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Runtime verification (RV) refers to methods for formal reasoning about all aspects of the dynamic execution of systems, including hardware, software, and cyber-physical systems. RV includes techniques to assess and enforce correctness of a system against systemic bugs or extrinsic uncertainties. These methods are typically considered lightweight as they may not involve exhaustive verification or proofs, but they provide a higher level of rigor and versatility compared to conventional testing methods. This article introduces the extended versions of selected papers from the peer-reviewed proceedings of the 20th International Conference on Runtime Verification (RV 2020). RV 2020 was supposed to be held in Los Angeles, California, USA in July 2020, but was instead held virtually due to the global Covid-19 pandemic. [ABSTRACT FROM AUTHOR]

Simultaneous Localization and Mapping (SLAM) is one of the research hotspots in the field of robotics, and it is also a prerequisite for autonomous robot navigation. The localization accuracy and stability of traditional SLAM based on static scene assumption declines due to the interference of dynamic objects. To solve the problem, this paper proposes a semantic SLAM system for dynamic environments based on object detection named DO-SLAM. Firstly, DO-SLAM uses YOLOv5 to identify objects in dynamic environments and obtains the semantic information; Then, combined with the outlier detection mechanism proposed in this paper, the dynamic objects are effectively determined and the feature points on the dynamic objects are eliminated; The combination method can reduce the interference of dynamic objects to SLAM, and improve the stability and localization accuracy of the system. At the same time, a static dense point cloud map is constructed for high-level tasks. Finally, the effectiveness of DO-SLAM is verified on the TUM RGB-D dataset. The results show that the Absolute Trajectory Error (ATE) and Relative Pose Error (RPE) are reduced, indicating that DO-SLAM can reduce the interference of dynamic objects. [ABSTRACT FROM AUTHOR]

Let (X , f) be a dynamical system. Using an equivalence relation ∼ on X , we introduce the quotient (X / ∼ , f ⋆) of the dynamical system (X , f) . In the first part of the paper, we give new results about sensitive dependence on initial conditions of (X / ∼ , f ⋆) , transitivity of (X / ∼ , f ⋆) , and periodic points in (X / ∼ , f ⋆) . In the second part of the paper, we use these results to study chaotic functions on the Cantor fan. Explicitly, we study functions f on the Cantor fan C such that (1) (C , f) is chaotic in the sense of Devaney, (2) (C , f) is chaotic in the sense of Robinson but not in the sense of Devaney, and (3) (C , f) is chaotic in the sense of Knudsen but not in the sense of Devaney. We also study chaos on the Lelek fan. [ABSTRACT FROM AUTHOR]

Flying Ad hoc Networks have emerged as a promising technology for number of real-time applications. However, the flexible and unstructured characteristics of these networks make them vulnerable to security threats posed by malicious nodes, such as denial of service attacks, node impersonation, and information breaches. Another major issue is the consideration of those nodes being unable to prove their trustworthiness due to factors like hardware or software failure, or by link interruptions, during the processing of detection of false nodes in the network. The existing mechanisms encompassing encryption, authentication, and intrusion detection highlight limitations to secure real-time applications and services due to the high speed of flying nodes and the absence of fixed network structures. To overcome these constraints, this research paper incorporates a novel framework for evaluating and improving the security of network by introducing an innovative cluster-based approach. Moreover, it presents a fuzzy model that dynamically estimates the trust levels of both individual nodes and clusters, by assigning weight to the parameters to address vulnerabilities. Additionally, a trust reconfiguration mechanism is further proposed to address the issue of nodes unable to substantiate their trust by providing them with additional chances based on the collective trust from previous evaluations. Further, the paper incorporates a dynamic reputation system to proficiently identify and separate malicious and selfish nodes from the network. Simulation results indicate a significant improvement in performance metrics, with a considerable reduction in delay and drop ratio by 41.46% and 36.37%, respectively, while the sufficient rise of 54.71% and 46.05% in throughput and coverage, respectively, comparing with the considered state-of-art. [ABSTRACT FROM AUTHOR]

This paper demonstrates the validity of the Naess–Gadai method for extrapolating extreme value statistics of second-order Volterra series processes through application on a representative model of a deep water small size tension leg platform (TLP), with specific focus on wave sum frequency effects affecting restrained modes: heave, roll and pitch. The wave loading was estimated from a second order diffraction code WAMIT, and the stochastic TLP structural response in a random sea state was calculated exactly using Volterra series representation of the TLP corner vertical displacement, chosen as a response process. Although the wave loading was assumed to be a second order (non-linear) process, the dynamic system was modelled as a linear damped mass-spring system. Next, the mean up-crossing rate based extrapolation method (Naess–Gaidai method) was applied to calculate response levels at low probability levels. Since exact solution was available via Volterra series representation, both predictions were compared in this study, namely the exact Volterra and the approximate one. The latter gave a consistent way to estimate efficiency and accuracy of Naess–Gaidai extrapolation method. Therefore the main goal of this study was to validate Naess–Gaidai extrapolation method by available analytical-based exact solution. Moreover, this paper highlights limitations of mean up-crossing rate based extrapolation methods for the case of narrow band effects, such as clustering, typically included in the springing type of response. [ABSTRACT FROM AUTHOR]

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph. Data-driven approximations of differential equations present a promising alternative to traditional methods for uncovering a model of dynamical systems, especially in complex systems that lack explicit first principles. A recently employed machine learning tool for studying dynamics is neural networks, which can be used for solution finding or discovery of differential equations. However, deploying deep learning models in unfamiliar settings-such as predicting dynamics in unobserved state space regions or on novel graphs-can lead to spurious results. Focusing on complex systems whose dynamics are described with a system of first-order differential equations coupled through a graph, we study generalization of neural network predictions in settings where statistical properties of test data and training data are different. We find that neural networks can accurately predict dynamics beyond the immediate training setting within the domain of the training data. To identify when a model is unable to generalize to novel settings, we propose a statistical significance test. Deep learning is a promising alternative to traditional methods for discovering governing equations, such as variational and perturbation methods, or data-driven approaches like symbolic regression. This paper explores the generalization of neural approximations of dynamics on complex networks to novel, unobserved settings and proposes a statistical testing framework to quantify confidence in the inferred predictions. [ABSTRACT FROM AUTHOR]

