Stability Of Dynamical Systems Research Articles

TWO APPROACHES TO THE FORMATION OF A QUANTITATIVE MEASURE OF STABILITY BASED ON MULTIPLE ESTIMATES OF THE PARAMETERS OF AN ENSEMBLE OF TRANSIENT PROCESSES

The article is devoted to the further development of the theory of stability of dynamic systems, namely of quantitative methods of stability assessment. A review and critical analysis of various approaches, which allow to introduce a quantitative measure of stability of dynamic systems to one degree or another, is given. The limitations of the existing methods, which are primarily related to the assessment of the behavior of the transient processes of individual trajectories, as well as the difficulty of obtaining an assessment of the behavior of the ensemble of transient processes when trying to apply the methods of N. D. Moiseyev. are substantiated. A method of quantitative assessment of a dynamic system stability based on the numerical estimates of the behavior of the area of initial deviations from the equilibrium position on the trajectories of the dynamic system is substantiated. Based on the Liouville formula, it is shown that changes in the volume of the area of the initial deviations on the trajectories of the system does not depend on the form of the latter one. This allowed to limit the area of initial deviations in the shape of a hypersphere and to obtain a simple expression for a quantitative measure of the stability of a linear stationary dynamic system, the geometric sense of which is to estimate the rate of change of the volume of the control surface. The article proposes and substantiates the criterion of uniformity of deformation of the area of initial deviations. The essence of the problem is that in the transient process, the values of some components of the phase vector may reach unacceptable deviations from the equilibrium position. A theoretical estimate of deformation non-uniformity for linear systems is obtained, which is taken to be the deviation of the trace of the ellipsoid matrix from the deviations of the trace of the hypersphere matrix of the corresponding volume. A method for a quantitative measure of the stability based on an integral quadratic functional calculated on a set of transient processes of initial deviations in the form of a set of ellipsoids with a normalized volume is proposed and substantiated. Diagonal positive normalized matrices are considered as a set of matrices of the integral quadratic criterion. A simple algorithm for calculation of the multiple integral quadratic criterion is proposed.

DYNAMIC MODELLING OF THREE-PHASE MICROGRIDS INCLUDING DQ0 CURRENT CONTROLLED PHOTOVOLTAIC GENERATION UNDER TRANSIENT CONDITIONS

ABSTRACT: The photovoltaic generation can be interconnected to power systems or to insulated grids to satisfy the growing electrical demand as an alternative renewable energy source. The photovoltaic generator dynamics affects the control, protection, stability, and power quality of the electrical grid, this network dynamics requires to be examined and conveniently regulated and adjusted. The dynamic averaged model for the dq0 current controlled DC/AC inverter is applied to obtain the time-domain response to electromagnetic transients under special conditions such as electrical load fluctuations, unbalanced faults, voltage and current transients to verify e.g., the ride through capability or to adjust the protection and control devices, these transients can be present during the operation of electrical microgrids and power systems interconnected with photovoltaic generation. The system modelling includes the photovoltaic plant interconnected with the microgrid using the dq0 current controlled DC/AC inverter. The case studies are applied to analyse three-phase electrical microgrids, their time-domain response, and the obtained voltage and current waveforms can be used to verify the dynamic behaviour and stability of the electrical system interconnected with photovoltaic generation and similarly to verify the operation of the dq0 current controller for the inverter. The results can be used to control the microgrid dynamic behaviour. Keywords: current control, dq0 transform, inverter, microgrids, photovoltaic generation, power quality, protection, time-domain, transients, unbalanced faults, unbalanced voltage sags, voltage source converter

Finite/fixed-time synchronized stability of autonomous discrete-time dynamical systems

Finite/fixed-time synchronized stability of autonomous discrete-time dynamical systems

Identification of potential PIM-2 inhibitors via ligand-based generative models, molecular docking and molecular dynamics simulations.

