Stability Of Systems Research Articles

Prediction interval: A powerful statistical tool for monitoring patients and analytical systems.

Monitoring is indispensable for assessing disease prognosis and evaluating the effectiveness of treatment strategies, both of which rely on serial measurements of patients' data. It also plays a critical role in maintaining the stability of analytical systems, which is achieved through serial measurements of quality control samples. Accurate monitoring can be achieved through data collection, following a strict preanalytical and analytical protocol, and the application of a suitable statistical method. In a stable process, future observations can be predicted based on historical data collected during periods when the process was deemed reliable. This can be evaluated using the statistical prediction interval. Statistically, prediction interval gives an "interval" based on historical data where future measurement results can be located with a specified probability such as 95%. Prediction interval consists of two primary components: (i) the set point and (ii) the total variation around the set point which determines the upper and lower limits of the interval. Both can be calculated using the repeated measurement results obtained from the process during its steady-state. In this paper, (i) the theoretical bases of prediction intervals were outlined, and (ii) its practical application was explained through examples, aiming to facilitate the implementation of prediction intervals in laboratory medicine routine practice, as a robust tool for monitoring patients' data and analytical systems.

Predefined-time stabilization of stochastic nonlinear systems with application to UAVs

The paper presents a new Lyapunov-type predefined-time stabilization control algorithm for stochastic high-order nonlinear systems with asymmetric output constraints. In contrast to stochastic finite-time and fixed-time stabilization, the average value of the settling-time function for stochastic predefined-time stabilization control is independent of both the initial value and the control factors. To mitigate the significant uncertainties arising from the asymmetric output constraint, a tan-type barrier Lyapunov function is formulated. Furthermore, by harnessing the previously mentioned barrier Lyapunov function and integrating the power integrator technique, a controller design strategy is formulated based on the backstepping method. The rigorous analysis in this study proves that the designed controller ensures both the attainment of predefined-time convergence of the system states to the origin in probability and the satisfaction of the output constraint. Finally, an example of a roll angle subsystem for quadrotor UAVs and a numerical illustration are presented to corroborate the theoretical analysis.

Robust H∞ consensus for uncertain linear multi-agent systems on directed topologies: A dynamic event-triggered strategy

Considering the asymmetry of the system matrix caused by directed communication networks, a dynamic event-triggered control protocol for the robust [Formula: see text] consensus of uncertain linear multi-agent systems accompanied by external disturbances on directed topologies is proposed. Through the introduction of the controlled output and generalized algebraic connectivity for directed graphs, the consensus problem is converted to the event-triggered stabilization of the uncertain linear closed-loop system with disturbance. On the basis of the relative state of neighbor agents at event-times and the introduced dynamic variables, a dynamic event-triggered control protocol is put forward, and the linear matrix inequality sufficient conditions for the system to achieve robust [Formula: see text] consensus are obtained after a rigorous proof. Then, linear matrix inequalities are further decoupled to greatly reduce the computational complexity, and the parameters of the control protocol are determined by solving the decoupled linear matrix inequalities. Finally, simulations are applied for the verification of conclusions.

Current Controller Design of Grid-Connected Inverter with Incomplete Observation Considering L-/LC-Type Grid Impedance

