Practical Stability Research Articles

Pseudo-dynamic viscoelastic stability analysis of anti-dip bedding rock slopes

Earthquakes contribute to the failure of anti-dip bedding rock slopes (ABRSs) in seismically active regions. The pseudo-static method is commonly employed to assess the ABRSs stability. However, simplifying seismic effects as static loads often underestimates rock slope stability. The development of a practical stability analysis approach for ABRSs, particularly in slope engineering design, is imperative. This study proposes a stability evaluation model for ABRSs, incorporating the viscoelastic properties of rock, to quantitatively assess the safety factor and failure surface under seismic conditions. The mathematical description of the pseudo-dynamic method, derived in this study, accounts for the viscoelastic properties of ABRSs and integrates the Hoek–Brown failure criterion with the Kelvin-Voigt stress-strain relationship of rocks. Furthermore, to address concurrent translation-rotation failure in ABRSs, upper bound limit analysis is utilized to quantify the safety factor. Through a comparison with existing literature, the proposed method considers the effect of harmonic vibration on the stability of ABRSs. The obtained safety factor is lower than that of the quasi-static method, with the resulting percentage change exceeding 5%. The critical failure surface demonstrates superior positional accuracy compared to the Aydan and Adhikary basal planes, with minimal error observed between the physical model test and the numerical simulation test. The parameter sensitivity analysis reveals that the inclination of ABRSs exhibits the highest sensitivity (Sk) value across the three levels of horizontal seismic coefficient (kh). The study aims to devise an expeditious calculation approach for assessing the stability of ABRSs during seismic events, intending to offer theoretical guidance for their stability analysis.

Boosting the intercalation reaction of FeOF-based cathode toward highly reversible lithium storage

FeOF as an intercalation-conversion cathode features a high theoretical capacity toward high energy density lithium-ion batteries (LIBs). However, the inadequate intercalation process and poor reversibility of redox reaction deteriorate its practical capacity and cycling stability. Herein, a S-substitution strategy in FeOF (FeOF-S) is proposed to boost the intercalation reaction and enhance the reaction kinetics, achieving a record-high capacity of 668 mAh g−1 at 0.05 A g−1 and a long cycling stability up to 1500 cycles at 0.5 A g−1. Under this strategy, the Li+ intercalation energy of FeOF-S is remarkably reduced in thermodynamics, promoting the intercalation capacity to 230 mAh g−1 which is 50% higher than that of FeOF. Furthermore, a nearly zero band gap with superior electronic conduction is achieved in FeOF-S, leading to excellent rate capability with much enhanced pseudo-capacitance contribution. This work presents new insights into the regulation of thermodynamics and kinetics toward the boosted electrochemical performance of conversion-type electrodes for high energy density LIBs.

Overcoming local extrema in torque-actuated source seeking using the divergence theorem and delay

We study the problem of seeking the source of a scalar signal with a force- and torque-controlled unicycle. The vehicle does not have the capability to measure or track its position. The only information about the vehicle’s position relative to the source is given by measurements of the signal. We propose a feedback law that induces a uniform forward motion and an almost uniform rotational motion. This in turn leads to an almost circular motion of the unicycle; i.e., a motion along the boundary of a disk. An application of the divergence theorem reveals that the measurements of the signal along the boundary of the disk provide access to the gradient of an averaged signal, where the average is taken over the entire disk. Such a local average of the sensed signal can eliminate undesired local extrema, which in turn is beneficial for the goal of reaching a global extremum. We prove practical asymptotic stability for the closed-loop system with respect to extrema of the averaged signal. Our theoretical analysis takes L∞-measurement errors of the signal into account. We compare the performance of the proposed control law to another source seeking method in the presence of local extrema through numerical simulations.

Practical stabilisation of discrete-time switched nonlinear systems without a common equilibrium and using hybrid switching functions

This paper presents a new practical stabilization method for discrete-time switched nonlinear systems without a common equilibrium point among all modes. The proposed method has two main features. First, the number of nonlinear terms in the stability conditions is independent of the number of switched system modes. The result is that the computational cost is reduced, and it can be applied to switched systems with a large number of subsystems. Second, using switched Lyapunov functions, hybrid switching laws are designed to preserve the practical stability property in both the closed-loop state-dependent switching function and the open-loop time-dependent one. As a result, when the state data is lost during sensor or communication failures, the controller can change the control scheme from a closed-loop state-dependent switching function to an open-loop time-dependent one without loss of stability property. Numerical examples are presented to illustrate the validity and efficiency of the proposed method.