Proviral Integrations of Moloney-2 (PIM-2) kinase is a promising target for various cancers and other diseases, and its inhibitors hold potential for treating related diseases. However, there is currently no clinically available PIM-2 inhibitor. In this study, we constructed a generative model for de novo PIM-2 inhibitor design based on artificial intelligence, performed molecular docking and molecular dynamics (MD) simulations to develop an efficient PIM-2 inhibitor generative model and discover potential PIM-2 inhibitors. First, we designed a generative model based on a Bi-directional Long Short-Term Memory (BiLSTM) framework combined with a transfer learning strategy and generated a new PIM-2 small molecule library using existing active drug databases. The generated compound library was then virtually screened by molecular docking and scaffold similarity comparison, identifying 10 initial hit compounds with better performance. Next, using the inhibitor in the crystal structure as a positive control, we performed two rounds of MD simulations, with lengths of 100ns and 500ns, respectively, to study the dynamic stability of the protein-ligand systems of the 10 compounds with PIM-2. Analyzed the interactions with key hinge region residues, binding free energies, and changes in the ATP pocket size. The generative model demonstrates good molecular generation capability and can generate efficient novel molecules with similar physicochemical properties as active PIM-2 drugs. Among the 10 initially selected hit compounds, 5 compounds C3 (-29.69kcal/mol), C4 (-33.31kcal/mol), C5 (-28.59kcal/mol), C8 (-34.68kcal/mol), and C9 (-25.88kcal/mol) have higher binding energies with PIM-2 than the positive drug 3YR (-26.18kcal/mol). The MD simulation results are consistent with the docking analysis, these compounds have lower and more stable RMSD values for the complex systems with the reported positive drug 3YR and PIM-2 complex system. They can form long-term stable interactions with active site and the hinge region of PIM-2, which suggests these compounds are likely to have potent inhibitory effects on PIM-2. This study provides an efficient generative model for PIM-2 inhibitor research and discovers 5 potential novel PIM-2 inhibitors.

Improvement of an AC microgrid system’s stability by using a fuzzy logic-based PSS controller

This research article presents the low-frequency oscillation damping control of an AC Microgrid. It is integrated with four distributed generation units in which two DGs are renewable energy source based solar PV and wind energy using DFIG and the other two DGs are conventional synchronous generator-based hydro and diesel generators. There is insufficient generation through renewable-based DG then a diesel generator is employed as an emergency unit to fulfil the requirements and maintain and control the deviation of the frequency of the system. The use of renewable-based DG affected the system's dynamic stability and the characteristics of an integrated microgrid differ from conventional sources of generation. This investigation explores the impression of the deployment of multiple forms of the power oscillation damping (POD) controllers to distributed generation sources of grid forming AC Microgrid. The main various types of POD controllers are conventional lead-lag PSSs, MBPSS-4B, and proposed robust fuzzy logic PSS (FLPSS) controllers are implemented on distributed generation units of AC Microgrid for the elimination of low-frequency oscillation. Low oscillation frequencies between 0.1 and 2 Hz are the focus of this work. The system's damping ratios and stability margins because of MG integration are observed using eigenvalues analysis. The results of the simulation test demonstrate the accomplishment of the robust fuzzy logic PSS controller regarding conventional lead-lag PSSs and the MBPSS-4B controller during circumstances of fault.

Data-driven identification of stable sparse differential operators using constrained regression

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics forecasting problems. In this article, we propose a novel methodology for learning differential operators that are theoretically linearly stable and have sparsity patterns of common discretization schemes. These differential operators are obtained by solving a constrained regression problem, involving local constraints to ensure the linear stability of the global dynamical system. We further extend this approach for learning nonlinear differential operators by determining linear stability constraints for linearized equations around an equilibrium point. The applicability of the proposed method is demonstrated for both linear and nonlinear partial differential equations such as 1-D scalar advection-diffusion equation, 1-D Burgers equation and 2-D advection equation. The results indicated that solutions to constrained regression problems with linear stability constraints provide accurate and linearly stable sparse differential operators.

Protocol-based state estimation of two-time-scale complex networks with nonhomogeneous sojourn probabilities

This paper is dedicated to researching the problem of the state estimation for two-time-scale complex networks (TTSCNs) subject to sojourn probabilities (SPs) under channel fadings and false data injection attacks (FDIAs). The network’s switching topology is governed by a novel switching law that incorporates time-varying SPs, with the variation of SPs being regulated through a persistent dwell-time (PDT) switching signal. Meanwhile, for the sake of achieving energy savings and mitigating data congestion, the dynamic probabilistic event-triggered weighted try-once-discard (DPEWTOD) policy is innovatively developed by integrating with the major merits of the dynamic probabilistic event-triggered mechanism (DPETM) and WTOD protocol (WTODP) based on hybrid compensation. Different from the traditional communication rules, this DPEWTOD concept not only captures stochastic behavior of the dynamic triggering threshold (DTT), but also enables a compensatory measurement that closely approximates the actual value. Subsequently, we construct time delay-, DTT-, and PDT-dependent Lyapunov functionals to analyze the stability of error dynamic systems in the presence of fading and malicious FDIAs. By employing a separation technique, our proposed solving algorithm transforms non-convex analysis conditions into tractable ones. Eventually, the rationality and effectiveness of the proposed method are demonstrated by an resistance–capacitance (RC) circuit example.