This paper presents a current control design for stabilizing an inductive-capacitive-inductive (LCL)-filtered grid-connected inverter (GCI) system under uncertain grid impedance and distorted grid environment. To deal with the negative impact of grid impedance, LC-type grid impedance is considered in both the system model derivation and controller design process of an LCL-filtered GCI system. In addition, the integral and resonant control terms are also augmented into the system model in the synchronous reference frame to guarantee the reference tracking of zero steady-state error and good harmonic disturbance compensation of the grid-injected currents from GCI. By considering the effect of grid impedance on the control design process, an incomplete state feedback controller will be designed based on the linear-quadratic regulator (LQR) without damaging the asymptotic stabilization and robustness of the GCI system under uncertain grid impedance. By means of the closed-loop pole map evaluation, the asymptotic stability, robustness, and resonance-damping capability of the proposed current control scheme are confirmed even when all the system states are not available. In order to reduce the number of required sensors for the realization of the controller, a discrete-time current-type full-state observer is employed in this paper to estimate the system state variables with high precision. The feasibility and effectiveness of the proposed control scheme are demonstrated by the PSIM simulations and experiments by using a three-phase GCI prototype system under adverse grid conditions. The comprehensive evaluation results show that the designed control scheme maintains the stability and robustness of the LCL-filtered GCI when connecting to unexpected grids, such as harmonic distortion and L-type and LC-type grid impedances. As a result, the proposed control scheme successfully stabilizes the entire GCI system with high-quality grid-injected currents even when the GCI faces severe grid distortions and an extra grid dynamic caused by the L-type or LC-type grid impedance. Furthermore, low-order distortion harmonics come from the background grid voltages and are maintained as acceptable limits according to the IEEE Std. 1547-2003. Comparative test result with the conventional one also confirms the effectiveness of the proposed control scheme under LC-type grid impedance thanks to the consideration of LC grid impedance in the design process.

Modified Multimachine Power System Design with DFIG-WECS and Damping Controller

Rotor angle stability, which involves electromechanical oscillation damping and control, is very important in maintaining the stability of modern power grid systems. Renewable energy sources like wind energy are undergoing massive integration into modern power grid systems to meet energy demands and decarbonize power grid systems of carbon emissions from fossil fuel generators. To enable increased integration of wind renewable energy sources, precise models are needed for research and analytical purposes. Wind renewable energy is generated through a wind energy conversion system (WECS); one such conversion system is the doubly fed induction generator (DFIG) system. In this study, a precise model of a DFIG-WECS was modeled and integrated into the IEEE’s two-area Kundur power test system, which represents the available power grid system, and is also a multimachine power system using the Matlab/Simulink 2023 software. A damping controller known as the power system stabilizer (PSS), whose optimal parameters were obtained using artificial eco-system optimization (AEO), was also incorporated into the integrated power grid system to control and damp electromechanical oscillations. The results showed that the PSS damping controller effectively damped electromechanical oscillations in the integrated power grid system.

Визначення коефіцієнтов гідродинамічної моделі кавітуючих насосів рідин-них ракетних двигунів за їх теоретичними передатними матрицями

The characterization of cavitating pumps of liquid-propellant rocket engines (LPRE) is an important problem because of the need to provide the pogo stability of liquid-propellant launch vehicles and the stability of liquid-propellant propulsion systems for cavitation oscillations. The development of a reliable mathematical model of LPRE cavitating pumps allows this problem to be resolved. The goal of this work is to determine the cavitation number and operating parameter dependences of the coefficients of a lumped-parameter hydrodynamic model of LPRE cavitating pumps from their theoretical transfer matrices obtained by a distributed-parameter model. The following coefficients are found as a function of operating parameters: the cavitation elasticity, the cavitation resistance, the cavity-caused disturbance transfer delay time, and the cavitation resistance distribution coefficient. The last two coefficients are new in the hydrodynamic model of cavitating pumps, and they were introduced when verifying the model using experimental and theoretical pump transfer matrices. Analyzing the cavitation resistance distribution coefficient as a function of operating parameters shows that it markedly decreases with increasing cavitation number. This testifies to that the location of the lumped cavity compliance is shifted from the mid position towards the pump inlet. Therefore, the assumption that the lumped cavity compliance is located in the middle of the attached cavity regardless of the cavitation number is not justified. The fact that the distribution coefficient as a function of cavitation number intersects the abscissa axis near a cavitation number of 0.25 may indicate the boundary of existence of attached cavities and thus the applicability boundary of the theoretical model. The disturbance transfer delay time as a function of cavitation number sharply increases at cavitation numbers of about 0.05. At cavitation numbers of about 0.25, it is close to a constant.