Continuous-time nonlinear model predictive control based on Pontryagin Minimum Principle and penalty functions

Pontryagin's Minimum Principle (PMP) is a powerful tool for solving Nonlinear Model Predictive Control problems (NMPC), enabling the handling of time-varying input constraints and cost functions. However, applying PMP encounters challenges when state constraints must be satisfied. This arises because the optimal trajectory often requires a blend of unconstrained and constrained arcs with unknown junction points. To address this issue, relaxation methods are frequently explored, where state constraints are replaced with penalty functions. The contributions of this paper are as follows. First, a method of penalty functions allowing for coping with soft state constraints is examined. We prove the recursive feasibility of this method and demonstrate its efficiency in a numerical example. Second, the finite-time practical stability for the optimal reference tracking NMPC problem is addressed. By appropriately choosing the terminal cost, one can guarantee the convergence of the state vector to a predefined neighbourhood of the target state.

A Practical Predefined-Time Stability Criterion and Its Application to Uncertain Nonlinear Systems

A Practical Predefined-Time Stability Criterion and Its Application to Uncertain Nonlinear Systems

Dynamic output feedback based fault tolerant control for continuous-time switched affine systems via reduced-order observer

In this study, the issue on dynamic output feedback fault-tolerant controller design is addressed for a class of continuous-time switched affine systems in the presence of actuator faults. The existence of affine terms gives rise to the lack of a common equilibrium point and further makes it more difficult to propose the desired output-feedback-based fault-tolerant control scheme. Firstly, the actuator fault estimation is achieved through a reduced-order observer design approach. Then, a kind of dynamic output feedback controller is constructed to perform the fault tolerance goal by utilizing fault estimation information. Moreover, the mode-dependent average dwell time switching constraint is borrowed to avoid the chattering owing to the high-frequency switching. The sufficient conditions with less conservative are derived to guarantee the practical exponential stability of closed-loop system with a prescribed L∞ gain. Finally, both the effectiveness and validity of the designed fault-tolerant control strategy are illustrated via a case study of a buck-boost DC-DC converter.

A high throughput approach for measuring soil slaking index

AbstractSoil wet aggregate stability is widely measured for soil health ratings, and two mobile applications have been recently developed that provide simple and fast measurements of wet aggregate stability on three pea‐sized soil aggregates. However, techniques are needed to scale the test to make it practical for studies with large sample numbers. Here, we describe an approach to measure 10‐min slaking index on 20–36 aggregates simultaneously using a multi‐well plate and automated image analysis. We used this approach to measure 160 soil samples (2120 aggregates) from a long‐term tillage and cover crop trial in a corn (Zea mays L.)‐based agroecosystem in central Iowa. We evaluated the statistical power of slaking index, needed replication, sensitivity to cultural practices, and sensitivity to sample collection date to inform future sampling efforts. We found that small numbers of highly unstable aggregates lead to skewed distributions for slaking index. We concluded that at least 20 aggregates per sample were useful to provide confidence in measurement precision, although the experiment had high statistical power with only 10–12 replicates per sample. Slaking index was not sensitive to the initial size of dry aggregates (3‐ to 10‐mm diameter); therefore, pre‐sieving soils was not necessary. Consistent with prior studies, the field trial showed greater aggregate stability under no‐till than chisel plow practice and changing stability over a growing season. This multi‐well method will help researchers measure a useful soil health indicator with greater precision, and more efficiently sample spatial and temporal variation.

Adaptive finite-time neural control of nonstrict-feedback nonlinear systems with input dead-zone and output hysteresis

This paper explores the adaptive finite-time neural control issue for nonlinear systems with input dead zone and output hysteresis in nonstrict-feedback form. The unknown functions are estimated by employing the radial basis function neural networks (RBFNN) approach. A systematic adaptive finite-time control method is introduced using the backstepping technique and neural network approximation properties. The stability of the system is also examined by using semi-global practical finite-time stability theory. The established control approach guarantees the boundedness of all signals within the closed-loop system, enabling the system output to accurately follow the desired signal within a finite time framework while maintaining a small and bounded tracking error. Finally, simulation results are shown to demonstrate the efficacy of the suggested strategy.

