This paper considers the creation of a minimax filtering algorithm in the form of an adaptive three-level algorithm consisting of several filters at each level for dynamic systems (DS) under uncertainty of the initial state caused by disturbances acting on the DS and by interference in information channels during operation. The filters are built based on either stochastic or deterministic information extensions of the process model. Same-level filters and the levels between themselves are covered by feedback, which allows for the adjustment of the a priori specified parameters. Thus, a filterbank is generated and the filters are integrated, which enhances the adaptability of each processing stage. The efficiency of the algorithms is exemplified.

Synthesis of regulators based on the output measured variable is considered more difficult than synthesis based on the state variables and synthesis of dynamic regulators. This problem has not been solved in its general form so far. In this paper, we consider the case when neither the necessary (mp ≥ n)  nor sufficient (mp > n) conditions for the pole placement synthesis at the output are fulfilled, where m is the number of inputs, p the number of outputs, and n the order of the system. At the same time, two approaches to solving this problem are being investigated: LQR and the pole placement approximation using gradient flows. In the first case, Lyapunov algebraic equations are solved and gradient equations are integrated. In this case, an extremum (local or global) is always reached. The second approach uses gradient flows on group Lie

GL(n, R) Ѕ R^mЅp, where a least squares pole assignment (mp < n) is performed with the choice of a part of the desired spectrum of a closed system. Here, optimization is performed before the modes enter a small neighborhood of the desired modes. To obtain gradient equations in both approaches, gradients of objective functions tr(M) from the matrix argument are derived. The properties of the function tr(M) and the rules for finding its gradient from the matrix argument are considered in detail. The obtained gradient equations are verified using a practical example: a 4th-order object with weakly damped dynamics with a large range of parameter uncertainty, where the task is to synthesize a robust static regulator of the minimum (second) order. This problem has been solved by both methods with the fulfillment of the set technical requirements.

The work is devoted to the construction of a mathematical model of the dynamics of a manipulator of a parallel structure with three degrees of freedom, based on reducing the kinetic and potential energies of the manipulator to a quadratic form relative to three independent generalized coordinates and velocities. The mechanical system of the manipulator includes seven masses: the masses of three housings, the masses of three actuator rods and the concentrated mass of a spherical hinge with a gripper and a load. The lengths of the actuating links, the angles of rotation of the actuating cylinders relative to the absolute coordinate system, and the Cartesian coordinates of the spherical hinge, on which stationary holonomic connections are superimposed, are used as generalized coordinates of the manipulator. Using the Lagrange formalism with indefinite multipliers, taking into account holonomic connections, a system of twelve nonlinear differential equations with respect to twelve generalized coordinates and nine Lagrange multipliers is formed. The parameters of dynamic models are determined using the method of quadratic approximation of functions over a given time interval for each type of basic displacement. The resulting system of linear algebraic equations is used to synthesize optimal control forces. Using the methods of calculus of variations, optimal control forces are determined that ensure the program law of motion of the manipulator grip from the condition of minimal heat losses of the drive electric motors. The results of mathematical modeling when moving the manipulator grip along a spatial straight line are presented.

The paper presents an adaptive control algorithm for a ground agricultural robot, designed to ensure task execution in crisis situations, such as the failure of one or more onboard devices. The algorithm considers the functional roles of the devices and their importance to the task at hand. The primary objective of this work is to enhance the robot’s autonomy by enabling dynamic adaptation in the event of device failures. А key component is a knowledge base that stores information about tasks, device purposes, their operational status, and the number of available onboard devices. The robot’s tasks are represented by predicates that account for both scenarios: operation with a fully functional set of devices and operation with a minimal set of devices required for task execution. Simulation modeling was conducted to evaluate the decision-making time under various conditions for three types of tasks. Each task type was analyzed in three scenarios: normal operation with all devices functional, partial device failure, and a crisis involving significant device failures. The results indicate that the shortest average decision-making time in crisis situations is 0.0072 μs, while for handling device failures it is 0.0083 μs. The longest decision-making time, 0.0112 μs, occurs during partial failures due to the need to search for solutions to enable task completion. The most time-consuming scenario involves enumerating all devices to identify those available for task execution. The simulation results confirm the algorithm's functionality and provide an estimate of decision-making times under various onboard device failure scenarios.

The article addresses the problem of control of an electric generator connected to the power grid while ensuring that the rotor speed remains within predefined limits set by the designer. Two methods are employed to solve this problem. The first method is based on disturbance compensation and allows for the identification and compensation of parametric uncertainty and disturbances in the power grid. Parametric uncertainty may arise due to unknown generator parameters and characteristics of network elements (such as transmission line resistance, transformer parameters, etc.). Disturbances are associated with sudden changes in network resistance due to load variations (e.g., connection or disconnection of generators, daily industrial operations, etc.) or short circuits in transmission lines. It is shown that the disturbance compensation method guarantees that the generator’s frequency remains within the specified range only in the steady-state mode, whereas in the transient mode, overshoot can be arbitrary. Excessive overshoot may lead to emergency situations where the rotor speed exceeds the regulatory limits set for the network. Additionally, if the overshoot is too high, the safety system may disconnect a working section of the power grid before the transient process in the control system is completed. To address this issue, an additional method of nonlinear coordinate transformation is used, which converts the constrained control problem into an unconstrained one. Subsequently, a control law in the new coordinates is proposed based on the disturbance compensation method. The inverse coordinate transformation ensures that the control goal is achieved. Simulation results confirm the theoretical findings.

The article presents the methodological and technological aspects of the theoretical analysis of the first group of motion equations (I. Newton’s dynamic equations), which are the core of the inertial navigation theory and systems. Conceptually, the notion of "analysis" is replaced by another methodological concept "interpretation" which "carries something significantly more important—the understanding that is necessary for producing new ideas" (Academician N. N. Moiseev). The purpose of the work is to verify and develop existing model concepts of motion based on their strict compliance with the axiomatics of Newtonian theory. By referring to the well-known matrix analysis procedure of symmetrization and alternation of a square matrix an expansion of the operator (3Ѕ3 dimension) of the total derivative of the differential motion equation is performed. The efficiency and relevance of the procedure is illustrated by an example of a partial solution of a two-point boundary value problem. The relevance of the decomposition of real square matrices of other dimensions for estimating their characteristic numbers is noted. The forms of the motion equations in various coordinate systems are presented. The general incorrectness of the Newtonian theory interpretation in a model of space built on a system of geodetic coordinates is shown due to the absence of attribute of the corresponding motion equations. At the same time, covariance takes place in a special identified case of motion.