The problems of estimating the known linear function of the nonlinear system state vector under the external disturbances, measurement noise, and parametric uncertainties is studied. А solution is provided by interval observers and based on the reduced order model of the original system estimating the prescribed linear function. The interval observer is constructed based on the Jordan canonical form with negative eigenvalues since it has properties which are necessary for correct operation of the interval observer, namely, it is stable and Meltzer. The problem is solved in several steps. At the first step, the nonlinear terms are removed from the original system and the linear reduced order model insensitive to the disturbances is designed. Then it is transformed into the interval observer accounting the parametric uncertainties in the matrix of system dynamic; a proof of correctness of such observer operation is given. The obtained solution is supplemented by addends accounting the parametric uncertainties in the actuators. Then the result is corrected by taking into account the disturbances and measurement noise. To construct the nonlinear interval observer, the nonlinear term is transformed and supplemented into the linear observer, and a proof of correctness of the nonlinear observer operation is given. The obtained interval solution is similar to the confidence interval in mathematical statistics. The theoretical results are illustrated by an example of tree tank systems where the problem of interval estimation of unmeasured component of the state vector is solved. Simulation results based on the package Matlab show the effectiveness of the developed theory.

Sliding Mode Control Methodology is an efficient technique for high dynamic performance, accuracy and robustness in solving diverse nonlinear control problems involving external disturbances. We propose a sliding mode method for robust stability of uncertain systems with delayed feedback based on linear compensation and Super Twisting algorithm. Our aim is to develop a robust control system for uncertain systems with time delay and unknown disturbances. The predictor is used to compensate for the delay in the control input, and the Super Twisting algorithm is used for known disturbances and model uncertainties. Compensation control is designed to reduce control errors due to dynamic characteristic variation and unknown disturbances. The linear compensation principle proposed in this paper is formulated in an equation with performance conditions, not inequalities as in Lyapunov methods, and convergence of the compensation process is guaranteed by linear control theory. Simulation results show the effectiveness of the proposed method. The simulation results demonstrate that sliding mode predictive control for uncertain systems with delays based on linear compensation is highly effective.

The article discusses the design of a non-conductive of electric current mechanized perforated screen, which provides vertical openings along which curtains move, connected by cables with stepper motors. The optimization problem is set and solved: for a given shape and size of the part, find the type of  blinds for each hole and the coordinates of the edges of the blinds at which the criterion of unevenness of the electroplating reaches a minimum. А two-level structure of an automated control system for a mechanized perforated screen is proposed. The upper level includes a computer, which searches for the optimal configuration of holes in the screen. The lower level includes a controller that, after receiving information from an upper-level computer, controls the stepper motors through drivers. The mathematical and software support control systems are described. To calculate the coating thickness, Faraday’s law is used; to determine the current density at any point in the galvanic bath, Ohm’s law is used in differential form; to find the potential distribution in the electrolyte volume, the Laplace differential equation with nonlinear boundary conditions of the 3rd kind is used. The central equation of the mathematical model is the Laplace equation, which is solved by combining the methods of splitting and relaxation with a string run-through. An example of solving an optimization problem for a part of complex shape is given. The use of the developed device and control system significantly reduces the cost of obtaining a galvanic coating with a given unevenness due to its versatility, since there is no need to manufacture screens for each coated part, when differing in shape and size.

This article addresses the development of algorithms for automatic mobile robot motion control in static environments with obstacles, aiming for safe and effective navigation to a target while avoiding collisions. It compares two key approaches: finite automata, characterized by discrete switching between "move to goal" and "obstacle avoidance" states, and fuzzy logic, which enables smoother transitions and adaptive control under sensor uncertainty. An original Logical-Dynamic Automatic Control System based on fuzzy logic principles is proposed. This system utilizes three specialized fuzzy controllers: an obstacle avoidance controller using data from three lidar sensors (right, left, center); a goal-seeking controller operating on the robot’s angular deviation from the target; and a group fuzzy controller-coordinator. The coordinator dynamically weighs and combines the control actions from the first two controllers, prioritizing obstacle avoidance when necessary. The proposed LogicalDynamic Automatic Control System’s effectiveness was evaluated through computer simulations in MATLAB Simulink using the Mobile Robotics Simulation Toolbox. А differential drive robot’s motion was simulated in environments containing various static obstacles. Performance was compared against a baseline finite automaton model using metrics such as trajectory length, time to reach the goal, average speed, and an integral objective function. The simulations demonstrated that the LogicalDynamic Automatic Control System provides smoother wheel angular velocity changes, reduces abrupt mode switching, and enhances overall control efficiency by 2.22 % compared to the automaton-based approach, highlighting its potential for practical application. This fuzzy logic approach shows promise for real-world robotic systems.

The article deals with the use of nonlinear programming to solve the problem of maximum aircraft range estimation. The advantage of this approach is that it allows setting the problem in a sufficiently general form, based only on the principal aerodynamic characteristics of the aircraft, for example, without requiring the determination of the guidance law. Due to this, it is possible to obtain the upper limit estimates. The maximum flight range is determined as a solution of optimal control problem. To obtain it, the control signal is expanded in some basis. Estimation of expansion coefficients, performed by parametric identification methods, is the single-criteria multi-parametric optimization problem, which can be solved numerically. In the article, cubic Hermite splines are used as the basis for control approximation. One of their characteristics is that they do not require continuity of the second derivative in their nodes. Therefore, Hermite splines manage to approximate a wider class of signals. This also causes their main drawback — they require larger number of parameters than the classic interpolation cubic splines. The paper considers natural candidate for target functional — maximum flight range. Optimization of control parameters is carried out by the zero order method. One of the more common varieties of population algorithms, particle swarm, is used. Such choice ensures that work with a parameter vector of significant dimension is possible. The article demonstrates that obtained solutions are stable with regard to variations of spline parameters’ values and boundary conditions. It also compares the range estimations obtained using nonlinear programming with another case, when the structure of the guidance law is set explicitly, and only the values of its parameters are subject to optimization. The experiments showed that with a fixed structure of the guidance law the maximum range is slightly lower, probably due to the introduction of additional restrictions. In addition, the paper considers the extension of class of controls to include signals that could be obtained using an artificial neural network. The results show that the application of neural networks in this task does not provide significant advantages compared to cubic splines, although it requires identification of a noticeably larger number of parameters.

This paper addresses the synthesis of control laws for the reorientation of a small nanosatellite spacecraft of the Cube- Sat standard in the case of severe degradation of actuator efficiency. Severe degradation (or reduction of efficiency) of actuators refers to a condition where the control torque generated by the actuator is reduced to 5 % of its maximum value under nominal operating conditions. The angular motion model accounts for gravitational, aerodynamic, and disturbance torques. The spacecraft reorientation problem is solved for the case of degradation in two control  channels using  sliding mode control. An original nonlinear sliding surface is used for the synthesis of the control laws. During the problem-solving process, quasi-adaptive and adaptive control laws were obtained, and their performance was compared using mathematical modelling. А quasi-adaptive control law is understood as a law in which the coefficients of the sliding surface are constant but depend on the initial angular velocity. An adaptive control law, on the other hand, is one in which the coefficients of the sliding surface change according to predefined differential equations. For adjusting the two coefficients of the sliding surface, an approach based on experimentally derived relationships between these two coefficients and the initial angular velocity was proposed and implemented. Based on the results of the numerical simulations, it can be concluded that the adaptive control law provides a shorter solution time compared to the quasi-adaptive control law. The quasi-adaptive law, however, is simpler to implement, as it does not require the adaptation of the coefficients.