Molecular strategies of the pygmy grasshopper Eucriotettix oculatus adapting to long-term heavy metal pollution

To study the heavy metal accumulation and its impact on insect exterior and chromosome morphology, and reveal the molecular mechanism of insects adapting to long-term heavy metal compound pollution habitats, this study, in the Diaojiang river basin, which has been polluted by heavy metals(HMs) for nearly a thousand years, two Eucriotettix oculatus populations was collected from mining and non-mining areas. It was found that the contents of 7 heavy metals (As, Cd, Pb, Zn, Cu, Sn, Sb) in E. oculatus of the mining area were higher than that in the non-mining 1–11 times. The analysis of morphology shows that the external morphology, the hind wing type and the chromosomal morphology of E. oculatus are significant differences between the two populations. Based on the heavy metal accumulation，morphological change, and stable population density, it is inferred that the mining area population has been affected by heavy metals and has adapted to the environment of heavy metals pollution. Then, by analyzing the transcriptome of the two populations, it was found that the digestion, immunity, excretion, endocrine, nerve, circulation, reproductive and other systems and lysosomes, endoplasmic reticulum and other cell structure-related gene expression were suppressed. This shows that the functions of the above-mentioned related systems of E. oculatus are inhibited by heavy metal stress. However, it has also been found that through the significant up-regulation of genes related to the above system, such as ATP2B, pepsin A, ubiquitin, AQP1, ACOX, ATPeV0A, SEC61A, CANX, ALDH7A1, DLD, aceE, Hsp40, and catalase, etc., and the down-regulation of MAPK signalling pathway genes, can enhanced nutrient absorption, improve energy metabolism, repair damaged cells and degrade abnormal proteins, maintain the stability of cells and systems, and resist heavy metal damage so that E. oculatus can adapt to the environment of heavy metal pollution for a long time.

Observer-based control for large-scale interconnected systems with parameter uncertainty and application to wireless power transfer systems

In the work, the observer-based control is designed and analyzed for a class of large-scale interconnected systems subject to parameter uncertainty. In the beginning, we build a large-scale interconnected system with parameter uncertainty and apply this model to a multi-level wireless power transfer system. By using this modeling method, the order of multi-level wireless power transfer system is greatly deduced. In addition, the multi-level wireless power transfer system include coupling terms and uncertain parameters considered in the observer-based control law design. We earn sufficient conditions of this model stability for multi-level wireless power transfer systems under this control law through the Lyapunov stability theorem and Young’s inequality. The stability analysis method suggested in the work could also be adopted in other practical plants. At last, the correctness and availability of this suggested approach are verified through simulation results.

Evolution of urban land and population system coupling micro–dynamics and macro-stability: Trends and paths

Cities are constantly dynamics, but emerge the stability of urban systems as evidenced by robust urban scaling. Both properties serve as necessary perspectives for understanding the evolution of cities and the complexity of urban systems. However, the evolution trends and mechanisms behind the above relationships, particularly concerning geographic processes, remain to be explored in depth. In this study, the dynamic fluctuations within individual cities and the macro-stability of the evolution of urban systems over the past two decades are systematically demonstrated. Subsequently, associations between urban systems and individual cities are established on the basis of micro- and macro-dynamic mechanisms. The trajectory of individual cities can be divided into scaled–driven growth (SG) and urban excess growth (EG). The former is the result of scaling effects within the system, while the latter is affected by global external effects. Taking as examples urban built-up area and social productions, the evolution pathways that vary from different attributes are analyzed. The results indicate that urban built-up area is more affected by scaling effects whereas social productions is driven more by global external effects. Moreover, we examine the driving forces and mechanism of EG from the aspects of economic development level, technological and economic progress, industrial structure and regional policy through an empirical analysis. This study provides a nuanced understanding of the trends and pathways of urban land–population system from the perspective of complex urban systems and holism to deepen the understanding for general properties of cities and co-evolution for urban population size and land expansion.

