Complex Nonlinear Systems Research Articles

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The paper investigates the problem of knowledge stability. The purpose of the article is to analyze the theoretical prerequisites for knowledge stability in the economy and society. The study considers the hypothesis about the existence and applicability of stable knowledge in the economy. There are several types of stability: stability in mechanical media, in complex nonlinear systems, asymptotic stability, stability based on the energy criterion, and stability in the institutional environment. “Mechanical approaches” to the stability of economic structures as well as data-driven approaches in management are not considered by the author as comprehensive enough to describe super-complex processes in nonlinear open systems. The article criticizes theories that do not give due regard to the explosive nature of knowledge, setbacks in development, and the existence of limits to growth. Methodologically, the study relies on the synthesis of systemic and synergistic approaches in economics. The research novelty stems from the fact that the study showcases the significance of chaos for knowledge-intensive activity and discusses threats to the stability of the economy and society. The study singles out two types of knowledge with unifying and separating properties. The author links these properties to the specifics of light in physics: civilizational knowledge is like a wave while competitive knowledge is like a particle. A particular emphasis is laid on those properties of knowledge that are based on its “quantum nature”. In this case, small things (knowledge) can control big things, they can completely transform the entire structure and disrupt the stability of the old institutional frameworks. The study puts forward the concept of knowledge genesis as a theoretical and practical transition of stable knowledge into practice. In conclusion, the dangers of reductionist tendencies in economic theory are outlined and avenues for further research are highlighted.

Sobolev Training for Data-efficient Approximate Nonlinear MPC

Model predictive control is a powerful advanced control technique to deal with complex nonlinear systems with constraints. Despite recent advances in computing hardware and optimization algorithms, solving the nonconvex optimization problems associated to nonlinear model predictive control in real time can still be intractable. There are several possibilities to alleviate the challenge of computational complexity. An increasingly popular approach is to use neural networks to approximate the mapping between current system state and the corresponding optimal control input, which is implicitly defined by an optimization problem. These approaches typically need a large amount of data. Although the data can be generated offline by sampling the state space and solving many model predictive control problems in advance, it can become intractable especially for increasing system dimensions.In this work, we propose to use the parametric sensitivities of the nonlinear optimization problems as additional information that is provided to the neural network during training. In this way, the neural network not only fits the solution of the optimization problems itself but also its gradients. This training method, usually called Sobolev training, can lead to a higher accuracy in the approximation for the same amount of data. We illustrate the potential of the approach with a simulation study of a nonlinear chemical reactor.

Characteristics of planar sextic indirect-PH curves

<abstract><p>By a fractional quadratic transformation, an indirect-PH curve can have rational offsets. In this paper, I study properties of planar sextic indirect-PH curves, in terms of their Bézier control polygon legs. With our results, sextic Bézier curves can be efficiently tested whether they are indirect-PH curves. The main strategy to achieve our results is using complex representation of planar parametric curve. Sextic indirect-PH curves can be classified into three classes according to different factorizations of their hodographs. Necessary and sufficient conditions for all classes of sextic indirect-PH curves can be described by non-linear complex systems. By analyzing these non-linear systems, algebraic conditions for a sextic Bézier curve to be an indirect-PH curve are first discussed, then geometric characteristics in terms of legs of its control polygon are revealed.</p></abstract>

Data-Driven Probabilistic Methodology for Aircraft Conflict Detection Under Wind Uncertainty

Assuming the availability of a reliable aircraft trajectory planner, this paper presents a probabilistic methodology to detect conflicts between aircraft in the cruise phase of flight in the presence of wind velocity forecasting uncertainty. This uncertainty is quantified by ensemble weather forecasts, the members of which are regarded as realizations of correlated random processes and used to derive the eastward and northward components of the wind velocity. First, the Karhunen-Loève expansion is used to obtain a series expansion of the components of the wind velocity in terms of a set of uncorrelated random variables and deterministic coefficients. Then, the uncertainty generated by these uncorrelated random variables in the outputs of the aircraft trajectory planner is quantified using the arbitrary polynomial chaos technique. Finally, the probability density function of the great circle distance between each pair of aircraft is derived from the polynomial expansions using a Gaussian kernel density estimator and used to estimate the probability of conflict. The arbitrary polynomial chaos technique allows the effects of uncertainty in complex nonlinear dynamical systems, such as those underlying aircraft trajectory planners, to be quantified with high computational efficiency, only requiring the existence of a finite number of statistical moments of the random variables of the Karhunen-Loève expansion while avoiding any assumptions on their probability distributions. To demonstrate the effectiveness of the proposed conflict detection method, numerical experiments are conducted via an optimal control-based aircraft trajectory planner for a given wind velocity forecast represented by an ensemble prediction system.