Application of virtual synchronous generator technology in power systems and its modeling in the Matlab software package

Currently, the commissioning of power plants based on renewable energy sources (RES) using inverters is becoming widespread. However, these power plants do not participate in maintaining the stability of the power system during emergency disturbances, since they are switched off by technological protections when a disturbance occurs. In the future, when power plants based on renewable energy sources become widespread, ensuring the possibility of their participation in maintaining sustainability will significantly increase the reliability of the energy system. A preliminary assessment of the effectiveness of participation in maintaining sustainability should be carried out through computer modeling.THE PURPOSE: To realize the possibility of participation of RES-based power plants in ensuring reliable and sustainable operation of the power system, as well as to realize the possibility of performing a preliminary assessment of the effectiveness of the proposed method.METHODS. In this paper, the application of virtual synchronous generator technology is proposed to realize the possibility of participation of RES-based power plants in ensuring the reliability and sustainability of the power system. Also, a method of modeling the virtual synchronous generator in Matlab software package is proposed.RESULTS. The technology of virtual synchronous generator is proposed, which with the use of inverter, electric energy storage and appropriate control system can provide the increase of dynamic stability of power system. A method of modeling the virtual synchronous generator in Matlab software package is proposed. The results obtained allow us to conclude that the constructed model of a virtual synchronous generator is efficient, maintains the stability of the system and ensures correct control of the inverter, as a result of which the parameters of the electrical network are maintained within acceptable limits. The resulting computer model can be used in further research.CONCLUSION. The technology of virtual synchronous generator allows to imitate in the inverter the inertial and damping characteristics of the traditional synchronous generator, and the proposed computer model will help to evaluate the effectiveness of this technology when implemented in the power system.

Study on the Solutions of Impulsive Integrodifferential Equations of Mixed Type Based on Infectious Disease Dynamical Systems

Since ancient times, infectious diseases have been a major source of harm to human health. Therefore, scientists have established many mathematical models in the history of fighting infectious diseases to study the law of infection and then analyzed the practicability and effectiveness of various prevention and control measures, providing a scientific basis for human prevention and research of infectious diseases. However, due to the great differences in the transmission mechanisms and modes of many diseases, there are many kinds of infectious disease dynamic models, which make the research more and more difficult. With the continuous progress of infectious disease research technology, people have adopted more ways to prevent and interfere with the derivation and spread of infectious disease, which will make the state of infectious disease system change in an instant. The mutation of this state can be described more scientifically and reasonably by the mathematical impulse dynamic system, which makes the research more practical. Based on this, a time-delay differential system model of infectious disease under impulse effect was established by means of impulse differential equation theory. A class of periodic boundary value problems for impulsive integrodifferential equations of mixed type with integral boundary conditions was studied. The existence of periodic solutions of these equations was obtained by using the comparison theorem, upper and lower solution methods, and the monotone iteration technique. Finally, combined with the practical application, the established time-delay differential system model was applied to the prediction of the stability and persistence of the infectious disease dynamic system, and the correctness of the conclusion was further verified. This study provides some reference for the prevention and treatment of infectious diseases.

Enhancing disturbance rejection in offshore drilling platforms: a dynamic positioning control scheme using equivalent-input-disturbance method with separated observers

This paper presents a dynamic positioning control scheme for offshore drilling platforms using the equivalent-input-disturbance (EID) method with separated observers. The scheme incorporates observer-based disturbance compensation, wave-filtering state estimation, input transformation, and state feedback control to achieve robust control performance. The main contributions include the design of an EID scheme with separated observers, enabling enhanced disturbance-rejection performance, incorporating a notch filter in the EID estimator to reduce energy loss, and giving an observer tuning scheme to achieve a balanced performance between disturbance rejection and wave filtering. Simulation results demonstrate the effectiveness of the proposed scheme. This work provides valuable insights into designing stable and efficient dynamic positioning systems for offshore drilling platforms.

