Stability Problem Research Articles

A parameter-free particle relaxation technique for smoothed particle hydrodynamics

In this paper, we present a parameter-free particle relaxation technique to improve the accuracy and stability of smoothed particle hydrodynamics (SPH). Instead of imposing a background pressure, particles are regularized following the criteria of 0th-order consistency, i.e., the gradient of a constant to be zero. Specifically, the modifications of particles' position are solved by a gradient decent method according to the error between zero value and the gradient of a constant. This modification decreases the integration error and leads a more uniform particles distribution. A set of challenging benchmarks including lid-driven cavity flow, Taylor-Green vortex, FSI (fluid-solid interaction) problem, 2D (two-dimensional) dam-break case, and water exit of a cylinder are investigated to validate the effectiveness of the present technique for addressing the well-known tensile instability and particle clumping problems. Finally, the study of 3D (three-dimensional) dam-break against an obstacle demonstrates the stability and versatility of the present method.

Energy dissipation damage constitutive relation of CFRP passively confined coal sample

In view of the stability problem of coal pillars left over during coal resource mining, (Carbon Fiber Reinforced Polymer) CFRP sheet is applied in coal pillar reinforcement. Uniaxial compression tests of CFRP passively confined coal samples are carried out to explore the mechanical response mechanism of passively confined coal samples under different layers, and the energy dissipation damage constitutive relationship of CFRP passively confined coal samples is established based on the energy dissipation principle. The conclusions are: As CFRP layers increased, the local damage of coal samples before the peak evolved from a 'cliff-like jagged' to a 'capillary jagged', with post-peak instability marked by a shift to more 'cliff-like' characteristics. The tests revealed improvements in peak strength and elastic modulus, with a defined functional relationship between these properties and CFRP layers. The energy storage capacity of passively confined coal samples improved with CFRP layers, requiring less axial deformation to achieve equivalent energy levels. The energy dissipation rate showed an initial decrease followed by an increase, with a minimum inflection point, the elastic energy consumption ratio tends to decrease slowly and then rapidly during post-peak instability. A damage constitutive relationship and evolution equation were developed, highlighting that the CFRP sheet significantly inhibits damage, with diminishing effectiveness beyond two layers. The study concludes that three-layer CFRP sheets provide optimal confinement, offering a novel strategy for the reinforcement of coal pillars and the prevention and control of rock burst, without considering the actual coal pillar dimensions and shape. To sum up, the use of CFRP sheet to strengthen coal pillar has considerable potential research value in strengthening coal pillar and improving the recovery rate of coal resources.

Polynomial Fuzzy Observer-Based Feedback Control for Nonlinear Hyperbolic PDEs Systems.

This article explores the observer-based feedback control problem for a nonlinear hyperbolic partial differential equations (PDEs) system. Initially, the polynomial fuzzy hyperbolic PDEs (PFHPDEs) model is established through the utilization of the fuzzy identification approach, derived from the nonlinear hyperbolic PDEs model. Various types of state estimation and controller design problems for the polynomial fuzzy PDEs system are discussed concerning the state estimation problem. To investigate the relaxed stability problem, Euler's homogeneous theorem, Lyapunov-Krasovskii functional with polynomial matrices (LKFPM), and the sum-of-squares (SOSs) approach are adopted. The exponential stabilization condition is formulated in terms of the spatial-derivative-SOSs (SD-SOSs). Additionally, a segmental algorithm is developed to find the feasible solution for the SD-SOS condition. Finally, a hyperbolic PDEs system and several numerical examples are provided to illustrate the validity and effectiveness of the proposed results.

Stability analysis of tunnel heading in clay with nonstationary random fields of undrained shear strength

The stability problem of a tunnel heading in clay remains a significant challenge in geotechnical engineering. Specifically, when considering the spatial variability of the soil, the stability factor may be influenced by geographically random fields. This study investigates the effect of random fields on a probabilistic analysis of a tunnel heading in undrained clay. The study assumes that the undrained shear strength of the clay increases linearly with depth due to a strength gradient factor. The random adaptive finite element limit analysis is employed to calculate the stability numbers for tunnel headings. Nonstationary random fields with varying vertical correlation lengths are simulated using Monte Carlo simulation technique. The stability analysis takes into account geometry parameters (i.e., cover depth ratio) and nonstationary random field of undrained shear strength parameters. (i.e., strength gradient, coefficient of variation, and vertical correlation length). The results of tunnel face stability using random adaptive finite element limit analysis have also been utilised to assess the probability of design failure over a practical range of deterministic factors of safety. In the context of probabilistic failure analysis, the failure mechanism resulting from varying vertical correlation lengths could influence the probability of design failure. The findings of this study can be of significant interest to tunnel engineering practitioners during the design phase of tunnel heading projects.