Instability of multi-mode systems with quadratic Hamiltonians

We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric perspective of instability: A quantum quadratic system is dynamically unstable if and only if its Hamiltonian is non-elliptic (i.e., hyperbolic or lineal). By applying our geometric method, we analyze the stability of two-mode and three-mode optomechanical systems. Remarkably, our approach demonstrates that these systems can be stabilized over a wider range of system parameters compared to the conventional rotating wave approximation (RWA) assumption. Furthermore, we reveal that the systems transit their phases from stable to unstable, when the system parameters cross specific critical boundaries. The results imply the presence of multistability in the optomechanical systems.

Reliable stabilization of discrete-time nonlinear singular systems with time-varying delays

The problem of delay-dependent reliable control for uncertain discrete-time nonlinear singular system with time-varying delays is investigated. A new set of delay-dependent sufficient conditions are established for the existence of a reliable controller which ensures the singular system to be regular, causal (absence of impulses) and stable for all admissible parameter uncertainties. First, the controller for singular system in the presence of known actuator fault matrix is designed. Further, the result is extended to study the robust stabilization of singular systems with unknown actuator fault matrix. The sensor failures of actuator are considered by a variable, which is varying in a given interval. The conditions for the existence of proposed controller design are established in the form of linear matrix inequality (LMI), which can be easily solved via standard numerical software. Finally, numerical examples with simulation results are provided to illustrate the usefulness of control design and results are compared with existing results to show the less conservatism of the proposed theory.

A new two-stage decomposition and integrated hybrid model for short-term wind speed prediction

Accurate wind speed prediction is of essential importance for the stability and safe operation of power systems. Given the complexity of wind speed sequence, this paper proposed a new two-stage decomposition and integrated hybrid model to improve the accuracy of wind speed prediction. A two-stage decomposition method combining robust local mean decomposition (RLMD), sample entropy (SE) and variational modal decomposition (VMD) was used to decompose the wind speed signal in the data preprocessing stage. Firstly, the wind speed signal was decomposed into various components by RLMD, and the complexity of each component was calculated using the SE to classify them into random, detail component and trend component. Then, a secondary decomposition of the random component with the highest SE was performed using the VMD. In the prediction stage, two different prediction models were used for prediction depending on the smoothness of each component. Stochastic configuration networks (SCN) was used to predict the detail and trend components with relatively smoothness. Echo state network (ESN) was used to predict the components of the secondary decomposition. Finally, the actual wind speed data were compared by different prediction models, which illustrated that the prediction method proposed in this paper had good prediction accuracy and generalizability.

Generalized quadratic embeddings for nonlinear dynamics using deep learning

The engineering design process often relies on mathematical modeling that can describe the underlying dynamic behavior. In this work, we present a data-driven methodology for modeling the dynamics of nonlinear systems. To simplify this task, we aim to identify a coordinate transformation that allows us to represent the dynamics of nonlinear systems using a common, simple model structure. The advantage of a common simple model is that customized design tools developed for it can be applied to study a large variety of nonlinear systems. The simplest common model – one can think of – is linear, but linear systems often fall short in accurately capturing the complex dynamics of nonlinear systems. In this work, we propose using quadratic systems as the common structure, inspired by the lifting principle. According to this principle, smooth nonlinear systems can be expressed as quadratic systems in suitable coordinates without approximation errors. However, finding these coordinates solely from data is challenging. Here, we leverage deep learning to identify such lifted coordinates using only data, enabling a quadratic dynamical system to describe the system’s dynamics. Additionally, we discuss the asymptotic stability of these quadratic dynamical systems. We illustrate the approach using data collected from various numerical examples, demonstrating its superior performance with the existing well-known techniques.