Simple Tuning of Arbitrary Controllers using Governors

The paper proposes a preliminary idea to an intuitive and straightforward mechanism for tuning arbitrary controllers and changing the closed-loop performance. While the structure and parameters of the original controller are kept unchanged, the inputs to the nominal controller are modified such that the closed-loop response becomes slower or faster. Such a governor setup implementation is advantageous, especially when re-tuning the original controller is impractical or impossible. The practicability and versatility of this approach is presented using several examples spanning from simple loops with PID controllers to complex nonlinear closed-loop systems with optimal and approximated explicit MPC.

Machine learning-assisted extreme events forecasting in Kerr ring resonators

Predicting complex nonlinear dynamical systems has been even more urgent because of the emergence of extreme events such as earthquakes, volcanic eruptions, extreme weather events (lightning, hurricanes/cyclones, blizzards, tornadoes), and giant oceanic rogue waves, to mention a few. The recent milestones in the machine learning framework o↵er a new prospect in this area. For a high dimensional chaotic system, increasing the system’s size causes an augmentation of the complexity and, finally, the size of the artificial neural network. Here, we propose a new supervised machine learning strategy to locally forecast bursts occurring in the turbulent regime of a fiber ring cavity.

Analysis of Numerical Integration in RNN-Based Residuals for Fault Diagnosis of Dynamic Systems

Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create residuals for fault diagnosis applications. While recurrent neural network models have been shown capable of modeling complex non-linear dynamic systems, they are limited to fixed steps discrete-time simulation. Modeling using neural ordinary differential equations, however, make it possible to evaluate the state variables at specific times, compute gradients when training the model and use standard numerical solvers to explicitly model the underlying dynamic of the time-series data. Here, the effect of solver selection on the performance of neural ordinary differential equation residuals during training and evaluation is investigated. The paper includes a case study of a heavy-duty truck's after-treatment system to highlight the potential of these techniques for improving fault diagnosis performance.

THE INFLUENCE OF GLOBALIZATION AND DIGITALIZATION ON THE ESTABLISHMENT AND CONCEPTUAL DIGITAL SPORTS DEVELOPMENT IN CHINA

The relevance of the formation and digital sports development in China is in great importance, because the country is at the forefront of digital sports, which refers to the high-quality sport industry. With the development of technologies such as artificial intelligence, big data and cloud computing, the sports industry has undergone profound changes, contributing to the sports equipment emergence such as smart watches and smart sneakers, the continuous development of online sport platforms. At the state level, national digital sports development programs are adopted, which can promote the smart sport industry modernization, cultivate new economically growing points, form mass sports consumption, and provide new impetus to promote the high-quality sports industry development. Research methodology. To analyze digital sports concept in China, systemic and structural analystic methods are proposed, which allow considering digital sports as a complex social non-linear system that has several subsystems that constantly interact with the environment. The combination of synergistic and systemic methods and approaches allows us to explain the globalization and digitalization impact on the formation and development of the digital sports concept in China. The object of the research is the digital sports concept in China as a complex social, economic and cultural phenomenon. The subject of the research is the globalization and digitalization influence on the formation and development of the digital sports concept in China. The purpose of the research is theoretical and practical formation and development aspects of the digital sports concept in China. Research result. 1 Digital technologies of the sports sphere and sports experience as a factor in improving the sports concept in China are studied. 2. Data collection and processing phenomenon of athletes in China’s sports industry digital transformation is revealed. 3. Conceptual development of digital people-oriented sports at the state level is demonstrated. 4. Conceptual development of a healthy sports life in China is substantiated. 5. Building concept of China sports state and its industrial development in the digitalization context was studied. It was concluded that the high-quality sports industry development is an important energetic source for acceleration the sports state construction. The “Program for building a sports state” clearly states that by 2035, the sports industry will become a pillar of the national economy. Digital sports can promote the smart sport industry modernization, cultivate new economic growth points, direct and shape mass sports consumption, and provide new impetus to promote the high-quality sports industry development.