Runtime verification (RV) refers to methods for formal reasoning about all aspects of the dynamic execution of systems, including hardware, software, and cyber-physical systems. RV includes techniques to assess and enforce correctness of a system against systemic bugs or extrinsic uncertainties. These methods are typically considered lightweight as they may not involve exhaustive verification or proofs, but they provide a higher level of rigor and versatility compared to conventional testing methods. This article introduces the extended versions of selected papers from the peer-reviewed proceedings of the 21st International Conference on Runtime Verification (RV 2021). RV 2021 was supposed to be held in Los Angeles, California, USA in November 2021, but was instead held virtually due to the global Covid-19 pandemic. [ABSTRACT FROM AUTHOR]

Temporal graphs have become an essential tool for analyzing complex dynamic systems with multiple agents. Detecting anomalies in temporal graphs is crucial for various applications, including identifying emerging trends, monitoring network security, understanding social dynamics, tracking disease outbreaks, and understanding financial dynamics. In this paper, we present a comprehensive benchmarking study that compares 12 data-driven methods for anomaly detection in temporal graphs. We conduct experiments on two temporal graphs extracted from Twitter and Facebook, aiming to identify anomalies in group interactions. Surprisingly, our study reveals an unclear pattern regarding the best method for such tasks, highlighting the complexity and challenges involved in anomaly emergence detection in large and dynamic systems. The results underscore the need for further research and innovative approaches to effectively detect emerging anomalies in dynamic systems represented as temporal graphs. [ABSTRACT FROM AUTHOR]

This paper uses the theory of planar dynamic systems and the knowledge of reaction-diffusion equations, and then studies the bounded traveling wave solution of the generalized Boussinesq equation affected by dissipation and the influence of dissipation on solitary waves. The dynamic system corresponding to the traveling wave solution of the equation is qualitatively analyzed in detail. The influence of the dissipation coefficient on the solution behavior of the bounded traveling wave is studied, and the critical values that can describe the magnitude of the dissipation effect are, respectively, found for the two cases of b3 < 0 and b3 > 0 in the equation. The results show that, when the dissipation effect is significant (i.e., r is greater than the critical value in a certain situation), the traveling wave solution to the generalized Boussinesq equation appears as a kink-shaped solitary wave solution; when the dissipation effect is small (i.e., r is smaller than the critical value in a certain situation), the traveling wave solution to the equation appears as the oscillation attenuation solution. By using the hypothesis undetermined method, all possible solitary wave solutions to the equation when there is no dissipation effect (i.e., r = 0) and the partial kink-shaped solitary wave solution when the dissipation effect is significant are obtained; in particular, when the dissipation effect is small, an approximate solution of the oscillation attenuation solution can be achieved. This paper is further based on the idea of the homogenization principles. By establishing an integral equation reflecting the relationship between the approximate solution of the oscillation attenuation solution and the exact solution obtained in the paper, and by investigating the asymptotic behavior of the solution at infinity, the error estimate between the approximate solution of the oscillation attenuation solution and the exact solution is obtained, which is an infinitesimal amount that decays exponentially. The influence of the dissipation coefficient on the amplitude, frequency, period, and energy of the bounded traveling wave solution of the equation is also discussed. [ABSTRACT FROM AUTHOR]

This paper presents an improved method for computing convex and concave relaxations of the parametric solutions of ordinary differential equations (ODEs). These are called state relaxations and are crucial for solving dynamic optimization problems to global optimality via branch-and-bound (B &B). The new method improves upon an existing approach known as relaxation preserving dynamics (RPD). RPD is generally considered to be among the best available methods for computing state relaxations in terms of both efficiency and accuracy. However, it requires the solution of a hybrid dynamical system, whereas other similar methods only require the solution of a simple system of ODEs. This is problematic in the context of branch-and-bound because it leads to higher cost and reduced reliability (i.e., invalid relaxations can result if hybrid mode switches are not detected numerically). Moreover, there is no known sensitivity theory for the RPD hybrid system. This makes it impossible to compute subgradients of the RPD relaxations, which are essential for efficiently solving the associated B &B lower bounding problems. To address these limitations, this paper presents a small but important modification of the RPD theory, and a corresponding modification of its numerical implementation, that crucially allows state relaxations to be computed by solving a system of ODEs rather than a hybrid system. This new RPD method is then compared to the original using two examples and shown to be more efficient, more robust, and of almost identical accuracy. [ABSTRACT FROM AUTHOR]

Due to the spectrum and complexity efficiency, the integrated radar and communications (RadCom) systems have been widely favored, in which orthogonal frequency division multiplexing (OFDM) is the most popular signal to conduct the two functions simultaneously. However, an unoptimized pulse could suffer from severe inter-carrier interference (ICI) and high out-of-band emission (OOBE), which greatly degrades the system performance. In this paper, we introduce the pulse shaping scheme dedicated to RadCom systems, in which both transmitter and receiver can adaptively design pulses with the assistance of radar estimation. We first optimize the transmitting pulse with the weighted sum of signal-to-interference-plus-noise ratio (SINR) and OOBE by employing the popular genetic algorithm. Then, we design an improved-matched pulse at the receiver for maximizing the SINR with the fmincon solver. In this way, they both utilize the readily available radar information and keep the pulse optimal even in highly dynamic scenarios, which makes the most of RadCom systems while avoiding the overhead of channel estimation and feedback. Simulations prove the feasibility of proposed scheme and reveal that the radar image and communications SINR stay close to their optimum in most cases with much lower OOBE. An improved-matched pulse can further improve the communications performance when severe ICI occurs compared with a matched pulse. [ABSTRACT FROM AUTHOR]