Pipe piles and split-cables: reinforcing weak mine pits

To mitigate the instability problem of heavy equipment foundations in deep coal mine chambers under high geo-stress, this study proposes a combined reinforcement strategy for foundation pits, which are mainly composed of pipe piles and split-level vertical cables. The weak rock mass around the pit is reinforced using combined cables and grouting. The split-level-arranged cables with different lengths improve the tensional strength of the rock mass, whereas the pipe pile at the pit corner can enhance the shear strength. The overall performance of the structure in terms of bearing capacity can be significantly enhanced by pouring pipe piles to integrate them and the pump foundation to form a cohesive structure. Both the foundation integrity and foundation pit strength can be improved by stepwise support technology. Finally, an improved reinforcement strategy is implemented in a deep-pump chamber in the Huainan mining area. The monitoring results indicate that the foundation pit stability was successfully controlled and floor cracking and tilting of the pump foundation were avoided by using the improved support method.

Robust stabilisation of uncertain nonlinear systems with matched and unmatched uncertainties

This paper considers the problem of robust stabilisation of uncertain nonlinear systems with both matched and unmatched uncertainties. A new robust controller is proposed to guarantee practical or asymptotic stability under non-vanishing or vanishing unmatched uncertainties. First, the system uncertainties are decomposed optimally into the matched and unmatched portions with an objective of the minimum norm for the unmatched part. Next, instead of a robust control design based on only the matched part of uncertainties commonly used in the previous works, a robust controller is synthesised based on both matched and mismatched portions of the uncertainties. It is shown that in uncertain systems whose state cannot simultaneously stay in a so-called null set and diverge to infinity, the proposed controller guarantees stability no matter how large the input-unrelated unmatched uncertainties are. Numerical examples illustrate that the proposed controller is more robust against uncertainties, and offers improved damping and stabilisation features.

Observer-based output feedback control for switched T–S fuzzy systems with local nonlinear segments by using past output measurements

This paper researches the observer-based exponential stabilization problem for switched Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables and local nonlinearities. The local nonlinear parts that satisfy the incremental quadratic constraint exist in the systems and observers, which have the merit of being able to contain many common nonlinearities in a unified framework. Because the premise variables are not measurable, the performance of the observers in estimation is critical. Different from existing observer-based control strategies, the strategy of this paper not only depends on the current outputs of the systems but also relates to the past outputs of the systems which can provide a way to improve performance. In order to tackle the difficulties caused by introducing the past outputs and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. Then, the conditions for designing the observer-based controller are derived by using auxiliary scalars, projection Lemma and S-procedure. Finally, the effectiveness of the control strategy obtained in this paper is proved by two examples.

Robust control design of uncertain nonlinear systems: a self-compensating and self-tuning approach

ABSTRACT The problem of robust stabilisation is considered for a class of uncertain nonlinear systems with linear control term. It is not required that the unforced nominal (nonlinear) system has to be stable and/or has to be known, which means that its Lyapunov function need not be known and/or found for designing a stabilising control scheme to compensate the effect of uncertainty on the systems like some traditional control design approaches. For such a class of uncertain nonlinear systems, a design approach, called a self-compensating and self-tuning one, is presented whereby some robust state feedback control schemes can be easily synthesised. The proposed design approach can result in a linear state feedback control scheme with a time-varying control gain for such a class of uncertain nonlinear systems, which implies the simplicity of the design approach and control results. In addition, the system uncertainty is also not required to have to satisfy the matching conditions.

Input-to-state hybrid impulsive formation stabilization for multi-agent systems with impulse delays

This paper addresses the input-to-state formation stabilization problem of nonlinear multi-agent systems within a hybrid impulsive framework, considering delay-dependent impulses, strong nonlinearity, and deception attack signals. By leveraging Lyapunov functionals, impulsive comparison theory, average impulsive interval methods, and graph theory, we develop novel criteria for possessing locally input-to-state and integral input-to-state formation stabilization across different impulse sequence classes. These criteria are expressed in terms of continuous/impulsive feedback gains, time delay size, nonlinearity strength, uniform upper bound of impulsive interval, and length of average impulsive interval. Notably, the design of control impulses benefit the destabilizing continuous dynamics in the formation stabilization process. To demonstrate the effectiveness and validity of the analytical results, we provide numerical simulation examples involving various types of external attack signals.