Picture Processing Optimization Technology Based on Mask R-CNN Algorithm

Picture processing is applied in all kind of fields, such as space science research, medical imaging, photography art. Because the human vision system is a complex nonlinear dynamic system, the traditional image enhancement methods often can not meet the requirements of real-time in practical applications. In the face of a large number of images, it is of great practical significance to obtain practical information from these data. With the rapid development of computer CnTech, image compression coding CnTech has also made great progress. And through the Mask R-CNN algorithm for effective segmentation and image recognition, can help people face massive image information, to their own needs as the goal, to achieve efficient retrieval, analysis, induction. The traditional methods of image classification by manually selecting features or manually extracting template matching have some defects. In this paper, a Mask R-CNN image optimization processing CnTech is proposed, which can accurately identify images and has higher accuracy for image feature extraction. It is meaningful to achieve automatic and accurate segmentation of microscopic images. Through training on COCO data set, it is verified through experiments that there are problems in image segmentation and recognition. In Mask R-CNN model, resource consumption is reduced and the efficiency of image segmentation and recognition is improved. Compared with the current cutting-edge algorithms, the image object detection on the strength of Mask R-CNN model has significant advantages.

Intelligent prediction of slope stability based on visual exploratory data analysis of 77 in situ cases

Slope stability prediction research is a complex non-linear system problem. In carrying out slope stability prediction work, it often encounters low accuracy of prediction models and blind data preprocessing. Based on 77 field cases, 5 quantitative indicators are selected to improve the accuracy of prediction models for slope stability. These indicators include slope angle, slope height, internal friction angle, cohesion and unit weight of rock and soil. Potential data aggregation in the prediction of slope stability is analyzed and visualized based on Six-dimension reduction methods, namely principal components analysis (PCA), Kernel PCA, factor analysis (FA), independent component analysis (ICA), non-negative matrix factorization (NMF) and t -SNE (stochastic neighbor embedding). Combined with classic machine learning methods, 7 prediction models for slope stability are established and their reliabilities are examined by random cross validation. Besides, the significance of each indicator in the prediction of slope stability is discussed using the coefficient of variation method. The research results show that dimension reduction is unnecessary for the data processing of prediction models established in this paper of slope stability. Random forest (RF), support vector machine (SVM) and k-nearest neighbour (KNN) achieve the best prediction accuracy, which is higher than 90%. The decision tree (DT) has better accuracy which is 86%. The most important factor influencing slope stability is slope height, while unit weight of rock and soil is the least significant. RF and SVM models have the best accuracy and superiority in slope stability prediction. The results provide a new approach toward slope stability prediction in geotechnical engineering.

Deep Reinforcement Learning-Based Optimal Control of DC Shipboard Power Systems for Pulsed Power Load Accommodation

To accommodate the pulsed power load (PPL) in the dc shipboard power system, the charging performance of the energy storage system (ESS) specialized for the PPL needs to be guaranteed, which leads to a challenging power system optimal control problem due to multiple objectives, operational constraints, complex nonlinear system structure, and uncertainties. This paper addresses this problem by using a model-free optimal control method based on the deep reinforcement learning (DRL). First, a dc shipboard power system optimal control problem with three control objectives and the input constraints is formulated, where three objectives include the fast ESS charge, the dc bus voltage regulation, and the proportional load current sharing. Then, to solve this problem, a DRL control framework based on the improved twin-delayed deep deterministic policy gradient (TD3) algorithm is developed, which adopts a modified critic network predicting technique and a stack-based data sampling strategy that are suitable for this fast-dynamic power system. The proposed method links the DRL framework with the optimal control. With the reward function being properly designed, the presented DRL control can well realize three control objectives. Case studies considering various operating conditions of the power system verify its effectiveness.

Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their suitability for control.

Realistic simulation of time-course measurements in systems biology.