In this paper, two dynamic models, recently proposed to describe the adaptive repeated choices of a boundedly rational consumer, are joined together. One considers a consumer adjusting the consumption level of a given good over time according to the observed discrepancy between expected and realized utility gain and modifies the utility function according to past consumption experience, also including saturation effects when past consumption is excessive. The other one considers the same adjustment mechanism with constant preferences but with a behavioral effect that introduces a tendency (or bias) to imitate a reference group of consumers. Merging these two models, a two-dimensional nonlinear dynamical system is obtained which describes consumers that decide their next period consumption of a given good by following two different (sometimes contrasting) criteria: their own utility maximization on the one side and imitation of a reference group of consumers on the other side. This leads to a greater uncertainty with respect to the model without the behavioral bias. Such uncertainty is studied through a numerical exploration of the long-run dynamics, guided by some global dynamical features of the nonlinear model, such as the folding action of the critical curves that characterize the behavior of the iterated noninvertible map and the singularities related to the presence of a vanishing denominator, namely focal points and prefocal curves. So, the aim of the paper is twofold: on the one side, it tries to contribute to the literature on the economic theory of boundedly rational consumers represented by evolutionary and behavioral approaches; On the other side, it tries to contribute to the recent literature about the global analysis of discrete dynamical systems characterized by contact bifurcations leading to the creation of complex topological structures of the attractors and their basins of attraction. [ABSTRACT FROM AUTHOR]

We consider systems with unboundedly many processes that communicate through shared memory. In that context, simple verification questions have a high complexity or, in the case of pushdown processes, are even undecidable. Good algorithmic properties are recovered under round-bounded verification, which restricts the system behavior to a bounded number of round-robin schedules. In this paper, we extend this approach to a game-based setting. This allows one to solve synthesis and control problems and constitutes a further step towards a theory of languages over infinite alphabets. [ABSTRACT FROM AUTHOR]

Transient stability is the key aspect of power system dynamic security assessment, and data-driven methods are becoming alternative measures of assessment. The current data-driven methods only construct correlations between variables while neglecting causal relationships. Therefore, they face problems such as poor robustness, which restrict their practical application. This paper introduces an improved constraint-inference approach for causality exploration of power system transient stability. Firstly, a causal structure discovery method of power system transient stability is proposed based on a PC-IGCI algorithm, which addresses the shortage caused by Markov equivalence and massive variables. Then, a relative average causal effect index is proposed to reveal the relationship between relative intervention strength and causal effects. The results of a case study verify that the proposed method can identify the causal structure between the transient stability variables entirely based on data. In addition, the causal effect sorting between "cause" and "outcome" of transient stability variables is revealed. This paper provides a new approach for data mining to uncover the causal mechanisms between variables in power systems and expand the capabilities of data-driven methods in power system application. [ABSTRACT FROM AUTHOR]

In this paper, interval observers are designed for linear dynamic systems described by continuous-time models with exogenous disturbances, measurement noises, and parametric uncertainties. Jordan canonical form-based relations are presented for an interval observer that estimates the set of admissible values of a given linear function of the system state vector. The theoretical results are illustrated by a practical example. [ABSTRACT FROM AUTHOR]

In the course of digitization, there is an increased interest in sensor data, including data from old systems with a service life of several decades. Since the installation of sensor technology can be quite expensive, soft sensors are often used to enhance the monitoring capabilities. Soft sensors use easy-to-measure variables to predict hard-to-measure variables, employing arbitrary models. This is particularly challenging if the observed system is complex and exhibits dynamic behavior, e.g., transient responses after changes in the system. Data-driven models are, therefore, often used. As recent studies suggest using Transformer-based models for regression tasks, this paper investigates the use of Transformer-based soft sensors for modelling the dynamic behavior of systems. To this extent, the performance of Multilayer Perceptron (MLP) and Long Short-term Memory (LSTM) models are compared to Transformers, based on two data sets featuring dynamic behavior in terms of time-delayed variables. The outcomes of this paper demonstrate that while the Transformer can map time delays, it is outperformed by MLP and LSTM. This deviation from previous Transformer evaluations is noteworthy as it may be influenced by the dynamic characteristics of the input data set, and its attention-based mechanism may not be optimized for sequential data. It is important to mention that the previous studies in this area did not focus on time-delayed dynamic variables. [ABSTRACT FROM AUTHOR]

This article investigates the phenomenon of bifurcation induced by double grazing in a piecewise-smooth oscillator with a play, which is a common occurrence in many non-smooth dynamical systems namely gear systems with approval, flange contact in wheel-rail systems, and spacecraft docking. The study is carried out using a composite Poincaré mapping with bilateral constraint, which extends the local normal form mapping of one discontinuity boundary to two discontinuity boundaries. The paper first derives the local discontinuous mapping at the unilateral grazing point using the normal form of discontinuity mapping and determines the type of 3/2 singularity of the zero-time discontinuous mapping with a continuous vector field at the discontinuity boundary. The composite Poincaré mapping is then used to obtain non-classical local bifurcations caused by double grazing, including bifurcation from period-1 motion to period-2 motion, bifurcation from period-1 motion to period-3 motion, and bifurcation from period-1 motion to chaos. The results of the study are consistent with those obtained via direct numerical simulations, demonstrating the efficacy of the composite Poincaré mapping of double grazing. The paper sheds light on the behavior of non-smooth dynamical systems and provides insights into the mechanisms underlying bifurcation induced by double grazing. The findings have potential applications in various fields including engineering, physics, and biology. [ABSTRACT FROM AUTHOR]

A hybrid system interacts with the discrete and continuous dynamics of a physical dynamical system. The notion of a hybrid system gives embedded control systems a great advantage. The Langevin differential equation can accurately depict many physical phenomena and help researchers effectively represent anomalous diffusion. This paper considers a fractional hybrid Langevin differential equation, including the ψ-Caputo fractional operator. Furthermore, some novel boundaries selected are considered to be a problem. We used the Schauder and Banach fixed-point theorems to prove the existence and uniqueness of solutions to the considered problem. Additionally, the Ulam-Hyer stability is evaluated. Finally, we present a representative example to verify the theoretical outcomes of our findings. [ABSTRACT FROM AUTHOR]

