Stability Of Such Systems Research Articles

A Study of The Geographical Information System (GIS) based Energy Station Identification and Frequency Analysis Using ETA

The energy corporation entity recently pays maximum attention to the environmental and social safe guards associated with its operations. In developing countries mainly suffers to balance the gap between generation and demand for effective operation by the energy utilities. An inadequate transmission capacity, non-uniform location of energy stations may lead to worst consequences when the occurrences of fault and may end up with black out. To overcome the above situation and to improve the stability of such system, In this research proposes a Geographical Information System (GIS) based identification of location of the uncertainty power stations and also a technique called Islanding Scheme to protect the severely affected system by measuring its frequency parameters. The severely disturbed large interconnected power system is divided into number of subsystems with two or more generating buses feeding its nearby loads by disintegrating the tie lines. The sample 50 bus test case system taken from Tamilnadu Electricity Board (TNEB), INDIA to analyze and simulate the results using Electrical Transient Analyzer Program (ETAP) and Geographical Information System (GIS). In this paper, ETAP and GIS effective software tools used for identify the energy station in various locations and analyzing the frequency status of different buses for better operation in electric utilities and thus ensure better management, enhance the improved stability by mapping the data and outage management.

The Possible Factors that Influence the Stability of Binary Star System

Binary star systems are a crucial subject in astrophysics, as they provide insights into stellar formation, evolution, and dynamics. Despite extensive research, there remains a gap in understanding the factors influencing the longterm stability of such systems. This paper discusses the factors that may affect the stability of binary star systems by analyzing and exploring the physical laws and formulas of the operation of binary star systems and using the operation data of specific binary star systems as evidence. It can be concluded that the factors affecting the stability of a binary star system may be as follows: 1. Mass ratio of two stars, 2. Stellar spacing, 3. Orbital eccentricity, 4. Influence of stellar evolution stage, 5. The influence of external bodies. Future research should further explore the combined effects of these factors in more complex systems to better understand binary star stability in various astrophysical environments. Additionally, understanding how these factors interact in multi-body systems could provide deeper insights into the evolution of complex stellar systems.

Investigation on luminescence photoswitching stability in diarylethene-perovskite quantum dot hybrids.

Perovskite quantum dots (pQDs) have gathered a lot of attention because of their outstanding optoelectronic properties. Photoswitchable pQDs have the potential for application in single particle optical memories and bio-imaging. Hybrids of photochromic diarylethenes (DAE) and pQDs show a luminescence photoswitching property, however, the cycle stability in such systems is low because of photoinduced electron transfer (PET) from pQDs to DAE. In this study, various hybrids of DAEs and pQDs with different spacer lengths between the pQD donors and DAE acceptors were synthesized and their stability towards multiple cycles of luminescence photoswitching was evaluated. It was found that the electron transfer pathway can be blocked and very stable switchable hybrids can be produced when the distance between the donors and acceptors was long enough. Furthermore, the effect of softness of the basic ligands and the synthesis method of the pQDs on the cycle stability of the hybrids were investigated. The findings of this study suggest that the photoswitching stability can be improved in hybrid systems by proper molecular design of the photochromic molecule.

Modular control architecture for safe marine navigation: Reinforcement learning with predictive safety filters

Many autonomous systems are safety-critical, making it essential to have a closed-loop control system that satisfies constraints arising from underlying physical limitations and safety aspects in a robust manner. However, this is often challenging to achieve for real-world systems. For example, autonomous ships at sea have nonlinear and uncertain dynamics and are subject to numerous time-varying environmental disturbances such as waves, currents, and wind. There is increasing interest in using machine learning-based approaches to adapt these systems to more complex scenarios, but there are few standard frameworks that guarantee the safety and stability of such systems. Recently, predictive safety filters (PSF) have emerged as a promising method to ensure constraint satisfaction in learning-based control, bypassing the need for explicit constraint handling in the learning algorithms themselves. The safety filter approach leads to a modular separation of the problem, allowing the use of arbitrary control policies in a task-agnostic way. The filter takes in a potentially unsafe control action from the main controller and solves an optimization problem to compute a minimal perturbation of the proposed action that adheres to both physical and safety constraints. In this work, we combine reinforcement learning (RL) with predictive safety filtering in the context of marine navigation and control. The RL agent is trained on path-following and safety adherence across a wide range of randomly generated environments, while the predictive safety filter continuously monitors the agents' proposed control actions and modifies them if necessary. The combined PSF/RL scheme is implemented on a simulated model of Cybership II, a miniature replica of a typical supply ship. Safety performance and learning rate are evaluated and compared with those of a standard, non-PSF, RL agent. It is demonstrated that the predictive safety filter is able to keep the vessel safe, while not prohibiting the learning rate and performance of the RL agent.