In systems biology, the analysis of complex nonlinear systems faces many methodological challenges. For the evaluation and comparison of the performances of novel and competing computational methods, one major bottleneck is the availability of realistic test problems. We present an approach for performing realistic simulation studies for analyses of time course data as they are typically measured in systems biology. Since the design of experiments in practice depends on the process of interest, our approach considers the size and the dynamics of the mathematical model which is intended to be used for the simulation study. To this end, we used 19 published systems biology models with experimental data and evaluated the relationship between model features (e.g., the size and the dynamics) and features of the measurements such as the number and type of observed quantities, the number and the selection of measurement times, and the magnitude of measurement errors. Based on these typical relationships, our novel approach enables suggestions of realistic simulation study designs in the systems biology context and the realistic generation of simulated data for any dynamic model. The approach is demonstrated on three models in detail and its performance is validated on nine models by comparing ODE integration, parameter optimization, and parameter identifiability. The presented approach enables more realistic and less biased benchmark studies and thereby constitutes an important tool for the development of novel methods for dynamic modeling.

Data-driven control of hydraulic servo actuator: An event-triggered adaptive dynamic programming approach.

Hydraulic servo actuators (HSAs) are often used in the industry in tasks that request great power, high accuracy and dynamic motion. It is well known that an HSA is a highly complex nonlinear system, and that the system parameters cannot be accurately determined due to various uncertainties, an inability to measure some parameters and disturbances. This paper considers an event-triggered learning control problem of the HSA with unknown dynamics based on adaptive dynamic programming (ADP) via output feedback. Due to increasing practical application of the control algorithm, a linear discrete model of HSA is considered and an online learning data driven controller is used, which is based on measured input and output data instead of unmeasurable states and unknown system parameters. Hence, the ADP-based data driven controller in this paper requires neither the knowledge of the HSA dynamics nor exosystem dynamics. Then, an event-based feedback strategy is introduced to the closed-loop system to save the communication resources and reduce the number of control updates. The convergence of the ADP-based control algorithm is also theoretically shown. Simulation results verify the feasibility and effectiveness of the proposed approach in solving the optimal control problem of HSAs.

SYNERGETIC PARADIGM IN LINGUISTICS

The article is devoted to the consideration of synergetics as a new scientific direction. The disclosure of the paradigmatic essence of the concept of synergetics, which is important for modern science, seems to be a very urgent problem.The article examines the basic concept of linguosynergetics as a new direction in modern linguistics, analyzes the views and concepts of scientists involved in the study of the concept of "synergy". Synergetics is a new interdisciplinary discipline, the subject of its research is the processes of self-organization of various complex systems, at present one of the most important problems is the definition of its methodological apparatus and the search for the most complete definition. Synergetics is a scientific direction, a methodological method, a self-organizer of complex, non-linear complex systems. Science of the twentieth century through selfdevelopment gradually formed its new paradigm, which in the early 70 G. Haken called "synergetics".Today, synergetics has become actively used in the field of integrated humanities. The problem of synergy, as in the natural sciences, began to penetrate into linguistics in accordance with the nature of integration and organization of the internal laws of the language. In accordance with the anthropocentric orientation of modern linguistics, in the process of learning a language, the definition of the actualized synergy of the word began to be considered.

Control of a Hydraulic Generator Regulating System Using Chebyshev-Neural-Network-Based Non-Singular Fast Terminal Sliding Mode Method

A hydraulic generator regulating system with electrical, mechanical, and hydraulic constitution is a complex nonlinear system, which is analyzed in this research. In the present study, the dynamical behavior of this system is investigated. Afterward, the input/output feedback linearization theory is exerted to derive the controllable model of the system. Then, the chaotic behavior of the system is controlled using a robust controller that uses a Chebyshev neural network as a disturbance observer in combination with a non-singular robust terminal sliding mode control method. Moreover, the convergence of the system response to the desired output in the presence of uncertainty and unexpected disturbances is demonstrated through the Lyapunov stability theorem. Finally, the effectiveness and appropriate performance of the proposed control scheme in terms of robustness against uncertainty and unexpected disturbances are demonstrated through numerical simulations.