System design is a challenging and time-consuming task which often requires close collaboration between several multidisciplinary design teams to account for complex interactions between components and sub-systems. As such, there is a growing demand in industry to create better performing, efficient, and cost-effective development tools to assist in the system design process. Additionally, the ever-increasing complexity of systems today often necessitates a shift away from manual expertise and a movement towards computer-aided design tools. This work narrows the scope of the system design process by focusing on one critical design aspect: the packaging of system components. The algorithm presented in this paper was developed to optimize the packaging of system components with consideration of practical, system-level functionalities and constraints. Using a dynamic acceleration methodology, the algorithm packages components from an initial position to a final packed position inside of a constrained volume. The motion of components from initial to final positions is driven by several acceleration forces imposed on each component. These accelerations are based on physical interactions between components and their surrounding environment. Various system-level performance metrics such as center of mass alignment and rotational inertia reduction are also considered throughout optimization. Results of several numerical case studies are also presented to demonstrate the functionality and capability of the proposed packaging algorithm. These studies include packaging problems with known optimal solutions to verify the efficacy of the algorithm. Finally, the proposed algorithm was used in a more practical study for the packaging of an urban air mobility nacelle to demonstrate the algorithm's prospective capabilities in solving real-world packaging problems. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of a reservoir that has a finite-dimensional output and makes the reservoir computing model universal. Reservoir computing is a method for dynamical system approximation that trains the static part of a model but fixes the dynamical part called the reservoir. Hence, reservoir computing has the advantage of training models with a low computational cost. Moreover, fixed reservoirs can be implemented as physical systems. Such reservoirs have attracted attention in terms of computation speed and energy consumption. The universality of a reservoir computing model is its ability to approximate an arbitrary system with arbitrary accuracy. Two sufficient reservoir conditions to make the model universal have been proposed. The first is the combination of fading memory and the separation property. The second is the neighborhood separation property, which we proposed recently. To date, it has been unknown whether a reservoir with a finite-dimensional output can satisfy these conditions. In this study, we prove that no reservoir with a finite-dimensional output satisfies the former condition. By contrast, we propose a single output reservoir that satisfies the latter condition. This implies that, for any dimension, a reservoir making the model universal exists with the output of that specified dimension. These results clarify the practical importance of our proposed conditions. [ABSTRACT FROM AUTHOR]

In order to realize the coordinated design of multiple flexible AC transmission systems (FACTS) devices in the wind–PV–thermal-bundled (WPTB) power transmission system to suppress the low-frequency oscillation (LFO) of the system, in this paper, the static synchronous compensator (STATCOM) and the static synchronous series compensator (SSSC) with additional power oscillation damping controller (PODC) are designed based on the tie line transmission power signal to enhance the improvement effect of FACTS devices on system stability. The objective function is constructed by considering the transient voltage stability of the WPTB power transmission system, the real part of the eigenvalues and damping level of the LFO modes. And the coordinated and optimized design of power system stabilizer (PSS), SSSC-PODC and STATCOM-PODC is performed by the hybrid particle swarm optimization algorithm and genetic algorithm (PSO-GA) and pattern analysis theory of LFO. Finally, it is verified that the design can give full play to the effect of different controllers and significantly improve the damping ratio of the oscillation mode between regions through the simulation under the output variation of the new energy unit and the transmission power variation of the liaison line. When the fault occurs, the amplitude of oscillation and the time required to recover stability of the system decrease obviously, which enhances the dynamic stability of the system. [ABSTRACT FROM AUTHOR]

Modern measurement systems have allowed the recording of ambient data containing oscillatory phenomena and high noise levels. The observed phenomena are associated with ambient oscillations, which can be identified for monitoring the power system's dynamic behavior. Therefore, a cross-correlation decomposition-based approach is proposed in this paper. This technique combines an extended natural excitation technique (ENEXT) with a parallel factor (PARAFAC) analysis. The ENEXT allows calculating correlation functions of the measured data, which can be employed to build a data tensor. From this data array, a set of dominant impulse responses and their spatial correlations can be extracted through the PARAFAC analysis. The cross-correlation decomposition-based approach is applied to ambient data from the IEEE 16-generator 5-area power system to characterize dominant inter-area oscillation modes. The results demonstrate that the impulse responses may be used to identify the modal parameters, and the spatial correlations may be used to identify the spatial distribution of the oscillatory modes. [ABSTRACT FROM AUTHOR]

The scope of this paper is to apply a model-correction-based strategy for efficient reliability analysis of uncertain dynamical systems based on a low-fidelity (LF) model whose outcomes are corrected in a probabilistic sense to represent the more realistic outcomes of a high-fidelity (HF) model. In the model-correction approach utilized, the LF model is calibrated to the HF model close to the so-called most probable point in standard normal space, which allows a more realistic assessment of the considered complex dynamical system. Since only few expensive limit state function evaluations of the HF model are required, an efficient reliability analysis is enabled. In an application example, the LF model describes an existing single-span railway bridge modelled as simply supported Euler–Bernoulli beam subjected to moving single forces representing the axle loads of a moving train. The HF modelling approach accounts for the bridge–train interaction by modelling the passing train as mass-spring-damper system, however increasing the computational effort of the limit state function evaluations. Failure probabilities evaluated with the model-correction approach are contrasted and discussed with failure probabilities of the sophisticated bridge–train interaction model evaluated with the first-order reliability method (FORM). It is demonstrated that the efficiency of the method depends on the correlation between the LF and the HF model. A comparison of the results of FORM and the model-correction-based approach shows that the latter provides reliable failure probability prediction of the HF model while leading to a significant reduction in computational effort. [ABSTRACT FROM AUTHOR]

This paper presents a diagnostic study on the monitoring, detection, and localization of faults in mechanical rotor dynamic systems. It is well known that the vital function of machine condition monitoring relies on the ability to reliably measure the "vital signs" of a machine, of which vibration is among the most important. The current diagnostic methods and other measurement and detection tools now allow for a much broader assessment of a machine's condition from its monitored vibration than simply checking the vibration level against the healthiest machines, i.e., the machine's vibration levels will exceed or have already exceeded the "normal" or the "allowable" levels based on experience for the machine. With this in perspective, this paper presents a study on the monitoring of bearing imbalance and failure through vibration analysis. The detection of imbalance and early deterioration of a bearing is highlighted by the use of a temporal quantity and the kurtosis. The proposed methodology can easily detect the most frequent imbalance and bearing faults and reflect their severity. It allows making better recommendations and maintenance decisions. It allows the development of a new form of maintenance commonly called conditional maintenance as well as the evaluation of predictive maintenance. [ABSTRACT FROM AUTHOR]