Structural design and control strategy of a cable-driven robot under high-altitude facade conditions with large span and multiple constraints

Purpose This paper explores the challenges of using cable-driven parallel robots on high-altitude, large-span facades, where redundancy in multicable systems and the elastic deformation of the cables are significant issues. This study aims to improve the accuracy and stability of the work platform through enhanced control strategies. These strategies address the redundancy in multicable systems and reduce the risks associated with cable deformation and mechanical failures during large-span movements. Design/methodology/approach The paper proposes a dynamic model for a four-rope parallel robot designed explicitly for large-span applications. The study introduces a position–force control strategy incorporating kinematic inverse solutions and a rope dynamics model to account for rope elasticity and its effects. This approach increases the number of system equations to match the unknowns, effectively solving the redundancy problem inherent in multicable systems. In addition, the tension changes of ropes and the stability of the working platform are examined under different motion distances (X = 50 m and X = 100 m) and varying Young’s modulus values (K = 5000 MPa and K = 8000 MPa). Findings This study’s large-span rope force–position control strategy successfully resolves the typical nonlinear characteristics and external disturbances in multicable parallel systems. By continuously monitoring and adjusting cable tension and end positions, this strategy ensures precise control over each cable’s tension, optimizes the distribution of cable tensions and maintains the system’s stability and response speed. The analysis in this paper indicates that this control strategy significantly improves the motion accuracy of robots operating on large-span high-altitude facades. Practical implications Industry adoption: The design and control strategies developed for the four-cable-driven parallel robot can be adopted by companies specializing in facade maintenance, construction or inspection. This could lead to safer, more efficient and cost-effective operations, especially in challenging environments like high-rise buildings. Innovation in robotic solutions: The research can inspire innovation within the field of robotics, particularly in developing robots for specific applications such as large surface maintenance. It showcases how adaptive control and stability can be achieved in complex operational scenarios. Safety improvements: By demonstrating a more stable and precise control mechanism for navigating large facades, the study could contribute to significant safety improvements, reducing the risk of accidents associated with manual facade maintenance and inspection tasks. Originality/value This paper combines the force/position hybrid control method with actual robotic applications, offering a novel solution to the complex issue of controlling cable-driven parallel robots in challenging environments. Thus, it contributes to the field. The proposed method significantly enhances the precision and stability of such systems and provides robust technical support for high-precision tasks in complex mechanical settings.

A Frequency-Domain Criterion for the Quadratic Stability of Discrete-Time Systems with Switching between Three Linear Subsystems

Connected systems with switching between three linear discrete-time subsystems are considered, and a new frequency-domain criterion for the existence of a quadratic Lyapunov function ensuring the stability of such systems under arbitrary switching is proposed. The application of this criterion is demonstrated on an example of a third-order system.

A constructive approach for investigating the stability of incommensurate fractional differential systems

This paper is devoted to studying the asymptotic behaviour of solutions to generalized incommensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary and sufficient to ensure the stability of such systems. Next, from the fractional order pseudospectrum definition proposed by Šanca et al., we formulate the concept of a rational approximation for the fractional spectrum of incommensurate fractional systems with general, not necessarily rational, orders. Our first important new contribution is to show the equivalence between the fractional spectrum of a incommensurate linear system and its rational approximation. With this result in hand, we use ideas developed in our earlier work to demonstrate the stability of an equilibrium point to nonlinear systems in arbitrary finite-dimensional spaces. A second novel aspect of our work is the fact that the approach is constructive. It is effective and widely applicable in studying the asymptotic behaviour of solutions to linear incommensurate fractional differential systems with constant coefficient matrices and linearized stability theory for nonlinear incommensurate fractional differential systems. Finally, we give numerical simulations to illustrate the merit of the proposed theoretical results.

