Theoretically, this work belongs to a fairly broad class of articles and books devoted to solving control problems for dynamic objects with constraints on control actions and the Bolza functional. The necessary conditions for the existence of optimal controls for a terminal differential game are described by a two-point boundary value problem and the condition for choosing the control itself as a function dependent on the behavior of the Hamiltonian along the optimal trajectory. The main problem of finding optimal control is associated with finding a solution to the two-point boundary value problem. It should be noted that the existence of an optimal control is not necessary: the set of admissible controls may not even contain controls that transform the object from the initial state to a given set of goals. Typically, numerical methods are used to solve such problems. In this paper, an alternative to numerical methods for solving two-point boundary value problems, applied to the problem of synthesizing controls for nonlinear objects, is proposed. This approach is based on the assumption of the validity of R. Bellman’s inverse optimality principle, which maintains the functional relationship between the components of a two-point boundary value problem not only at the end of the transient process but throughout the entire control interval. Based on this, a new analytical method for constructing control for nonlinear objects, called the pseudo-optimal control synthesis method, is proposed. A condition is formulated for determining the set of initial conditions of the original nonlinear system that ensure the execution of the formulated control problem. Mathematical modeling of a quadcopter control system with synthesized control confirmed the theoretical results of the proposed method for synthesizing pseudo-optimal control for nonlinear dynamic objects.

The problem of fault identification in technical systems described by linear equations under the external disturbances is considered. The problem is solved based on sliding mode observers of two types: on the basis of high-order observers and on the basis of observers with weakened existing conditions. The peculiarity of such observers is that they do not rely on the matching condition, which is necessary for designing conventional sliding mode observers, but require the fulfillment of minimum phase condition for the original system. In contrast to the standard approach, both types of observers are designed not on the basis of the original system, but on the basis of its reduced-order model, which has selective sensitivity to faults and disturbances. The model is constructed in an identification canonical form and allows reducing the complexity of estimation procedure and removing the minimum phase condition. To implement the first type, an ordinary reduced-order Luenberger observer and a high-order sliding mode observer are constructed using information from the first observer; the identification expression uses information from the second observer and data on the coefficients of the characteristic equation of the first observer. To implement the second type, a reduced-order sliding mode observer is designed, which directly generates the required estimate. The disadvantage of high-order observers is that they require the linearity of the original system. In some cases, the disadvantage can be overcome by using virtual sensors, which are nonlinear observers that estimate the unmeasured components of the system state vector. An example is given that demonstrates the capabilities of virtual sensors. Based on the Matlab package, the original system and the constructed observers were simulated both in the absence of measurement noise and in their presence. The simulation confirmed the correctness of the assumptions and theoretical constructions and showed that high-order observers are less sensitive to such noises.

The problem of ensuring the quality of technical documentation in the development of cyber-physical systems (CFS) was considered. It has been shown that inconsistencies in requirements, specifications and design solutions are one of the main causes of errors in the integration and testing stages, which is critical for the tasks of automation and management of complex technical objects. Disclosed is a method for automated verification of connectivity of technical documentation based on an optical-wave model of semantics. The novelty of the approach lies in the presentation of the document as a sequence of semantic events displayed in Minkowski space with the introduction of "semantic time" and light cones, which makes it possible to formalize causal relationships between requirements and their implementation. To quantify the quality of documentation, the following was introduced: coherence coefficient C, which characterizes structural connectivity; Coverage coverage index, which assesses the completeness of implementation; the proportion of logical breaks R; integrated quality metric Q. The method was tested on a case of 15 educational design works on mechatronics and automated control systems. A high correlation of the proposed metrics with expert assessment is shown: the Q integral metric shows a strong correlation (ρ = 0.94, p <0.001), the coverage index of Coverage requirements is ρ = 0.85 (p <0.001). ROC analysis confirmed the high diagnostic ability of the Q metric (AUC = 1.00). The proposed method can be used as an element of the CSF development quality management system to automatically review project documentation and ensure traceability of requirements.

