Viktor Chertopolokhov

This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for online use. Compared with delay-dependent functionals, the proposed approach avoids state augmentation and reduces computational overhead while preserving formal guarantees. The analysis is developed for a fixed delay, while extensions to bounded time-varying and multiple delays are discussed. Numerical studies of geodesic motion, an aircraft model, and a head-rotation task demonstrate fast transients, accurate prediction, and graceful degradation as the delay increases. The results indicate that stable learning with delayed inputs is practical and competitive with recent delay-aware identifiers in terms of accuracy, complexity, and reproducibility.

This research presents a novel, robust controller for acceleration tracking in robotic manipulators with time-varying joint limitations, accounting for articulation constraints. The proposed robotic system comprises an arm with limited joint mobility, simulating the dynamic movements required for effective motion cueing in flight simulators. The proposed robust control approach utilizes adaptive state-dependent gains to achieve finite-time convergence of the acceleration tracking error. Controller gains are determined using a class of controlled tangent barrier Lyapunov functions, ensuring that state constraints are satisfied. A stability analysis of the tracking error provides an explicit design for the state-dependent gains. A convex optimization technique based on matrix inequalities enhances the controller’s convergence rate. Given the complete forward characteristic of the recommended manipulation device, a finite-time convergent super-twisting-based differentiator may be employed to conduct the output feedback of the proposed controller specifically. The robust controller is tested on a reliable platform, a digital replica of the robotic manipulator. Indirect validation of tracking error convergence is provided through numerical evaluations, which also comply with articulation constraints and demonstrate the impact of gain optimization design. A standard state feedback control architecture serves as a benchmark for comparison. The origin is shown to be a fixed-time stable equilibrium point for the tracking error space, provided state space constraints are met, as evidenced by the faster convergence of the mean square estimation of the tracking error. Experimental assessments demonstrate that the barrier controller effectively tracks reference trajectories despite modeling uncertainties and implementation challenges, thereby validating the proposed controller.

The article outlines an approach to quantify the change in human perception of virtual reality (VR). VR systems have made significant progress, reducing the impact of their errors. Changes in postural characteristics are particularly distinct in tests where visual information is used more actively, such as when a person balances on a compliant surface. A series of tests were conducted where subjects maintained a vertical posture while standing on a hard force plate. During the tests, the subjects stood on both a regular hard surface (the force plate) and a compliant surface made of polyurethane foam. Maintaining balance on the compliant surface complicates the control task and requires the mobilization of human sensory systems, leading to an increased reliance on visual information. While maintaining posture, the subjects either looked at an image placed on the wall at eye level on a plain background or viewed the same image using virtual reality hemlet. During the examination with VR hemlet, the VR software used coordinates data, orientation and information from the VR helmet inertial sensors to reproduce a stationary environmentimage. For the current sample of volunteers tested on a compliant surface, stabilometric parameters with a stable tendency to change were identified: the average speed of the centre of pressure, an indicator of the quality of the equilibrium function, and the normalised area of the vectorogram. No noticeable changesrelated in the type of support in oculographic data were observed. Noticeable changes in oculographic data were also noted, however, the errors in their determination associated with the discrepancy between the frequencies of oculographic measurements allow us to draw only a preliminary conclusion on this issue.

Описан подход к количественной оценке изменения восприятия человеком виртуальной реальности (ВР). Системы ВР достигли заметного прогресса, и влияние их погрешностей не столь заметно. Изменение постуральных характеристик заметнее для задач, в которых зрительная информация используется человеком активнее: таких как удержание равновесия человеком, стоящем на податливом основании. Проведена серия тестов, в ходе которых человек поддерживал вертикальную позу, стоя на платформе стабилоанализатора. В ходе проведения обследования испытуемые поддерживали вертикальную позу, как стоя на обычной твердой поверхности (платформе стабилоанализатора), так и на податливом основании в виде пластины пенополиуретана. Удержание равновесия в этом случае усложняет задачу управления и требует мобилизации сенсорных систем человека, в том числе приводит к повышению роли зрительной информации. При поддержании ортоградной позы человек смотрел на изображение, размещенное на стене на уровне глаз на однотонном фоне, или на такое же изображение в очках виртуальной реальности. При проведении обследования в очках виртуальной реальности программное обеспечение ВР использовало информацию инерциальных сенсоров шлема ВР и данные о координатах и ориентации для воспроизведения образа неподвижной окружающей среды. Для имеющейся выборки добровольцев для пробы на податливом основании выявлены стабилометрические параметры, которые имеют устойчивую тенденцию к изменению: средняя скорость центра давления, показатель качества функции равновесия и нормированной площади векторограммы. Также отмечены заметные изменения окулографических данных, однако погрешности их определения, связанные с несоответствием частот окулографических измерений, позволяют де лать только предварительный вывод по этому вопросу.