An improved algebraic approach to proving global stability of autonomous polynomial differential systems with applications to epidemic models

Global stability of autonomous polynomial differential systems is an important issue in applications. By means of the Lyapunov direct method, an improved algebraic approach to proving the global stability of such systems in the positive cone is presented in this paper. This approach is based on an important finding that the derivative of a Volterra-type Lyapunov function along a polynomial differential system can be expressed as a linear combination of some Volterra-type functions. Applications to some epidemic models demonstrate the effectiveness and universality of the approach. Moreover, according to the property of the Volterra-type function and the relation between the endemic equilibrium and the disease-free equilibrium, the applicable Lyapunov function for the disease-free equilibrium can be derived by reformulating the Lyapunov function for the endemic equilibrium. The approach proposed here greatly simplifies the discussion on global stability of the feasible equilibria of some models described by polynomial differential systems.

Valence study of Li(Ni0.5Mn0.5)1−xCoxO2 and LiNi1−xCoxO2 : The role of charge transfer and charge disproportionation

The series of LiMO2 (M: transition metal) materials are highly relevant as cathode materials of Li-ion batteries. The stability of such systems remains an important factor for their usability in batteries, and depends strongly on the electronic configuration of the transition-metal ions. In particular, the promising class of multi-transition-metal systems exhibits complicated valence states due to intermetallic charge transfer and charge disproportionation. Here we perform a systematic study on the valence of the transition-metal ions using x-ray absorption spectroscopy on the M−L2,3 edges and O-K edges. In Li(Ni0.5Mn0.5)1−xCoxO2 we established that the valence is Co3+ and Ni0.52+Mn0.54+ throughout the whole series. Meanwhile, in LiNi1−xCoxO2 we found that the Ni displays a behavior consistent with a charge disproportionated negative charge transfer system, and that with increased concentration of Co3+, the disproportionation signal decreases. Since the number of O 2p holes also gets reduced, we infer that the material will also become more unstable. Published by the American Physical Society 2024

Numerical simulation of a fractional stochastic delay differential equations using spectral scheme: a comprehensive stability analysis

The fractional stochastic delay differential equation (FSDDE) is a powerful mathematical tool for modeling complex systems that exhibit both fractional order dynamics and stochasticity with time delays. The purpose of this study is to explore the stability analysis of a system of FSDDEs. Our study emphasizes the interaction between fractional calculus, stochasticity, and time delays in understanding the stability of such systems. Analyzing the moments of the system’s solutions, we investigate stochasticity’s influence on FSDDS. The article provides practical insight into solving FSDDS efficiently using various numerical techniques. Additionally, this research focuses both on asymptotic as well as Lyapunov stability of FSDDS. The local stability conditions are clearly presented and also the effects of a fractional orders with delay on the stability properties are examine. Through a comprehensive test of a stability criteria, practical examples and numerical simulations we demonstrate the complexity and challenges concern with the analyzing FSDDEs.

Evaluating stability of rigid-column-supported and geosynthetic-reinforced embankments

Field observations and centrifuge tests indicate that progressive column bending failure accompanies most instabilities of rigid-column-supported and geosynthetic-reinforced (RCGR) embankments. However, recognized guidelines specifically for evaluating the overall stability of such systems featuring bending failure remain limited. A general methodology to calculate the factor of safety (FS) for RCGR embankments using the limit equilibrium method is presented in this article. The focus is on deep-seated slope failures, wherein rigid columns progressively fracture due to subsoil overstressing. The concentric arches model, along with tensioned geosynthetic analysis, informs the determination of vertical and horizontal loads on the column heads. The column's resisting moment stems from its flexural and compression resistance. A mobilization factor for the net thrust on each column is defined to capture the progressive failure. The methodology involves an iterative computational procedure to identify the critical slip surface and the FS using the Fellenius' method. The solution was validated using three case studies, including both centrifuge models and field tests, as well as finite-element analysis. The results indicate that the soil mass contributes the most to resisting sliding and overall stability, followed by columns and geosynthetics. In addition, axial force mainly provides the resisting moment of columns.