New exponentially weighted inequality and its application to finite-time stability of descriptor time-delay systems

The paper considers the finite-time stability of descriptor time-delay systems. Firstly, we establish a set of exponentially weighted orthogonal polynomials, and based on this, we obtain a new exponentially weighted inequality(EWI). Secondly, an augmented Lyapunov-like functional (LLF) is established driven by the presented EWI. Finally, by applying the EWI and the LLF, some sufficient conditions for ensuring the finite-time stability of the system are obtained. A small partial element equivalent circuit model and two numerical examples are used to verify the effectiveness of the method.

Stabilization of nonlinear stochastic systems with input and output delays via event‐triggered predictive control

AbstractThe stabilization of nonlinear stochastic systems with input and output delays is investigated in this article. First, an observer that includes input delay information is designed to estimate the state information after eliminating the effect of input delay. Second, a predictive scheme with delay information is utilized to predict the system state affected by output delay, and an event‐triggered predictive controller is established to eliminate the effects of input and output delays simultaneously. Subsequently, the convergence of the prediction error is analyzed by utilizing a recursive method, and a sufficient condition to ensure the global exponential stability is given by constructing a new closed‐loop system. Finally, numerical simulations of two nonlinear stochastic systems with different delay sizes are utilized to verify the impact of the event‐triggered predictive control in addressing the stabilization of nonlinear stochastic systems with time delays.

The residual life prediction of power grid transformers based on GA-ELM computational model and digital twin data

As one of the core equipment of the power grid, the operation status of transformers directly affects the stability and reliability of the power system. To accurately evaluate the remaining life of power grid transformers, a genetic algorithm is applied to optimize the Extreme Learning Machine based on digital twin technology. Then, considering changes in load rate, a residual life prediction model for power grid transformers is constructed. From the results, the error of the research method was within 2℃, with a maximum error of only 1.76℃. The research model converged with a fitness value of 0.04 at 150 iterations. It showed good predictive performance for hot spot temperatures under different load rates, with an average accuracy of 99.97%. Compared with backpropagation models and extreme learning machine models, the research method improved accuracy by 2.85% and 1.01%, respectively, with small and stable prediction errors. It verified the superiority of the research model, indicating that the research method can improve the accuracy of predicting the remaining life for power grid transformers. By monitoring the operation status of transformers in real-time, potential faults can be detected in a timely manner. The maintenance and replacement can be carried out in advance to avoid power outages caused by equipment damage. In addition, the research can provide reference for the planning and design of power systems, and support the stability and reliability of power systems.

Enhancing Automated Test Case Generation Through KNN algorithm in Software Testing

In the ever-evolving world of software development, assuring the stability and resilience of software systems remains a vital task. This study aims to tackle this problem by suggesting a novel method for generating automated test cases. It involves incorporating the robust KNN algorithm into the domain of data mining methods. The research intends to exploit previous testing data to detect patterns and trends, increasing the production of effective and targeted test scenarios.
 The literature study highlights the increasing overlap between data mining and software testing, underscoring the need for sophisticated methods to address the requirements of contemporary, ever-changing applications. In this regard, our study presents the KNN algorithm as a new addition to the collection of data mining tools for software testing. The process entails gathering extensive historical testing data, including information on test cases, errors, and the attributes of tested software applications. By using rigorous preprocessing and feature selection techniques, the KNN method is used to examine the correlations between various variables and the probability of flaws. The KNN model is trained and optimized using the dataset, and the resultant predictions are then used in an automated system for generating test cases. The experimental results confirm the efficacy of the suggested method in finding crucial test scenarios and prioritizing test cases according to past fault trends. The practical usefulness and advantages of incorporating the KNN algorithm into the automated test case-generating process are further confirmed by real-world case studies. In conclusion, this study expands the discourse on data mining in software testing by proposing the KNN algorithm as a vital component in automated test case development. By using KNN, testing teams can adjust to the ever-changing characteristics of contemporary applications, leading to enhanced efficiency and effectiveness in testing procedures. The results of this research enhance the continuous development of software quality assurance methods and provide opportunities for additional investigation at the convergence of machine learning and software testing