ASYMMETRIC FUNCTIONAL-BASED APPROACHTO EXPONENTIAL STABILITY OF LINEAR DISTRIBUTEDTIME-DELAY SYSTEMS

In this paper, the problem of exponential stability of linear time-delay systems with mixed discrete and distributed delays is studied. Based on an asymmetric Lyapunov-Krasovskii functional approach, sufficient conditions are derived in terms of linear matrix inequalities to guarantee the exponential convergence of the system state trajectories with a prescribed decay rate. The efficacy of the obtained results is demonstrated by a given numerical example and simulations.

Exponential stability of switched systems with state-dependent delayed impulses via B-equivalent method

This paper studies the stability problem of switched systems with state-dependent delayed impulses (SDDIs), where switching times satisfy the definition of average dwell-time. Firstly, the pulse phenomenon of the systems with SDDIs is avoided under some necessary assumptions. Subsequently, the state-dependent delayed impulsive switched systems can be transformed into the corresponding time-dependent ones by using the B-equivalent method. Furthermore, the stability of stable and unstable systems with time-dependent delayed impulses (TDDIs) are analyzed, where the limitation that the impulsive delays are less than the impulsive intervals is relaxed. Based on the equivalence of the original system and the corresponding switched system with TDDIs, some new stability conditions for the switched systems with SDDIs are derived. Finally, the theoretical results are applied to a switched neural network with SDDIs to demonstrate the validity of the results.

Stabilization of delayed Markovian jump systems with sampled controllers

This paper mainly studies the stabilization problem of continuous-time delayed Markovian jump systems by a sampled controller. Not only the state is sampled, but also the switching signals, where the latter sampled signal makes the synthesis and analysis of delayed systems more complex and difficult. To address these issues, this paper develops an augmented system approach, resulting in a novel system model that incorporates two delayed exponential matrices. It has been demonstrated that the stability properties of original delayed system can be ensured by the constructed auxiliary system. The correlation among Markov process, sampling interval and time delay is first established, and several stabilization results are given. More special situations about the proposed sampled are further considered. The validity and superiority of the method proposed in this paper are verified through two numerical examples.

STABILIZATION OF DISCRETE 2D LINEAR SYSTEMS IN FORNASINI-MARCHESINI MODEL

This paper is concerned with the stabilization problem of discrete 2D linear systems described by the second Fornasini-Marchesini model. A necessary and sufficient condition involving the characteristic polynomial is first quoted by which the unforced system is structurally or exponentially stable. On the basis of the derived stability condition, a tractable condition is formulated in the form of linear matrix inequality for obtaining the controller gain of a desired stabilizing state-feedback controller.

Adaptive fixed-time stabilization for high-order uncertain nonlinear systems with unknown measurement sensitivities

This paper investigates the adaptive fixed-time stabilization problem for a class of uncertain high-order nonlinear systems with unknown measurement sensitivities and unknown control magnitude. Compared to existing practical fixed-time control approaches, our control strategy is capable of driving all states of uncertain high-order systems to the origin within a fixed time, rather than just ensuring their boundedness. Additionally, this study relaxes the restrictions on the nonlinear functions of the system, while overcoming challenges such as unknown control magnitude and unknown measurement sensitivity without prior boundaries. To achieve the control objectives, our control strategy consists of two main steps. Firstly, we divide the initial value of the high-order system into two cases, and construct adaptive controllers separately for each case by adding a power integral technique and backstepping method. Subsequently, the reliance of the stability time of the closed-loop high-order system on the initial value is eliminated by designing an appropriate controller switching mechanism. Finally, we provide a simulation example to validate the effectiveness of our control strategy.

Analysis of the Stability of a High Fill Slope under Different Gradients and Precipitation Conditions

The stability problem of high fill slopes has always been a research hotspot. Its failure mechanism is complex and prominent, featuring strong concealment, a short occurrence time and great harmfulness. In this paper, the stability of a high fill slope under rainfall conditions will be studied by using indoor tests, numerical simulations, etc. The study is based on a high fill slope in Yichang City. The evolution law of high fill slope stability under the maximum rainfall condition is revealed. The results show the following: The influence of moisture content on stress–strain curves is reflected in both the curve’s shape and the peak value of deviatoric stress. Under the constraint of confining pressure, the curve decreases and the peak value of deviatoric stress decreases with the increase of moisture content at the same confining pressure. The safety factor obtained by a rigid body limit equilibrium analysis and numerical calculation indicates that the safety factor for a 30° slope meets the requirements for slope stability evaluation and remains in a fundamentally stable state. An on-site investigation suggests that surface failure and shallow failure may be primary failure modes for this slope; therefore, it is recommended to implement slope protection measures. This study provides valuable references for similar high fill slopes.