Fault identification of centrifugal pump using WGAN-GP method with unbalanced datasets based on kinematics simulation and experimental case

Abstract In practical engineering applications, the accuracy and stability of fault identification for centrifugal pump will be significantly reduced due to unbalanced distribution between normal and fault datasets, i.e., the number of normal working samples is far more than the fault samples. To alleviate this bottleneck issue, this paper explores the fault identification of centrifugal pump based on Wasserstein generative adversarial network with gradient penalty (WGAN-GP) through combining kinematics simulation and experimental case. Specifically, ideal unbalanced vibration datasets from failure patterns such as damaged impeller of centrifugal pump are simulated and collected by prototype ADAMS software, then the unbalanced vibration signals are transformed into 2D grey-scale images. Furtherly, the generated grey-scale image datasets are feed into the original grey-scale image dataset as new datasets for training when the Nash equilibrium of the WGAN-GP model is reached. Eventually, the fault patterns of centrifugal pump are identified using confusion matrix graph. Meanwhile, another public dataset of centrifugal pump is employed for verifying the accuracy of the WGAN-GP model. Results indicate that fault identification accuracies with 95.07% and 98.0% of both kinematics simulation and experimental case are obtained, respectively, and the issues of unbalanced distribution and insufficient dataset can be overcome effectively.

Practical exponential stability and applications of switched homogeneous nonlinear systems with external inputs and impulses

The practical exponential stability of switched homogeneous nonlinear systems (SHNS) with external inputs and impulses is studied in this paper, which includes two types of continuous-time systems and discrete-time systems. Specifically, we add a kind of nonnegative impulses which is consistent with the switching behaviours for the systems. We first study switched homogeneous positive nonlinear systems (SHPNS) case, then we extend the SHPNS to a time-varying SHNS case. The primary difficulty of this research is the estimation of Lyapunov function value at switching-impulse points under the coupling effects of synchronous switches and state jumps. By employing the max-separable Lyapunov function approach, we present new sufficient stability criteria and design new switching-impulse signals, and successfully establish the new relation between the average dwell time parameter and impulse strength. Then, we apply the obtained results to the time-varying vehicle formation model with impulses. At last, four examples are given to demonstrate the feasibility of our results, which includes the specific algorithm verification process.

The Discrete, Fractional Order Model of a Two-Dimensional Temperature Field using Grünwald-Letnikov Definition

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow to estimate the orders of the model. Theoretical considerations are validated using exprimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length.

Distributed finite-time adaptive consensus output-feedback control of multi-agent systems under switching topologies

The paper investigates the finite-time adaptive consensus control of nonlinear multi-agent systems (MASs) by output-feedback. During the process of control design, the fuzzy logic system (FLS) is employed to approximate nonlinear function, as well as constructing a fuzzy state observer to estimate unmeasured states. Combining the dynamic surface control (DSC) with adaptive backstepping method conquers the complexity explosion issue. Then, semi-global practical finite-time stability (SGPFS) for closed-loop system is obtained under arbitrary switching communication topologies. All the signals of the overall system are uniformly ultimately bounded (UUB). Finally, the availability of developed control approach will be demonstrated through a simulation.

Practical stabilizability of a class of homogeneous bilinear systems

Practical stabilizability of a class of homogeneous bilinear systems

Global practical stabilization of the double integrator system with an imperfect sensor and subject to a bounded disturbance

This paper is concerned with global practical stabilization of the double integrator system with an imperfect sensor and subject to an additive bounded output disturbance. The imperfect sensor nonlinearity possesses the nonlinear characteristics of saturation and dead zone. Because of the presence of output dead zone and the additive disturbance, the states cannot be expected to driven into an arbitrarily small neighborhood of the origin. To solve the global practical stabilization problem, we proposes a low gain-based linear dynamic output feedback law, under which the first state enters and remains in a bounded set whose size is depended on the bound of disturbance and the range of dead zone and the second state enters and remains in a pre-specified arbitrarily small set, both in finite time. Simulation results illustrate the effectiveness of our proposed control method.

Practical stabilization of multi-links highly nonlinear Takagi-Sugeno fuzzy complex networks with Lévy noise based on aperiodically intermittent discrete-time observation control

This paper investigates practical stabilization of multi-links highly nonlinear Takagi-Sugeno fuzzy complex networks with Lévy noise (MHFNLs) via aperiodically intermittent discrete-time observation control (AIDOC). It is worth pointing out that AIDOC is considered into MHFNLs for the first time. Due to the difficulty of satisfying linear conditions in real life, polynomial growth conditions are used instead of linear growth conditions. Meanwhile, a global Lyapunov function is constructed and sufficient conditions which can remain MHFNLs practically stable are gained. Finally, an application and its numerical simulations are presented to verify the effectiveness and availability of the theoretical results.