Enhancing Magnetohydrodynamic Stability in Channel Flows through Porous Media Incorporating Darcy-Forchheimer Modifications into the Orr-Sommerfeld Analysis

This research paper investigates the stability characteristics of magnetohydrodynamic (MHD) flow within channels filled with porous media. Specifically, the study explores modifications to the classical Orr-Sommerfeld equation using the Darcy-Forchheimer model to account for the presence of porous media. The analysis aims to elucidate the combined influence of porous media and magnetic fields on flow stability in such systems. Numerical simulations and analytical techniques are employed to assess the impact of varying parameters on the stability behavior of the flow. The study revealed that the velocity profile increases with increase in Schmidt and Prandtl’s number and stabilizes with the increase in Grashof number and the buoyancy. The temperature profile increases with Reynold’s Number and Hartmann number. It stabilizes with Schmidt, Prandtl and Grashof number. The profile of species concentration stabilizes with thermo-phoretic parameter, Prandtl number and Darcy-Forchheimer’s parameter augumentation.

Stability Properties of Multi-Order Fractional Differential Systems in 3D

This paper is devoted to studying three-dimensional non-commensurate fractional order differential equation systems with Caputo derivatives. Necessary and sufficient conditions for the asymptotic stability of such systems are obtained.

Development and Evaluation of Accelerated Durability Tests Under Realistic Operating Conditions for PEMFC Stacks – a Systematic Approach

Over the last decade, significant progress has been achieved in the commercialization of Polymer Electrolyte Membrane (PEM) fuel cells for mobile applications. However, long-term durability and stability of such systems still needs further improvement. To overcome today’s time-consuming long-term durability tests, the development of so-called accelerated durability tests (ADT) is urgently necessary. In this work, we present our recent results on such ADT test-protocols based on research promoting a detailed understanding of the individual aging mechanisms in PEM fuel cells.Various stressors had been investigated separately to understand their impact on overall fuel cell ageing. Certain levels of cell potential, temperature and humidity could be identified as major stressors and were successively added to the test protocol. In addition to the electrochemical test results, additional focus was put on different in-situ and ex-situ characterization methods. This combination enables a detailed understanding of individual stressors and their interply. The PEM-stack used in this study is an automotive high-performance stack developed within the publically funded Auto Stack Industry (ASI) project. An extensive long-term test over 5,500 operating hours was carried out as baseline test using the New European Driving Cycle, but with additional features to mimic realistic automotive load-profiles. Based on the results of this reference protocol, four different ADT protocols of only 1,200 hours test duration were derived. All tests were performed using short stacks with automotive-size active area. In-situ measurements include spatially resolved current measurement, cyclic voltammetry and impedance spectroscopy. After each test, selected cells were additionally analyzed ex-situ using layer thickness measurement via SEM, IR-thermography and contact angle measurements.The results from ex-situ investigations underline the degradation models postulated from in-site measurements. The overall data show that detailed understanding of individual stressors is necessary to successfully develop reliable accelerated ageing tests for PEM fuel cells.

On linear stabilization of a class of nonlinear systems in a critical case

In this paper, we address the stabilization problem for nonlinear systems in a critical case. Namely, we study the class of canonical nonlinear systems. Canonical nonlinear systems or chain of power integrators is an important subject of research. Studying such systems is complicated by the fact that they cannot be mapped onto linear systems. Moreover, they have the uncontrollable first approximation. Previous results on smooth stabilization of such systems were obtained under the assumption that the powers in the right-hand side are strictly decreasing. In this work, we consider a case of non-increasing powers in the right-hand side for a three-dimensional system. A popular approach for studying such systems is the backstepping method, which is a method of step-wise stabilization. This method requires a sequential investigation of lower-dimensional subsystems. Backstepping enables the study of a wide range of nonlinear triangular systems but requires technically complex and cumbersome computations. Therefore, a natural question arises about constructing stabilizing controls of a simple form. Polynomial controls can serve as an example of such controls. In the paper, we demonstrate that linear controls can be considered as stabilizing controls. We derive sufficient conditions for the coefficients of the linear control that ensure the asymptotic stability of the zero equilibrium point of the corresponding closed-loop system. The asymptotic stability is proven using the Lyapunov function method, which is found as the sum of squares. The negative definiteness of the Lyapunov function derivative in a neighborhood of the origin guarantees asymptotic stability. In contrast to the case of strictly decreasing powers, additional conditions on the control coefficients, apart from their negativity, emerge. The obtained result extends to a broader class of nonlinear systems through stabilization by nonlinear approximation. This allows the consideration of systems with higher-order terms in the right-hand side. The effectiveness of the applied approach is illustrated by several model examples. The method used in this work to investigate the case of non-increasing powers can be applied to systems of higher dimensions.