Dynamic mechanical properties of sandstone with two circular inclusions under impact loading

Inclusions are often present in rock defects, which can compensate for some of the problems of low rock strength and poor stability caused by hole defects. Specimens containing inclusions exhibit different mechanical properties under dynamic loading, and the strength change, energy evolution law and fracture mechanism deserve to be clearly discussed. In this work, a dynamic impact test of sandstone with circular inclusions was carried out. The failure process of each sample was recorded by a high-speed camera, and the influences of the inclusion strength and strain rate on the dynamic impact performance of the sandstone were analysed. Increasing the strain rate and inclusion strength can significantly improve the dynamic compressive strength of a sample. The dissipated energy density and impact toughness index are positively correlated with the strain rate. The dissipated energy density increased the most when the sample type was FA, at 10.6%. When the sample type was FD, the impact toughness index increased the most, which was 49.1%. In the early stage of loading, the localized strain is mainly concentrated inside the filler and gradually evolves into deformation of the filler and extension of shear cracks in the late stage of loading. The failure modes of a sample are not the result of a single factor but are influenced by both the strain rate and the filler. The types of cracks in the samples are mainly shear cracks and shear–tension composite cracks.

An optimization‐based method for robust stabilization of linear delay systems

AbstractThis paper investigates the robust stabilization problem of linear delay systems with parametric uncertainty. First, by means of the argument principle, a delay‐dependent sufficient condition is derived for designing a feedback controller, with which the closed‐loop system can achieve robust stability. Then, based on the fundamental matrix of the linear delay systems, a constrained optimization problem is formulated for solving the feedback gain matrices. The effectiveness of the proposed method is verified by some simulation results.

On [formula omitted]-error moment stability and stabilization for discrete-time semi-Markov jump linear systems

In this paper, we study the σ-error moment stability and stabilization for a class of discrete-time semi-Markov jump linear systems (S-MJLS). It is shown that the existing results on σ-error moment stability for discrete-time S-MJLS can be obtained under weaker conditions, and based on the established stability results, the high-order moment stabilization problem is investigated for the first time.

Stochastic configuring networks based adaptive sliding mode control strategy to improving stability of SG-VSG paralleled microgrid

This article proposes an adaptive sliding mode control (SMC) strategy based on stochastic configuring networks (SCNs) to improve the stability of synchronous generator (SG) and virtual synchronous generator (VSG) paralleled microgrid and enhance the dynamic performance. First, derives an equivalent swing equation what coupling of inherent inertia/damping of SG and virtual inertia/damping of VSG, the parameters design problem is established to a stabilization problem of second-order uncertain nonlinear system with bounded uncertainties. Second, an adaptive sliding mode control based on variable-speed reaching law is designed to maintain the second-order nonlinear system stable, and the switch function of adaptive reaching law is improved to reduce system chattering. Then, the stochastic configuring networks is introduced to approximate the nonlinear term, and the approximation ability of SCNs is improved by designing the configuration range of input parameters of hidden layer nodes. The stability of proposed control strategy is proved by Lyapunov theory. Finally, the feasibility and effectiveness of the proposed control strategy are verified by the designed simulations and experiments.

Surface Cladding Engineering via Oxygen Sulfur Distribution for Stable Electrocatalytic Oxygen Production.

Inevitable leaching and corrosion under anodic oxidative environment greatly restrict the lifespan of most catalysts with excellent primitive activity for oxygen production. Here, based on Fick' s Law, we present a surface cladding strategy to mitigate Ni dissolution and stabilize lattice oxygen triggering by directional flow of interfacial electrons and strong electronic interactions via constructing elaborately cladding-type NiO/NiS heterostructure with controlled surface thickness. Multiple in situ characterization technologies indicated that this strategy can effectively prevent the irreversible Ni ions leaching and inhibit lattice oxygen from participating in anodic reaction. Combined with density functional theory calculations, we reveal that the stable interfacial O-Ni-S arrangement can facilitate the accumulation of electrons on surficial NiO side and weaken its Ni-O covalency. This would suppress the overoxidation of Ni and simultaneously fixing the lattice oxygen, thus enabling catalysts with boosted corrosion resistance without sacrificing its activity. Consequently, this cladding-type NiO/NiS heterostructure exhibits excellent performance with a low overpotential of 256 mV after 500 h. Based on Fick's law, this work demonstrates the positive effect of surface modification through precisely adjusting of the oxygen-sulfur exchange process, which has paved an innovative and effective way to solve the instability problem of anodic oxidation.