Springs are an important component of many mechanical products used in mechanical engineering, instrumentation and other industries. Despite the apparent simplicity of manufacturing the springs themselves, modern spring winding machines are complex multi-axis machines capable of winding springs with variable pitch at wire feed speeds up to 500 m/min, as well as performing automatic correction of geometric parameters based on intermediate optical control. Despite the importance of springs for industry, disproportionately fewer research papers have been devoted to control systems for spring-loading machines compared to other types of machine tools. This research attempts to close this gap by developing a universal approach to automating the winding of springs based on the use of electronic cams. The paper proposes a three level software and hardware architecture for spring coiling machine as well as three level hierarchy of electronic cams. It includes the implementation of a lower-level control system based on existing industrial solutions that are not subject to restrictions on dual-use systems, with automatic generation of control programs based on standardized tabular descriptions of springs, with the further possibility of optimizing them. The conducted experimental studies demonstrate that the application of this approach to various types of machine tools allows winding springs up to 5 times faster than on currently used machines based on CNC systems, and the application of the developed algorithm for automatic spring pitch correction has provided up to 1.26 times a reduction in the spread of spring lengths and minimizing the number of defects.

A methodology for intelligent control of the detonation-gas spraying (DGS) process of reactive Ni/Al composite coatings is presented, based on a Decision Support System (DSS) integrated with a digital twin of the technological process. The proposed hierarchical control architecture includes PLC-based sequencing, real-time stabilization of jet parameters using diagnostic data, predictive quality regulation, and a multi-objective optimization loop ensuring adaptive adjustment of process modes. The coating responses were evaluated from SEM image analysis: average pore area, number of unmelted particles, specific length of interphase boundaries, and fraction of pre-formed intermetallic phases. The relationships between technological parameters (barrel filling degree, C2H2/O2 ratio, spray distance, powder feed rate, gas temperature, and pressure) and structural characteristics were described using the Response Surface Methodology (RSM) with second-order regression models. Analysis of variance (ANOVA) confirmed the statistical significance of the factors and the adequacy of the model. Simulation and experimental verification demonstrated that gas temperature and spray distance exert the strongest influence on the formation of interphase boundaries. Optimization using the Harrington desirability function combined with a genetic algorithm enabled minimization of porosity and unmelted particles, while maximizing specific length of interphase boundaries. The mean prediction error across all structural metrics did not exceed 5—8 %. The developed DSS provides adaptive control and automatic optimization of DGS parameters, significantly reducing experimental workload and improving the reproducibility of coating structures. The methodology is suitable for integration into intelligent control systems and digital twin platforms for thermal spraying processes. Future work will focus on applying machine-learning-driven hybrid models combining empirical and physicochemical simulations for enhanced prediction accuracy and autonomy.

The Denavit-Hartenberg (DH) convention, while foundational in robot kinematics, contains a critical representational flaw in a specific class of anthropomorphic manipulators. This paper identifies and formalizes the "vanishing length problem", a singularity arising in kinematic chains featuring three consecutive joints where the z (yaw), x (roll), and y (pitch) axes form a mutually orthogonal triad. This configuration, characteristic of sequences like Roll-Yaw-Pitch or Pitch-Yaw-Roll, causes the origin of the middle (yaw) joint’s frame to become coincident with the origin of the subsequent joint’s frame. Consequently, the two physical link lengths preceding and following the yaw joint collapse into a single, combined length in the kinematic model, thereby losing a critical degree of freedom in the representation. We introduce the Auxiliary Virtual Joint (AVJ), a passive joint with a fixed constraint, to decouple this collapsed chain. The AVJ reintroduces the missing frame origin, restoring the two distinct link lengths and ensuring kinematic integrity. We provide a complete kinematic and dynamic formulation of the AVJ-augmented system, proving its equivalence to the physical manipulator. Validation on a 6-DoF humanoid arm demonstrates kinematic consistency to machine precision and, through dynamic simulations in MATLAB, confirms the feasibility of computing physically consistent joint torques—a computation rendered impossible for the middle yaw joint in the degenerate model due to the indeterminate inertial properties of the collapsed link.