Anisotropic flow, typically defined as the azimuthal correlations of the produced particles with respect to the common symmetry plane over a large kinematic, has been a popular approach in the last three decades to explore the properties of hot and dense QCD matter in high-energy heavy-ion collisions. These flow studies are usually based on the multi-particle correlations method, assuming that multi-particle correlations can be factorized into the product of flow coefficients. However, recent LHC measurements, based on new four-particle correlation observables, show evidence of flow angle decorrelation and flow magnitude decorrelation. These decorrelations break the assumption of the common symmetry plane and factorization. In this paper, we perform systematic studies to investigate the decorrelation with A Multi-Phase Transport (AMPT) model. We examine different tunings of the initial conditions, partonic cross sections, and hadronic interactions, revealing that the decorrelations are mainly driven by the initial geometry fluctuations while weakly influenced by the system's dynamic evolution. Comparison to experimental data and the AMPT calculations presented in this paper promotes a new possibility to further constraints on the initial conditions of the heavy-ion collisions. [ABSTRACT FROM AUTHOR]

Data clustering belongs to the category of unsupervised learning and plays an important role in the dynamic systems and big data. The clustering problem of sampled time-series data is undoubtedly much more challenging than that of repeatable sampling data. Most of the existing time-series clustering methods stay at the level of algorithm design, lacking rigorous theoretical foundation and being inefficient in dealing with large-scale time series. To address this issue, in this paper, we establish the mathematical theory for the large-scale time series clustering of dynamic system. The main contributions of this paper include proposing the concept of time series morphological isomorphism, proving that translation isomorphism and stretching isomorphism are equivalent relations, developing the calculation method of morphological similarity measure, and establishing a new time series clustering method based on equivalent partition and morphological similarity. These contributions provide a new theoretical foundation and practical method for the clustering of large-scale time series. Simulation results in typical applications verify the validity and practicability of the aforementioned clustering methods. [ABSTRACT FROM AUTHOR]

The stability analysis of a rocking rigid rod is investigated in this paper using a time-delayed square position and velocity. The time delay is an additional safety against the nonlinearly vibrating system under consideration. Because time-delayed technologies have lately been the core of several investigations, the subject of this inquiry is extremely relevant. The Homotopy perturbation method (HPM) is modified to produce a more precise approximate outcome. Therefore, the novelty of the exciting paper arises from the coupling of the time delay and its correlation with the modified HPM. A comparison with the fourth-order Runge–Kutta (RK4) technique is employed to evaluate the precision between the analytical as well as the numerical solutions. The study allows for a comprehensive examination of the recognition of the outcome of the realistic approximation analytical methodology. For different amounts of the physical frequency and time delay factors, the time histories of the found solutions are depicted in various plots. These graphs are discussed in the context of the shown curves according to the relevant parameter values. The organized nonlinear prototype approach is examined by the multiple-time scale method up to the first approximation. The obtained results have periodic behavior and a stable manner. The current study makes it possible to carefully examine the findings arrived at by employing the analytical technique of practicable estimation. Additionally, the time delay performs as extra protection as opposed to the system potential for nonlinear oscillation. [ABSTRACT FROM AUTHOR]

This paper extends the method originally proposed in [1] to systems with an arbitrary number of inputs and outputs. The method ensures that these signals will be in given domains. Two sequential changes of coordinates are introduced to solve the problem. The first change reduces the plant's output to a new variable of a dimension not exceeding that of the control vector (input). The second change allows passing from the control problem with constraints to the one without them. The effectiveness of this method is illustrated for two problems. The first problem is designing a state-feedback controller for linear systems with constraints imposed on the input and state variables. The second problem is designing an output-feedback controller for linear systems with constraints imposed on the output and input. In both problems, the stability of the closed loop system is verified in terms of linear matrix inequalities. The results are accompanied by simulation examples to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

By taking a low-frequency excited modified Chua's circuit model with discontinuous vector field as an academic example, this paper introduces the periodic bursting patterns characterised by stick–slip motions as well as the underlying generation mechanism uniquely belonging to Filippov-type slow–fast dynamical systems (FSFDSs). Based on the tangencies and the visibilities, this paper is the first to clearly explain the unique transition routes to bursting phenomena involving stick–slip motions by introducing the subdivisions of the sliding region. The results indicate that such transition routes are heavily dependent on the local structures of pseudoequilibrium (PE), performing distinct non-conventional bifurcation schemes. Furthermore, two transition routes respectively corresponding to a stable node-type PE and a stable focus-type PE as well as the induced periodic bursting oscillations are further discussed in numerical simulations. Particularly, it should be pointed out that the second one is a novel route to bursting oscillation in FSFDSs. [ABSTRACT FROM AUTHOR]

This paper presents a modified minimal realization technique to reduce single input single output (SISO) systems from higher-order SISO systems. The reduction process is based on restructuring the Hankel matrix, which consists of two major elements, i.e., Time Moments and Markov parameters. The system transformation is executed to reduce the order of the system by maintaining the desired system properties. The modified Hankel Matrix is proposed to obtain an expected reduce order model, i.e., kth order reduced model by selecting k × k order square matrix and using Silverman's algorithm. This paper presents a simple solution of model order reduction with the advantages of minimizing the steady-state error, fast convergence of steady-state behavior, better approximation in terms of rise time, peak time, and settling time at higher frequencies. Three different cases have been taken from the literature to validate the proposed technique with the comparisons of performance in terms of a quality check through performance indices and response matching between original and reduced-order models. [ABSTRACT FROM AUTHOR]