Asymptotic voltage restoration in islanded microgrids via an adaptive asynchronous event-triggered finite-time fault-tolerant control

As the actuators of distributed generators involved in Microgrids (MGs) may experience different faults, it is highly recommended to design an appropriate secondary Fault Tolerant (FT) controller to provide resilience and robustness with respect to these malicious events. Meanwhile, the reduction of communication network workload from controller-to-actuator may be helpful to mitigate actuators stress. By virtue of the above, this article aims at introducing a novel distributed adaptive FT-Event-Triggered Control (FT-ETC) scheme for secondary voltage regulation control in AC islanded MG able to compensate faulty actuators effects while reducing the waste of communication network resources. The proposed control scheme is derived with the aid of the backstepping method and the ETC theory, whose combination ensures resilience with respect to possible faulty signals, while no knowledge of global information is required. Adaptive mechanisms are derived by exploiting Lyapunov theory, while Zeno-freeness property is proven by contradiction. Compared with the existing state-of-the-art on FT-ETC in islanded MG, here the main novelty relies in achieving the asymptotic rather than the practical stability of the voltage tracking errors despite an unhealthy environment, while the remaining adaptive signals involved in the closed-loop systems are bounded in finite-time. Finally, an extensive simulation analysis, also involving real-time Hardware In-the-Loop (HIL) experiments, confirms the theoretical derivation.

Adaptive Fuzzy Fixed-Time Control for Uncertain Nonlinear Systems with Mismatched Disturbances

This paper focuses on addressing the adaptive fuzzy fixed-time issue for a class of nonlinear systems with uncertainty functions and mismatched disturbances. Fuzzy logical systems are utilized for identifying unknown functions. Additionally, to tackle challenges posed by mismatched disturbances, disturbance observers are constructed based on the backstepping method. Utilizing the adding one power integrator approach and the fixed-time control method, this paper introduces a fixed-time adaptive fuzzy control algorithm. Notably, this algorithm accommodates the presence of unknown mismatched disturbances and nonlinear functions. The paper establishes, through the application of the Lyapunov stability theory, that the designed adaptive fixed-time fuzzy control algorithm ensures practical fixed-time stability for the resulting closed-loop systems. Finally, the effectiveness of the derived strategy is demonstrated through an illustrative example involving two cases.

A Hierarchical Data-Driven Predictive Control of Image-Based Visual Servoing Systems With Unknown Dynamics.

In this article, a hierarchical predictive control (PC) algorithm is designed for visual servoing mobile robot systems. At the kinematic level, the image-based visual servoing model of a wheeled mobile robot is established. By defining the corresponding performance index of the PC, an iterative linear quadratic regulator (iLQR) is used to obtain the velocity controller and to provide reference velocity for dynamics. In dynamics, a data-driven PC controller based on the Gaussian process (GP) is proposed to obtain the torque controller with unknown dynamics. The input-to-state practical stability (ISpS) of the system based on the proposed data-driven PC method is proved by introducing reasonable assumptions. The corresponding theorem also analyzes the maximum upper bound of GP inference error. Finally, the effectiveness of the proposed hierarchical controller is verified by simulations and experiments.

Practical Finite-Time Command-Filtered Adaptive Backstepping With Its Applications to Quadrotor Hovers.

In this article, a practical finite-time command-filtered adaptive backstepping (PFTCFAB) control method is presented for a class of uncertain nonlinear systems with nonparametric unknown nonlinearities and external disturbances. Unlike PFTCFAB control techniques that use neural networks (NNs) or fuzzy-logic systems (FLSs) to deal with system uncertainties, the proposed method is capable of handling such uncertainties without the need for NNs or FLSs, thus reducing complexity and increasing reliability. In the proposed approach, novel function adaptive laws are designed to directly estimate unknown nonparametric nonlinearities and external disturbances by means of command filter techniques, and a type of practical finite-time command filters is proposed to obtain such laws. Moreover, the PFTCFAB controllers and finite-time command filters are designed with practical finite-time Lyapunov stability, which ensures finite-time stability of system tracking and filter estimation errors. Experimental results with a quadrotor hover system are presented and discussed to demonstrate the advantages and effectiveness of the proposed control strategy.