied to any fourth-order systems modally controllable by static output feedback, including the systems irreducible to control (observation) with a single input (output). The method is based on linear matrix dependence of a closed-loop control system characteristic polynomial on coefficients and determinant of a matrix of controller by output. The suggesting approach gives the necessary and sufficient condition for static output feedback pole placement – it allows defining all possible matrices of controllers by output and the conditions of their existence. A new algebraic criterion of complete modal controllability by output is formulated and proved. Examples of the approach application to controlling the aviation and space systems based on linearized models both in numerical and symbolic form are given.

A solution to a three-dimensional case of a time-optimal control problem for a point object moving in a viscous medium under the action of a control force limited in magnitude in the presence of uniform gravity is constructed in analytical form. For the general case, expressions are found in elementary functions that include two unknown constant vectors that must be found from the boundary conditions. In the case where the final position of the object is not specified, all unknown vectors are found in analytical form. An example of using the obtained relations is given, for which all necessary physical quantities are replaced by one dimensionless parameter.

The problem of the speed of a discrete linear non-stationary system of variable dimension is considered, the sets of admissible control values of which are convex compacts. It is assumed that the support functions of these sets are specified. At the first stage of solving the problem, the minimum time to reach the specified final state is found, at the second stage, control is constructed that brings the system to this final state in the found time. In the algorithm for solving the problem, only the specified support functions are used.

The paper develops single-period and multi-period models for assessing the efficiency of projects related to the creation of production enterprises in conditions of both deterministic setting of the parameters of these models and taking into account the uncertainty of indicators. The use of the method of branches and boundaries based on directed search with iterative calculation of upper current and lower estimates to solve the problem of choosing the optimal output of final products is proposed. Approaches to analyzing the stability of optimal solutions under changes in model parameters and model optimality criterion are considered. The methodology of quantitative assessment of possible risks of production programs is proposed. The use of the developed methods and models will provide the possibility of making managerial decisions in the presence of risk factors and uncertainty, increasing the efficiency of project management implementation at production enterprises.

The work is devoted to the development of principles for constructing hardware architecture of neural network computers used as accelerators and coprocessors for the implementation of expert and intelligent systems in objects with a high degree of criticality, including on-board equipment of aircraft. A model of a neural network computer built on the basis of an FPGA crystal has been developed, which allows dynamic deployment of artificial neural networks on its basis without the need to reprogram the FPGA crystal itself. The principles of deployment and training of a neural network based on the presented neural network computer are described. An example of its use in an expert system that analyzes the state of an onboard information and computing network of an aircraft for the occurrence of abnormal situations in real time and performs parrying of arising failures by the method of dynamic reconfiguration is given.

Strapdown inertial navigation systems are one of the most important elements of the control systems for various vehicles. Navigation errors depend on both inertial navigation system instrumental errors and the trajectory of the object. In this article we described a domain in the space of constant instrumental errors, ensuring that the radial position error is less than some tolerance for a given set of trajectories. The same approach enables finding the most significant error sources.

The problem of reference trajectories tracking for spatial motion of a quadcopter as a rigid body is considered. The state feedback linearization approach is used for synthesis of stabilizing control. The reference trajectory is constructed for three coordinates of the spatial motion of the quadcopter’s center of mass and its rotational motion along the yaw angle based on third-order polynomials depending on time, taking into account constraints on the coordinates, velocities and accelerations during the entire process of motion. The performance of the proposed control law is verified numerically and experimentally on the Parrot Mambo quadcopter model using the MATLAB/Simulink software.

The problem of the maximum width of the zone forbidden for stepping, which an n-legged robot can overcome in the static stability mode, is solved. For the six-legged and four-legged robots, the footprints sequences of the robot’s feet placement that ensure the achievement of the value of the maximum zone width are specified. The results of computer simulation are given.