Exponential Stability for Second-Order Neutral Stochastic Systems Involving Impulses and State-Dependent Delay

Exponential stability criteria for neutral second-order stochastic systems involving impulses and state-dependent delay have been addressed in this paper based on stability theory, stochastic analysis, and the inequality technique. Some sufficient conditions are given to establish the exponential stability of such systems, which is well-established in the deterministic case, but less known for the stochastic case. In our model, the noise effect can be described as a symmetric Wiener process. By formulating the impulsive integral technique, exponential stability analysis of the pth moment of the second-order system involving stochastic perturbation is established. As an application that illustrates the theoretical formulation, an example is presented.

A novel robust discrete-time integral sliding mode tracking control design for time-varying delay MIMO systems with unknown uncertainties

This paper proposes a novel robust tracking control scheme for discrete time linear uncertain Multiple-Input Multiple-Output (MIMO) systems subject to time-varying delay on the states. The considered system is affected by unknown but norm bounded uncertainties on parameters as well as matched disturbances on the states. The designed controller is based upon a proposed novel integral sliding surface and a new switching type of reaching law. Sufficient conditions based on Linear Matrix Inequalities (LMIs) and a suitable Lyapunov–Krasovskii Functional (LKF) are derived in order to guarantee the asymptotic stability of such system. The proposed controller ensures a good tracking performance despite the presence of the time varying delay and the matched/unmatched disturbances. Moreover and thanks to the proposed integral surface, the time reaching phase is eliminated and the chattering phenomenon is significantly reduced. The proposed controller is applied on an Autonomous Underwater Vehicle (AUV) to follow a prescribed desired trajectory. The simulation results illustrate the effectiveness of such controller.

In Ukrainian

Сreation of new therapeutic materials based on nucleic acids encourages the combination of the latter with materials capable of adsorbing them. One of the most promising materials for such purposes is nanocrystalline titanium dioxide due to its low toxicity, stability of its physical and chemical parameters, and high biocompatibility. Accordingly, understanding the nature of the interaction of the surface of titanium oxide with biologically active substances is a very important issue. It is also always a relevant question whether the biopolymer immobilized on the surface of a solid remains capable of serving as a reservoir for drug delivery or a tool for the treatment of a particular disease. The aim of the work was to investigate the interaction of the biologically active substance rivanol with the surface of DNA-containing titanium dioxide. It has been found that prior adsorption of deoxyribonucleic acid on the surface of titanium dioxide does not prevent its interaction with rivanol, which was confirmed by the methods of electron spectroscopy, atomic force and scanning electron microscopy. The mode of interaction of rivanol with deoxyribonucleic acid depends on the ratio of their concentrations and can be either intercalated or semi-intercalated, and electrostatic. Based on the calculated thermodynamic characteristics, the process of interaction of deoxyribonucleic acid adsorbed on the surface of a solid carrier is arbitrary and occurs by an ion exchange mechanism. These hybrid organo-mineral sorbents can serve as model structures for research in biotechnological fields, be used for the development of new methods of drug or gene delivery, reservoir systems at a molecular level, and serve as biocompatible carriers. The creation of organo-mineral sorbents, which combine nucleic acids and metal oxides, contributes to the stabilization of such systems and expands the scope of their possible application in medicine and biotechnology, increasing their target specificity.

Free Energy, Stability, and Particle Source in Dynamical Holography

We study dynamical holographic systems and the relation between thermodynamical and dynamical stability of such systems, using the conserved currents in the bulk spacetime. In particular, in the probe limit a generalized free energy is defined with the property of monotonic decreasing in dynamic processes. It is then shown that the (absolute) thermodynamical stability implies the dynamical stability, while the linear dynamical stability implies the thermodynamical (meta-)stability. The holographic superfluid is taken as an example to illustrate our general formalism, where the dynamic evolution of the system in contact with a particle source is clarified by theoretical investigation and numerical verification. The case going beyond the probe limit is also discussed.

Stability properties of multidimensional symmetric hyperbolic systems with damping, differential constraints and delay

Multidimensional linear hyperbolic systems with constraints and delay are considered. The existence and uniqueness of solutions for rough data are established using Friedrichs method. With additional regularity and compatibility on the initial data and initial history, the stability of such systems are discussed. Under suitable assumptions on the coefficient matrices, we establish standard or regularity-loss type decay estimates. For data that are integrable, better decay rates are provided. The results are applied to the wave, Timoshenko, and linearized Euler–Maxwell systems with delay.