A new hybrid scheme of model order reduction (MOR) technique is developed for the simplification and control design of linear large-scale dynamical systems. MOR deals with a high-dimensional problem in a compact representation and plays an important role in fields where complicated simulation studies are still problematic in terms of simulation time. This paper proposes a strategy to derive a reduced order model (ROM) using Balanced Singular Perturbation Approximation. This way reduces the higher order system into a reduced order model. The proposed method guarantees the preservation of all essential parameters of the original model in the reduced system. The results of the proposed method are compared with the results of the reduced order model by previously published work. Further, this ROM has been used for the design of a compensator for the large-scale original plant by using the proposed method. The compensator obtained by using the reduced model gives the approximately same time domain specification as the compensator obtained by using a large-scale original system, and the design of the compensator by using the reduced model is comparatively easier. The performance of the higher and lower-order controllers is also analysed with numerical examples in terms of time response characteristics and time domain specifications and performance indices. [ABSTRACT FROM AUTHOR]

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. While current methods can identify such equations, they often require extensive manual hyperparameter tuning, limiting their applicability. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques to smooth the signal, sparse regression to identify the relevant parameters, and bootstrap confidence intervals to quantify the uncertainty of the estimates. We evaluate our method on well-known ordinary differential equations with an ensemble of random initial conditions, time series of increasing length, and varying signal-to-noise ratios. Our algorithm consistently identifies three-dimensional systems, given moderately-sized time series and high levels of signal quality relative to background noise. By accurately discovering dynamical systems automatically, our methodology has the potential to impact the understanding of complex systems, especially in fields where data are abundant, but developing mathematical models demands considerable effort. Discovering nonlinear differential equations from empirical data is a significant challenge, often requiring manual parameter tuning. This paper introduces a machine learning method integrating denoising techniques, sparse regression, and bootstrap confidence intervals, which shows consistent accuracy in identifying 3D dynamical systems with moderate data size and high signal quality. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the validity of the so-called cosmic no-hair conjecture in the framework of anisotropic inflation models of non-canonical scalar fields non-minimally coupled to a two-form field. In particular, we focus on two typical k-inflation and Dirac–Born–Infeld inflation models, in which we find a set of exact anisotropic power-law inflationary solutions. Interestingly, these solutions are shown to be stable and attractive during an inflationary phase using the dynamical system analysis. The obtained results indicate that the non-minimal coupling between the scalar and two-form fields acts as a non-trivial source of generating stable spatial anisotropies during the inflationary phase and therefore violates the prediction of the cosmic no-hair conjecture, even when the scalar field is of non-canonical forms. In connection with the Planck 2018 data, tensor-to-scalar ratios of these anisotropic solutions are investigated. As a result, it appears that the tensor-to-scalar ratio of the anisotropic power-law inflationary solution of k-inflation model turns out to be more highly consistent with the Planck 2018 data than that of Dirac-Born-Infeld model. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel learning-based shared control framework. This framework deploys first-order Dynamical Systems (DS) as motion generators providing the desired reference motion, and a Variable Stiffness Dynamical Systems (VSDS) (Chen et al. 2021) for haptic guidance. We show how to shape several features of our controller in order to achieve authority allocation, local motion refinement, in addition to the inherent ability of the controller to automatically synchronize with the human state during joint task execution. We validate our approach in a teleoperated task scenario, where we also showcase the ability of our framework to deal with situations that require updating task knowledge due to possible changes in the task scenario, or changes in the environment. Finally, we conduct a user study to compare the performance of our VSDS controller for guidance generation to two state-of-the-art controllers in a target reaching task. The result shows that our VSDS controller has the highest successful rate of task execution among all conditions. Besides, our VSDS controller helps reduce the execution time and task load significantly, and was selected as the most favorable controller by participants. [ABSTRACT FROM AUTHOR]

In recent years, the researches on parameter estimation of uncertain differential equations have developed significantly. However, when we deal with some nonparametric uncertain differential equations, the parameter estimation may not be used directly. To deal with these uncertain differential equations, it is important to consider the nonparametric estimation with the help of the observations. As an important branch of uncertain differential equation, autonomous uncertain differential equation may be properly applied to model some uncertain autonomous dynamic systems. In this paper, we propose a Legendre polynomial based method for the nonparametric estimation of autonomous uncertain differential equations. After that, some numerical examples are given and the residuals as well as uncertain hypothesis tests are used to prove the acceptability of these estimations. In application, we consider an atmospheric carbon dioxide model by the proposed method of nonparametric estimation. [ABSTRACT FROM AUTHOR]

The paper proposes a method for the correct by design coordination of autonomous driving systems (ADS). It builds on previous results on collision avoidance policies and the modeling of ADS by combining descriptions of their static environment in the form of maps, and the dynamic behavior of their vehicles. An ADS is modeled as a dynamic system involving a set of vehicles coordinated by a Runtime that based on vehicle positions on a map and their kinetic attributes, computes free spaces for each vehicle. Vehicles are bounded to move within the corresponding allocated free spaces. We provide a correct by design safe control policy for an ADS, if its vehicles and the Runtime respect corresponding assume-guarantee contracts. The result is established by showing that the composition of assume-guarantee contracts is an inductive invariant that entails ADS safety. We show that it is practically possible to define speed control policies for vehicles that comply with their contracts. Furthermore, we show that traffic rules can be specified in a linear-time temporal logic as a class of formulas that constrain vehicle speeds. The main result is that, given a set of traffic rules, it is possible to derive free-space policies of the Runtime such that the resulting system behavior is safe by design with respect to the rules. [ABSTRACT FROM AUTHOR]

This paper analyzes the fingerprint characteristics of a memristor model and proves that this memristor model conforms to the definition of generalized memristor. Using this memristor model, a new class of memristive circuit is built. A new memristive system is obtained through the mathematical modeling of the memristive circuit. The equilibrium points and stability of the new memristive system are analyzed by mathematical theory, and the complex dynamic behavior of the system under different parameters is analyzed by using simulation tools such as phase diagram, bifurcation diagram, Lyapunov exponent spectrum and time-domain waveform. Through simulation, it is found that this system can have quasi-periodic, periodic, chaotic and hyperchaotic attractors and wing-variable phenomenon under the change of parameters. The sensitivity of hyperchaos and chaos to the change of initial value is studied, and the phenomena of chaotic bursting and periodic bursting are observed. For physical verification, the hardware implementation of digital circuit based on FPGA is given. The experimental results are consistent with the numerical simulation ones, which prove its physical realizability. [ABSTRACT FROM AUTHOR]

