A new control algorithm is proposed for unstable linear systems with a time delay in the input channel in the presence of external bounded disturbances. The output signal of the plant is measurable, but not its derivatives. The Luenberger observer is used to estimate the state vector of the plant. A subpredictor is designed that predicts future values of the observer state, based on which a control signal is formed that ensures the stability of the closed-loop system. An auxiliary loop approach and an observer of derivatives are used to obtain an estimate of the external disturbance. Based on the disturbance estimate, a disturbance subpredictor is designed that performs multi-step prediction of these disturbances. Such a multi-step approach leads to the structure of the closed-loop system with a state time delay, where the new value of the delay is less than the original one by as many times as the number of subpredictors used. This approach allows to control of plants with a greater delay in the control channel than when using a single predictor. Using the Lagrange mean value theorem, a disturbance subpredictor is formed, where the future value of the disturbance estimate depends on its present value and a finite set of previous measurements. Unlike existing results, where the prediction is carried out by decomposing the disturbance using the Taylor formula, in this paper, to implement the future value of the disturbance, it is not necessary to estimate its derivatives, which improves the quality of regulation in the presence of interference in the measurement channel. The use of a disturbance subpredictor allows us to significantly reduce the disturbance prediction time compared to using one disturbance predictor by as many times as there are subpredictors. Using the Lyapunov-Krasovsky functional methods, sufficient conditions for the stability of the closed-loop system are obtained in the form of a solution to linear matrix inequalities. The use of linear matrix inequalities allows us to calculate the limiting value of the delay time at which the closed-loop system remains stable. The efficiency of the proposed approach is confirmed by the results of modeling in the MATLAB.

The specific features of bridges are considered. It is noted that in the process of operation bridges are exposed to the influence of external factors, such as temperature changes, wind gusts, ice, heavy rain, seismic and landslide impacts, etc., which cause damage, corrosion, malfunction, etc. in bridge structures. Therefore, systems for monitoring the technical condition of bridges are developed. However, these monitoring systems do not allow to reveal the latent period of occurrence of a malfunction in the bridge structure and trace the dynamics of its development. It is noted that the formation of even the most insignificant faults in the bridge structures is accompanied by the emergence in the vibration signal of an additive noise correlated with the useful signal. Characteristics of this noise carry information about the formation of defects and malfunctions in the bridge structures. However, the noise cannot be isolated from the noisy vibration signal in order to calculate estimates of these characteristics using traditional methods. Therefore, algorithms for calculating the characteristics of the noise characteristics of the noisy vibration signal are developed. Technologies for early detection of bridge malfunctions are proposed, as well as analysis of the dynamics of their development using interval estimates of the noise variance. The matrix and model of the faulty technical condition of bridges are built. To control the dynamics of malfunction development, confidence intervals for the estimates of the variance of the noise of noisy vibration signal at different time instants are compiled. The correspondence between each value of the confidence interval of the variance of the noise of the noisy vibration signal and the degree of development of the malfunction or defect of the bridge structure is established. For each upper boundary of the confidence interval of the noise variance, the ratio of the noise variance to the variance of the useful signal is calculated, and the dynamics of the hazard degree development is determined. It is shown that using the developed algorithms and technologies in monitoring systems will make it possible to signal the emergence of malfunctions and defects in the latent period of their inception, which ensures safety, reliability and efficiency of the operation of bridge structures and reduces the risk of possible accidents.

The article discusses the impact of the obsolescence of components, which is accompanied by a decrease in their availability due to their removal from production, on the technical and economic efficiency of complex organizational and technical systems of continuous use. The article reveals a link between the decrease in availability of spare parts and an increase in the duration of forced system downtime. It is proposed to compensate for technical and economic obsolescence by proactive management of obsolescence associated with the early adoption of measures to form reserves of elements based on forecasts of the residual service life of a complex organizational and technical system based on the criterion of decreasing technical and economic efficiency. The paper presents the main results of the development of a mathematical model for predicting the full and residual resources of a complex organizational and technical system based on the criterion of technical and economic efficiency. The paper introduces the concepts of "ultimate state of a complex organizational and technical system based on the criterion of reduced technical and economic efficiency," "full service life before technical and economic obsolescence," and "residual service life before technical and economic obsolescence" of a complex organizational and technical system. The paper presents the results of the development of a mathematical model for predicting the full and residual service life of a complex organizational and technical system based on the criterion of technical and economic obsolescence. The mathematical model takes into account the costs of creating the system, ensuring its operation with the required reliability, and the cost of damage caused by forced downtime. The article presents graphs showing the dependence of the resulting useful actual effect of the system’s operation on time, taking into account the increasing failure rates and decreasing recovery rates of components, which reflect the combined effects of physical aging and obsolescence. The article also provides an algorithm and an example of predicting the total and residual service life of a complex organizational and technical system for continuous use before it becomes technically and economically obsolete.

This paper presents and compares three approaches to solving forward kinematics in serial-chain robotic manipulators: homogeneous transformation matrices, quaternions, and biquaternions. The study addresses stringent demands for speed and accuracy in modern robotic systems — particularly in safety-critical domains like medicine and nuclear industry, where delays or computational errors may lead to critical consequences. Each method’s mathematical framework is described. A detailed, operation-level analysis of computational complexity is conducted, accounting for arithmetic and trigonometric operations. Emphasis is placed on practical performance when implemented on the ARM Cortex-M4F microcontroller — widely used in robotic control. Experimental comparisons are performed across compilation modes and single/double-precision data. Results show that, despite higher theoretical operation counts, quaternion and biquaternion methods outperform the classical matrix approach in execution speed. This stems from fewer memory accesses, simpler structure enabling efficient pipelining, and faster trigonometric evaluations via half-angle formulations. Moreover, these methods offer compact representation and key advantages: elimination of gimbal lock, smooth orientation interpolation, robustness against numerical error accumulation, and efficient Jacobian computation — making them especially valuable for real-time robotic systems with constrained computational resources.

Savonius wind turbines, like all vertical-axis turbines, do not require a wind orientation system and they start rotating at low wind speeds. These features along with the relative simplicity of manufacturing such wind turbines, allow considering them as a promising design option, including for operation in remote areas. This paper considers a small wind power generator consisting of a Savonius wind turbine, a three-phase permanent magnet electric generator, a rectifier, a battery, and a unit intended to control voltage at the battery input. The charging process is controlled by regulating the voltage supplied to the battery. A closed mathematical model is developed that describes both the mechanical and electrical parts of the system under consideration. The aerodynamic moment acting on the wind turbine blades is described using the quasi-steady approach. A qualitative analysis of the resulting dynamic system is carried out. A laboratory model of the described setup is manufactured. A series of experiments with this model are carried out in the wind tunnel of the Institute of Mechanics of Moscow State University. During these experiments, steady modes of the system were studied at different states of battery charge and different values of the control voltage generated by the control unit. An algorithm to control this voltage is proposed intended to carry out the parameter identification procedure. Based on the obtained data, parameters of the developed mathematical model are identified. It is shown that the parameter values found in the result of this procedure provide a good agreement between the results of numerical simulation and the experimental data.