Generalization of KCC-theory to fractional dynamical systems and application to viscoelastic oscillations

As a geometrical method for analyzing the stability of dynamical systems, Kosambi–Cartan–Chern (KCC)-theory determines the Jacobi stability of a perturbation given to a trajectory based on the deviation curvature tensor. In this study, KCC-theory is generalized to dynamical systems with fractional derivatives, and the deviation curvature tensor is obtained from the fractional differential equation under the condition that the order of the fractional derivatives is close to an integer. Fractional KCC-theory is then applied to a one-dimensional spring–mass–damper model in which the damping force is expressed as a fractional derivative. In this case, three solution types are obtained depending on the damping coefficient and the fractional derivative order. One is damped oscillation with overshoot, which also appears in models with integer order derivatives, and another is damped oscillation without overshoot. The remaining one is overdamping, which neither oscillates nor overshoots. The deviation curvature tensor obtained from the fractional oscillatory model shows that both the damped oscillation without overshoot and the overdamping are Jacobi stable. When a discontinuous Jacobi instability appears on the solution curve, the solution type is classified as damped oscillation with overshoot. This result indicates that damped oscillation with overshoot and other solutions can be classified according to Jacobi stability.

Asymptotical Stabilization of Logic Dynamical Systems via Output-Based Random Control

Asymptotical Stabilization of Logic Dynamical Systems via Output-Based Random Control

Динамическая стабильность как категория диалектического взаимодействия хаоса и космоса в онтологии сетевого бытия

The increasing information flow has led to, inter alia, the dominant role of networking in communications. Devirtualization of networking in information and physical networks has made it possible to introduce network discourse into modern philosophy. The study of writings by Laozi, Confucius and their followers demonstrates that network discourse and network thinking were developed in the philosophical works of ancient Chinese scholars as representatives of Eastern philosophical discourse. At the same time, Western philosophical discourse, which can be traced to Plato and Aristotle, rests on linear logic and linear thinking. It is only towards the end of the 20th century that the linear/network thinking opposition weakened with the recognition of network interaction, under the influence of a profound transformation during the transition to a new stage of civilization’s development, that is, to the information/digital society. This can be illustrated by the evolution of the perception of the categories chaos and cosmos in Western (linear) and Eastern (network) philosophical discourse as the basis of the development of the modern representation of dynamic stability of the network interaction system. Using the information and communication method, this paper analyses Western and Eastern philosophical discourse from the Axial Age to the present day and substantiates the introduction of the category of dynamic stability. The latter stands for a dialectically connected process of creation/destruction of communications between actors of a network interaction under the influence of the dynamics of information exchange, which indicates that a network interaction system is autopoietic. Further development of the concept of dynamic stability requires creating a mathematical apparatus for calculating measures, that is, information entropy, of a dynamically stable network. These purely abstract studies are expected to be of practical importance for the development of social networks of interpersonal and intergroup communication.

An approach to nonlinear optimisation via set stabilisation of dynamical systems with an application to synchronous machines

An approach to constraint nonlinear optimisation is proposed, where the variables of the objective function and of the constraint function belong to the state of a nonlinear dynamical system. A nonlinear closed-loop feedback system is designed, whose solutions converge to a target set consisting of the optimal points of the underlying optimisation problem. The feedback law for the control input of the nonlinear dynamical system is designed by exact linearisation of a dynamical formulation of a first-order optimality condition. For the problem formulation and the stability analysis of the nonlinear closed-loop feedback system, the notion of V-detectability is considered. An application to energy-optimal feed-forward torque control for different types of synchronous machines is presented, which demonstrates the usefulness of the method. In this regard, anisotropic permanent magnet synchronous machines and electrically excited synchronous machines are covered.

Exploring electronic features in monolayer and bilayer MX2 (M = Hf, Zr; X = S, Se) structures under shear strain

This study employed first-principles calculations to investigate the dynamic stability of monolayer, bilayer, and heterostructure systems of four MX2 (M = Hf, Zr and X = S, Se) TMDCs, as well as the influence of shear strain on their electronic properties. The computed binding energies and phonon dispersions demonstrate the excellent dynamic stability of bilayer systems, while the small effective masses of electrons and holes in monolayer systems suggest high carrier mobility. Under shear strain, the bandgap size and type of monolayer MX2 system and their vdW heterostructures are effectively modulated, transitioning to metallic behavior under certain strain conditions. Both types of heterostructures exhibit type-II band alignment, serving as direct bandgap semiconductors, facilitating effective electron-hole separation between different layers and thereby reducing recombination. This study elucidates the tunability of the electronic properties of monolayers, bilayers, and heterostructures of MX2 systems under shear strain, which is important for expanding material functionalities and optimizing device performance.