The precise modeling of dynamic systems with periodic trajectories is required to describe diverse systems in mechanical, electrical, and many other disciplines. Nevertheless, the modeling task based on traditional methodologies could be complicated, considering the specific nature of periodic motions in actual systems. Differential neural networks (DNNs) are modeling tools for dynamic systems that can be useful for developing precise representations of periodic systems. This study presents the design of a novel family of DNN identifiers that could reproduce the trajectories of periodic systems with an uncertain mathematical model. The suggested DNN identifiers may produce an approximate model with periodic properties similar to the system under analysis exhibiting an one-period convergence of DNN weights. The fundamentals of the Floquet’s theory drive the design of the learning laws to ensure the reproduction of the periodic properties in the DNN. The design of a controlled Lyapunov function allows the learning laws to be derived for the DNN weights whose evolution depends on the positive definite solution of a periodic differential Lyapunov equation. Several numerical evaluations on periodic systems confirmed the modeling performance of the proposed identifier when the approximation performance is compared with traditional DNN identifiers using sigmoidal functions.

Differential neural networks (DiNNs) encounter a trade-off between the approximation quality and structural complexity. One promising approach to address this trade-off is incorporating dynamic complexity adjustment as an integral part of the learning process. Taking inspiration from the Fourier approximation theory, this study introduces a novel method for adapting the architecture of DiNNs, when they serve as nonparametric identifiers for dynamic systems with uncertain mathematical models. The structural adaptation process is executed through a recursive algorithm based on a modification structure strategy, which dynamically adjusts the number of neurons within the network’s structure. By applying a projection operator to the set of neurons, this method identifies the most relevant sequence of sigmoidal functions, intending to minimize the mean square error in approximating the trajectories of uncertain systems. This simultaneous reduction in overall complexity enhances the quality of the approximations. Moreover, the proposed method can implement a coarse-to-fine approach, wherein selecting necessary neurons occurs in multiple steps. These steps are determined by an adaptive structure strategy that alters the topology of the DiNN. The resulting framework’s effectiveness is demonstrated by evaluating the proposed identifier’s performance in approximating the evolution of real-life data associated with the ocular response during controlled motions or virtual reality engagement. In both experimental cases, there was a noticeable improvement in the accuracy of eye motion approximation by the DiNN, thanks to the variable structure approximation basis determined by the adaptive structure strategy. Overall, this study presents a formal method to automatically determine a feasible DiNN topology.

В настоящее время существуют различные современные технологии, позволяющие изучать корреляты развития профессионально важных качеств спортсменов. Одной из таких технологий, активно использующихся в спортивной практике, является технология отслеживания движения глаз, или окулография (еye-tracking). В статье показано применение окулографии в тестировании спортсменов-единоборцев с помощью демонстрации виртуальной среды в шлеме HTC Vive Pro Eye. Одной из существенных проблем при использовании, встроенных в шлем окулографов становится их низкая частота дискретизации и возможные потери зрачка в процессе работы. Для борьбы с этими эффектами можно применять фильтрацию, в том числе фильтр Калмана и аналоги. Для решения задачи оценивания с использованием данных фильтров обычно требуется наличие адекватной математической модели в пространстве состояний. Обычно по экспериментальным данным входных и выходных сигналов строится параметрическая либо непараметрическая модель рассматриваемой системы. В случае наличия информации об уравнениях модели задача обычно сводится к идентификации параметров системы. Далеко не всегда удается дать адекватное математическое описание процессов, происходящих в системе, либо сама система может представляться «черным ящиком». К подобным системам можно отнести и глазодвигательную систему. В таких случаях применима непараметрическая идентификация, то есть идентификация динамики системы. В данной работе предлагается идентифицировать динамику системы, используя дифференциальные нейронные сети. Они обладают хорошими аппроксимирующими свойствами для нелинейных систем. Стандартная сигмоидальная функция активации была заменена на функцию активации Ижикевича, описываемую дифференциальными уравнениями. Результатом работы нейросетевого идентификатора стала приближенная система, описывающая динамику движения глаза. Проведено численное моделирование. Исследована работоспособность модели на нескольких наборах данных, полученных при записи глазодвигательной реакции спортсменов-борцов на визуальные стимулы в виртуальной среде, показана эффективность работы законов обучения нейросети.