Gas Turbine Model Identification Based on Online Sequential Regularization Extreme Learning Machine with a Forgetting Factor

Due to the advantages of high convergence accuracy, fast training speed, and good generalization performance, the extreme learning machine is widely used in model identification. However, a gas turbine is a complex nonlinear system, and its sampling data are often time-sensitive and have measurement noise. This article proposes an online sequential regularization extreme learning machine algorithm based on the forgetting factor (FOS_RELM) to improve gas turbine identification performance. The proposed FOS_RELM not only retains the advantages of the extreme learning machine algorithm but also enhances the learning effect by rapidly discarding obsolete data during the learning process and improves the anti-interference performance by using the regularization principle. A detailed performance comparison of the FOS_RELM with the extreme learning machine algorithm and regularized extreme learning machine algorithm is carried out in the model identification of a gas turbine. The results show that the FOS_RELM has higher accuracy and better robustness than the extreme learning machine algorithm and regularized extreme learning machine algorithm. All in all, the proposed algorithm provides a candidate technique for modeling actual gas turbine units.

Machine-learning-accelerated Bose-Einstein condensation

Machine learning is emerging as a technology that can enhance physics experiment execution and data analysis. Here, we apply machine learning to accelerate the production of a Bose-Einstein condensate (BEC) of $^{87}\mathrm{Rb}$ atoms by Bayesian optimization of up to 55 control parameters. This approach enables us to prepare BECs of $2.8\ifmmode\times\else\texttimes\fi{}{10}^{3}$ optically trapped $^{87}\mathrm{Rb}$ atoms from a room-temperature gas in 575 ms. The algorithm achieves the fast BEC preparation by applying highly efficient Raman cooling to near quantum degeneracy, followed by a brief final evaporation. We anticipate that many other physics experiments with complex nonlinear system dynamics can be significantly enhanced by a similar machine-learning approach.

Research on Attitude Control System of Quadrotor Unmanned Aerial Vehicle based on Fuzzy PID Control Algorithm

The control of quadrotor aircraft mainly includes attitude control and position control. Because the change of position is caused by the change of attitude, it is most important to control the attitude of quadrotor aircraft. PID control principle is simple, easy to master, convenient to use, strong adaptability and good robustness, and its control quality is insensitive to the change of the controlled object, so it is most widely used. Quadrotor UAV is a strongly coupled underactuated system, and its stability is easily affected by system uncertainty and external interference during flight. Therefore, an improved fuzzy PID control method is proposed. In this article, the significance and ideas of constructing the attitude control system of quadrotor UAV based on fuzzy PID control algorithm are analyzed. This control strategy not only keeps the advantages of fuzzy control algorithm, which is independent of accurate model, and flexible and fast control, but also combines the advantages of PID control algorithm with small static error, and can achieve good control of nonlinear complex system.

Dynamic Formation of Quality Expectations: Theory and Empirical Evidence

Abstract The evolution of quality expectations over time is an important driver of customer satisfaction and retention. This study investigated the dynamic properties of customers’ quality expectation updating from an analytical perspective and provides new evidence on the psychological correlates of the discrepancies between expectations and experiences in the realm of consumer decision making. In doing so, we focus on the dynamics of expectation formation by adopting a nonlinear complex systems approach based on well-established behavioral theories. Using stability analysis, we find analytical results which are supported empirically by an experiment that there is considerable heterogeneity in how consumers calibrate their quality expectations. Specifically, we demonstrate analytically that in some cases individuals will converge to a specific quality expectation (reach a stable fixed point), while in other cases their expectations will oscillate between a small number of points periodically. This is remarkable because the existence of the latter is not due to changes in quality performance but merely accrue endogenously and depend on individuals’ disconfirmation functions. To our knowledge, this is the first time in the marketing literature that the corresponding gaps between quality expectations and quality provided are analyzed in the long run. Our analytical and empirical findings also suggest that being more responsive to a person’s expectations can increase the portion of those individuals that are able to better calibrate. Finally, we also demonstrate that calibration ability is associated with how thoughtful or impulsive information is used to update one’s expectation. A more deliberative processing style, which includes using a wider range of information, seems to be related to fewer unrealistic expectations and better calibrations, while a more impulsive processing style is related to more unrealistic expectations. In addition to providing a better understanding of dynamic expectation formation, these results can pave the way for interventions that foster more accurate quality expectations. From a managerial perspective, our findings imply that communicating quality perceptions are only to a certain extent under managerial control. To recognize this, firms are advised to segment customers based on their information processing style and to customize their marketing actions accordingly.