Research of stochastic stability of constructions parametric vibrations by the Monte-Carlo method

The stochastic parametric vibrations of the elastic systems behave to the statistical dynamics section of the nonlinear systems. Under stochastic parametric influence the vibrations of the elastic systems, which is a random process more frequent are not stabilized, but their amplitudes are fading or unlimited are growing. Therefore important is stability of stochastic vibrations, which can be examined as stability by probability, on average or by the moment functions of different orders. The mathematical models which describe the stochastic parametric vibrations of the elastic systems are building by analytical or numeral approaches. Researches of stochastic stability of parametric vibrations are executing by probabilistic methods. Stability of parametric vibrations of modern constructions under the action of operating random loads are not enough investigated. In the article the numeral method of research of dynamic stability of the elastic systems under stochastic parametric influence was presented. The mathematical model of stochastic parametric vibrations of construction in the form of a reduсed finite element model was formed. Matrixes of the reduced model were obtained using calculated procedures of finite element analysis software NASTRAN. The dynamic loading as stationary ergodic random process with the spectral density was presented in the form of a finite amount of harmonic functions. Stochastic stability of the constructions was investigated using the Monte Carlo method and the Runge Kutta method of direct numeral integration of the equations of reduсed model. Stochastic stability as stability by probability of appearance of tendency to fading or unlimited growth of amplitude of parametric vibrations was examined during the time interval in space of the random parameters of loading. Dynamic stability of a I-beam with corrugated wall under narrow-band parametric influence was investigated using the numeral method.

Assessment of spilled oil dispersion affected by dispersant: Characteristic, stability, and related mechanism

Oil dispersion, a crucial process in oil transport, involves the detachment of oil droplets from slicks and their introduction into the water column, influencing subsequent oil migration and transformation. This study examines oil dispersion, considering characteristics, stability, and mechanisms, while evaluating the impact of dispersants and salinity. Results show the significant role of surfactant type in dispersants on oil dispersion characteristics, with anionic surfactants exhibiting higher sensitivity to salinity changes compared to nonionic surfactants. The dispersion efficiency varies with salinity, with anionic surfactants performing better in low salinity (<20‰) and nonionic surfactants showing superior performance at 30–35‰ salinities. Rheological analysis illustrates the breakup and coalescence of oil droplets within the shear rates of breaking waves. An increase in interfacial film rigidity impedes the coalescence of oil droplets, contributing to the dynamic stability of the oil-water hybrid system. The use of GM-2, a nonionic dispersant, results in the formation of a solid-like interface, characterized by increased elastic modulus, notably at 20‰ salinity. However, stable droplet size distribution (DSD) at 35‰ salinity for 60 h suggests droplets can remain dispersed in seawater. The enhancement of stability of oil dispersion is interpreted as the result of two mechanisms: stabilizing DSD and developing the strength of viscoelastic interfacial film. These findings offer insights into oil dispersion dynamics, highlighting the importance of surfactant selection and salinity in governing dispersion behavior, and elucidating mechanisms underlying dispersion stability.

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.

Distributed Time-Varying Optimization-An Output Regulation Approach.

This article deals with distributed algorithm design for time-varying optimization problems, which include unconstrained time-varying optimization and a special constrained problem commonly known as a resource allocation problem. The time-varying nature exists in the individual cost functions and the demand functions, and they are then captured by neutrally stable linear dynamic systems known as exosystems. To address the time-varying nature, new distributed algorithm structures are developed and two algorithms are designed for distributed time-varying optimization (DTVO) and distributed time-varying optimal resource allocation (DTVORA) to ensure that there exist time-varying solutions and the solution states will converge to the time-varying solutions. The driving terms for tracking the variation in the solutions are designed using exosystem dynamics. Rigorous convergence analyses are carried out using Lyapunov theory, and the examples are included to demonstrate the potential applications of the two proposed algorithms.

Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems

This paper addresses the problem of Neural Network (NN) based adaptive stability certification in a dynamical system. The state-of-the-art methods, such as Neural Lyapunov Functions (NLFs), use NN-based formulations to assess the stability of a non-linear dynamical system and compute a Region of Attraction (ROA) in the state space. However, under parametric uncertainty, if the values of system parameters vary over time, the NLF methods fail to adapt to such changes and may lead to conservative stability assessment performance. We circumvent this issue by integrating Model Agnostic Meta-learning (MAML) with NLFs and propose meta-NLFs. In this process, we train a meta-function that adapts to any parametric shifts and updates into an NLF for the system with new test-time parameter values. We demonstrate the stability assessment performance of meta-NLFs on some standard benchmark autonomous dynamical systems.