Nowadays there are different multiple modern technologies that allow studying cor-relates of development of sportsmen’s professional qualities. Eye tracking is one of such technologies, widely used in sport practice. The article demonstrates application of eye tracking to the task of testing wrestling athletes using a virtual environment demonstra-tion in a HTC Vive Pro Eye headset. Built-in eye-tracking systems of VR headsets often suffer from a low sampling rates and possible pupil loss during recording. Filtering can be applied in order to combat these effects, for example Kalman and similar filters. In this case, an adequate mathematical model in the state space is required. Usually a parametric or nonparametric model of the system in question is created. If dynamics of the model is known, the problem is usually reduced to identification of system parameters. It is not always possible to give an adequate mathematical description of the processes occur-ring in the system, or the system itself can be represented as a "black box". The oculomo-tor system may also be described as one such system. In such cases, nonparametric identification is applicable, that is, identification of the dynamics of the system. This pa-per proposes to identify the dynamics of the system using differential neural networks. They have good approximating capabilities for non-linear systems. The standard sig-moidal activation function was replaced by the Izhikevich activation function described by differential equations. The result of the work of the neural network identifier was an approximate system describing the dynamics of the ocular movement. Computational modeling was carried out. The workability of the model is studied on several data sets obtained by recording the oculomotor reaction of athletes-wrestlers to visual stimuli in a virtual environment, showing the effectiveness of the neural network learning laws.

Purpose: There are common problems in the identification of uncertain nonlinear systems, nonparametric approximation, state estimation, and automatic control. Dynamic neural network (DNN) approximation can simplify the development of all the aforementioned problems in either continuous or discrete systems. A DNN is represented by a system of differential or recurrent equations defined in the space of vector activation functions with weights and offsets that are functionally associated with the input data.Design/methodology/approach: This study describes the version of the toolbox, that can be used to identify the dynamics of the black box and restore the laws underlying the system using known inputs and outputs. Depending on the completeness of the information, the toolbox allows users to change the DNN structure to suit specific tasks.Findings: The toolbox consists of three main components: user layer, network manager, and network instance. The user layer provides high-level control and monitoring of system performance. The network manager serves as an intermediary between the user layer and the network instance, and allows the user layer to start and stop learning, providing an interface to indirectly access the internal data of the DNN.Research limitations/implications: Control capability is limited to adjusting a small number of numerical parameters and selecting functional parameters from a predefined list.Originality/value: The key feature of the toolbox is the possibility of developing an algorithmic semi-automatic selection of activation function parameters based on optimization problem solutions.

There is little research on the study of specific characteristics that contribute to the faster adaptation of athletes during the transition from one sport to another. We used virtual reality (VR) to study the differences between professional ice hockey players and other sport professionals (freestyle wrestlers), who were novices in hockey in terms of motor responses and efficiency performance, on different levels of difficulty. In the VR environment, four levels of difficulty (four blocks) were simulated, depended on the speed of the puck and the distance to it (Bl1—60–80 km/h and 18 m; Bl2—60–100 km/h, distances 12 and 18 m; Bl3—speeds up to 170 km/h and 6, 12, and 18 m; Bl4—the pucks are presented in a series of two (in sequence with a 1 s interval)). The results of the study showed that the hockey professionals proved to have more stable movement patterns of the knee and hip joints. They also made fewer head movements as a response to stimuli during all runs (0.66 vs. 1.25, p = 0.043). Thus, working out on these parameters can contribute to the faster adaptation of wrestlers in developing professional ice hockey skills.