As a first, the paper proposes modelling and learning of specific behaviors for dynamic obstacle avoidance in end-to-end motion planning. In the literature many end-to-end methods have been used in simulators to drive a car and to apply the learnt strategies to avoid the obstacles using the lane changing, following the vehicle as per the traffic rules, driving in-between the lane boundaries, and many more behaviors. The proposed method is designed to avoid obstacles in the scenarios where a dynamic obstacle is headed directly towards the robot from different directions. To avoid the critical encounter of the dynamic obstacles, we trained a novel deep neural network (DNN) with two specific behavioral obstacle avoidance strategies, namely "head-on collision avoidance" and "stop and move". These two strategies of obstacle avoidance come from the human behavior of obstacle avoidance. Looking at the current frame only, for a very similar visual display of the scenario, the two strategies have contrasting outputs and overall outcomes that makes learning very difficult. A random data recording over general simulations is unlikely to record the corner cases of both behaviors that rarely occur, and a behavior-specific training used in this paper intensifies the same cases for a better learning of the robot in such corner cases. We calculate the intention of the obstacle, whether it will move or not. This proposed method is compared with three state-of-the-art methods of motion planning, namely Timed-Elastic Band, Dynamic Window Approach and Nonlinear Probabilistic Velocity Obstacle. The proposed method beats all the state-of-the-art methods used for comparisons. [ABSTRACT FROM AUTHOR]

This paper concerns with the existence, uniqueness, Ulam's Hyer (UH) stability and total controllability results for the Hilfer fractional switched impulsive systems in finite-dimensional spaces. Mainly, this paper can be divided into three parts. In the first part, we examine the existence of a unique solution. In the second part, we establish the UH stability results, and in the third part, we study the total controllability results. The main outcomes are acquired by utilising the nonlinear analysis, fractional calculus, Mittag–Leffler function and Banach contraction principle. Finally, we have given two examples to validate the obtained analytical results. [ABSTRACT FROM AUTHOR]

Born globals (BG)' post-entry evolution is a process characterized by superior growth opportunities, but also higher risks of failure. These concerns lead to the fundamental question regarding the factors that may play a role in BGs' post-entry performance and survival. To provide a comprehensive picture on this issue, this paper critically examines 185 articles that have appeared in 39 academic journals over the past three decades. Drawing on complexity theory, we map a dynamic complex system comprising the interplay of six components relating to system inputs, managerial and firm-level capabilities – e.g., innovativeness, learning, and experience – , networks and system outputs – e.g., international growth and survival. Our review also suggests that strategic choices and orientations may act as change catalysts that bring BGs' complex systems to the next stages of evolution, with further consequences on firm expansion. Our review contributes to the extant literature by taking stock of the present state of knowledge, and providing a taxonomy on the components of the dynamic system that influences the post-entry performance and survival of BGs. Furthermore, this paper and the resulting taxonomy unpacks the various sources of BGs' heterogeneity, based on factors such as their different resources, capabilities, and strategies. In doing so, the paper uncovers significant gaps and contradictions in the literature, which opens important opportunities for future research. The paper concludes with a discussion of managerial and public policy implications. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional Jerk chaotic system with saddle-focus equilibrium point and special rotational characteristics of attractors is proposed by constructing a three-dimensional chaotic system. Based on the three-dimensional Jerk chaotic system, a four-dimensional chaotic system based on the sign function and cosine function is proposed. Through detailed numerical simulations and theoretical analysis, we induce and control the emergence of multi-vortex structures in the system by adjusting system parameters, thereby influencing the overall dynamic characteristics of the system. The dynamical behavior of the system is analyzed using the 0–1 test, attractor coexistence, multiple bifurcations, two-parameter Lyapunov exponent, and complexity. It is found that the new four-dimensional chaotic system has the properties of multi-stability, transient chaos and offset enhancement. The circuit of this chaotic system was designed and simulated, and the digital circuit was implemented using field programmable gate array. The consistency between the simulation and implementation results proves the existence and feasibility of the system. Finally, based on the adaptive synchronization control algorithm, the system is applied to secure communication synchronization and the analysis confirms the superiority of the adaptive synchronization strategy, while enhancing the system's ability to cope with external variations and demonstrating that it has a wide range of applications in various fields. [ABSTRACT FROM AUTHOR]

In the integrated energy system, the transmission delay of the cooling and heating pipeline network is long, which has an essential impact on the optimal scheduling of the integrated energy system. In this paper, a day-ahead optimal scheduling method of integrated energy systems considering the dynamic delay of the pipeline network is proposed. The method takes into account the impact of pipe network delay on day-ahead optimal scheduling of the system, solves the problem of considerable time lag of pipe network in the process of optimal scheduling of the system, and improves the real-time, safety, and economy of the system scheduling. The method uses the nodal method to establish a dynamic model of the pipeline network system. It analyses the impact of dynamic characteristics on the system equipment's output and system scheduling. A mixed integer linear programming method is used to establish an optimal scheduling model for the integrated energy system, and the system is optimized to maximize the daily revenue in combination with time-of-day tariffs. Finally, the proposed model is validated based on the energy station data in a park in Wuhan. The results show that the optimal scheduling strategy of the integrated energy system that considers the dynamic time-delay characteristics of the pipeline network can effectively improve the system's economy, the system scheduling's real-time performance, and the system operation's safety. [ABSTRACT FROM AUTHOR]

This paper considers output-based adaptive event-triggered control of saturated system with the dynamic anti-windup compensator. An adaptive event-triggered condition with a time-varying threshold function is proposed, under which the system has better performance in saving communication resources. A dynamic anti-windup compensator is employed to overcome the potential performance degradation caused by input saturation. For the prescribed dynamic anti-windup compensator, an optimization problem is proposed for enlarging the domain of attraction. Moreover, if dynamic anti-windup compensator is not given in advance, co-design of the dynamic anti-windup compensator and adaptive event-triggered condition is developed. In addition, the Zeno behavior is excluded by calculating the minimum triggering time interval. Finally, the theoretical result is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