Revealing the mechanism of combining best properties of homogeneous and heterogeneous catalysis in hybrid Pd/NHC systems

The formation of transient hybrid nanoscale metal species from homogeneous molecular precatalysts has been demonstrated by in situ NMR studies of catalytic reactions involving transition metals with N‐heterocyclic carbene ligands (M/NHC). These hybrid structures provide benefits of both molecular complexes and nanoparticles, enhancing the activity, selectivity, flexibility, and regulation of active species. However, they are challenging to identify experimentally due to the unsuitability of standard methods used for homogeneous or heterogeneous catalysis. Utilizing a sophisticated solid‐state NMR technique, we provide evidence for the formation of NHC‐ligated catalytically active Pd nanoparticles (PdNPs) from Pd/NHC complexes during catalysis. The coordination of NHCs via C(NHC)‐Pd bonding to the metal surface was first confirmed by observing the Knight shift in the 13C NMR spectrum of the frozen reaction mixture. Computational modeling revealed that as little as few NHC ligands are sufficient for complete ligation of the surface of the formed PdNPs. Catalytic experiments combined with in situ NMR studies confirmed the significant effect of surface covalently bound NHC ligands on the catalytic properties of the PdNPs formed by decomposition of the Pd/NHC complexes. This observation shows the crucial influence of NHC ligands on the activity and stability of nanoparticulate catalytic systems.

Semi-global exponential stabilization of stochastic nonlinear systems with distributed delay under discrete-time state observations and application to circuit systems

This paper is aimed at studying the semi-global exponential stabilization problem for stochastic nonlinear systems with distributed delay under discrete-time state observations. An extended definition of horizontal translation of the segment function along the investigated systems is given, related to the stochastic disturbance and Brownian motion. Basically, the right and upper Dini’s derivative of the constructed functional is presented. Combining this with the global exponential stability of the stochastic nonlinear systems with distributed delay under continuous-time feedback control, the Lyapunov method and Halanay inequality, the maximum observation interval and some stabilization criteria to make the investigated systems under discrete-time state observations reach semi-global exponential stabilization are provided. The results indicate that the semi-global exponential stabilization is dependent upon stochastic disturbance, initial condition range, and maximum observation interval. Finally, an application to the circuit systems is discussed and the involved sufficient conditions for the circuit systems to keep semi-global stabilization are also proposed. Besides, the numerical simulation results confirm the effectiveness of the theoretical results.

Revealing the mechanism of combining best properties of homogeneous and heterogeneous catalysis in hybrid Pd/NHC systems.

The formation of transient hybrid nanoscale metal species from homogeneous molecular precatalysts has been demonstrated by in situ NMR studies of catalytic reactions involving transition metals with N-heterocyclic carbene ligands (M/NHC). These hybrid structures provide benefits of both molecular complexes and nanoparticles, enhancing the activity, selectivity, flexibility, and regulation of active species. However, they are challenging to identify experimentally due to the unsuitability of standard methods used for homogeneous or heterogeneous catalysis. Utilizing a sophisticated solid-state NMR technique, we provide evidence for the formation of NHC-ligated catalytically active Pd nanoparticles (PdNPs) from Pd/NHC complexes during catalysis. The coordination of NHCs via C(NHC)-Pd bonding to the metal surface was first confirmed by observing the Knight shift in the 13C NMR spectrum of the frozen reaction mixture. Computational modeling revealed that as little as few NHC ligands are sufficient for complete ligation of the surface of the formed PdNPs. Catalytic experiments combined with in situ NMR studies confirmed the significant effect of surface covalently bound NHC ligands on the catalytic properties of the PdNPs formed by decomposition of the Pd/NHC complexes. This observation shows the crucial influence of NHC ligands on the activity and stability of nanoparticulate catalytic systems.