State estimation for large-scale non-Gaussian dynamic systems remains an unresolved issue, given nonscalability of the existing particle filter algorithms. To address this issue, this paper extends the Langevinized ensemble Kalman filter (LEnKF) algorithm to non-Gaussian dynamic systems by introducing a latent Gaussian measurement variable to the dynamic system. The extended LEnKF algorithm can converge to the right filtering distribution as the number of stages become large, while inheriting the scalability of the LEnKF algorithm with respect to the sample size and state dimension. The performance of the extended LEnKF algorithm is illustrated by dynamic network embedding and dynamic Poisson spatial models. [ABSTRACT FROM AUTHOR]

This paper introduces dual fairness concerns into the classic two-level supply chain consisting of the fairness neutral supplier and fairness concerned retailers. The bargaining process is modeled under both simultaneous and sequential game to analyze the different situation of fairness concerns. The impact of dual fairness concerns is considered comprehensively on both short-term and long-term games. In short-term game, we conduct a sensitivity analysis on the optimal decision in a single cycle and find that the bargaining power and distributional fairness concern has opposite effects on the optimal solutions. Similarly, the impact of dual fairness concerns on that is also opposite. In long-term game, the dynamic system is constructed to investigate the influence of dual fairness concerns on system stability. At last, comparing the performance of the supplier and retailers, this paper explores the supplier's timing choice based on the equilibrium point. The comparison shows that sequential game is more beneficial to the supplier because peer-induced fairness concern exacerbates the internal friction of retailers. [ABSTRACT FROM AUTHOR]

This paper presents a physics-informed neural network (PINN) approach for monitoring the health of diesel engines. The aim is to evaluate the engine dynamics, identify unknown parameters in a "mean value" model, and anticipate maintenance requirements. The PINN model is applied to diesel engines with a variable-geometry turbocharger and exhaust gas recirculation, using measurement data of selected state variables. The results demonstrate the ability of the PINN model to predict simultaneously both unknown parameters and dynamics accurately with both clean and noisy data, and the importance of the self-adaptive weight in the loss function for faster convergence. The input data for these simulations are derived from actual engine running conditions, while the outputs are simulated data, making this a practical case study of PINN's ability to predict real-world dynamical systems. The mean value model of the diesel engine incorporates empirical formulae to represent certain states, but these formulae may not be generalizable to other engines. To address this, the study considers the use of deep neural networks (DNNs) in addition to the PINN model. The DNNs are trained using laboratory test data and are used to model the engine-specific empirical formulae in the mean value model, allowing for a more flexible and adaptive representation of the engine's states. In other words, the mean value model uses both the PINN model and the DNNs to represent the engine's states, with the PINN providing a physics-based understanding of the engine's overall dynamics and the DNNs offering a more engine-specific and adaptive representation of the empirical formulae. By combining these two approaches, the study aims to offer a comprehensive and versatile approach to monitoring the health and performance of diesel engines. [ABSTRACT FROM AUTHOR]

Causal inference in complex systems has been largely promoted by the proposal of some advanced temporal causation models. However, temporal models have serious limitations when time series data are not available or present insignificant variations, which causes a common challenge for earth system science. Meanwhile, there are few spatial causation models for fully exploring the rich spatial cross-sectional data in Earth systems. The generalized embedding theorem proves that observations can be combined together to construct the state space of the dynamic system, and if two variables are from the same dynamic system, they are causally linked. Inspired by this, here we show a Geographical Convergent Cross Mapping (GCCM) model for spatial causal inference with spatial cross-sectional data-based cross-mapping prediction in reconstructed state space. Three typical cases, where clearly existing causations cannot be measured through temporal models, demonstrate that GCCM could detect weak-moderate causations when the correlation is not significant. When the coupling between two variables is significant and strong, GCCM is advantageous in identifying the primary causation direction and better revealing the bidirectional asymmetric causation, overcoming the mirroring effect. Temporal causation models perform poorly in causal inference for variables with limited temporal variations. This paper establishes a causal inference model, which can reveal the nonlinear complex casual associations based on cross-sectional Earth System data. [ABSTRACT FROM AUTHOR]

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications. Many challenging problems in science and engineering rely on the study of dynamical systems that evolve continuously in time, and yet this feature proves difficult to be captured reliably using modern machine learning (ML) models. This paper develops a convergence test based on numerical analysis and illustrates how this methodology can be combined with existing ML techniques to validate models for science and engineering applications. [ABSTRACT FROM AUTHOR]

The conveyance of fluid through pipes is a common occurrence in practical applications, and the dynamic stability of such systems has been a subject of interest for many decades. In this paper, we investigate the dynamic stability of a cantilevered pipe conveying fluid, considering the lateral distributed load as a critical factor. To achieve this, we employ the differential quadrature method to solve the eigenvalue equations for various load patterns. Remarkably, we observe excellent agreement with exact solutions and the Argand diagram. By analyzing the relationship between circular frequency and dimensionless velocity, we demonstrate that the descending distributed load pattern exhibits the highest stability. For certain conditions, it is possible to enhance stability. The results obtained in this study provide valuable insights for improving the stability of cantilevered pipe conveying fluid through a different approach. [ABSTRACT FROM AUTHOR]

This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the solids at relative rest, are exponentially stable if and only if the axis of rotation is the principal axis of inertia corresponding to the largest moment of inertia of the outer body. All other equilibria are normally hyperbolic, and hence unstable. In addition, we show that all solutions to the governing equations converge to an equilibrium configuration, no matter which initial conditions are chosen. Numerical evidence of the above results as well as conditions ensuring attainability of the stable configurations are also presented. For the stability analysis we use a linearization principle for dynamical systems possessing a center manifold. The characterization of the long-time behaviour is obtained by a careful analysis of the partially dissipative system of equations governing the motion of the coupled system. [ABSTRACT FROM AUTHOR]