Stability Criterion Research Articles

First-Principles Analysis of the Effects of Halogen Variation on the Properties of Lead-Free Novel Perovskites AlGeX3 (X = F, Cl, Br, and I).

To commercialize optoelectronic products and perovskite-based solar cells, nontoxic inorganic cubic metal halide perovskites have gained popularity. This study presents the structural, mechanical, electronic, and optical properties of novel lead-free metal cubic halide perovskites AlGeX3 (X = F, Cl, Br, and I) using the first-principles Density Functional Theory (DFT) approach. The verification of the mechanical stability of all compounds is conducted through Born stability criteria and formation energy. All of the compounds in the elastic investigations exhibit anisotropy, ductility, and elastic stability. The electronic band structures estimated by HSE06 and GGA-PBE functional demonstrate indirect to direct band gap transformation after substituting the halide F with the halides Cl, Br, and I. The tunability of halide-dependent energy bandgaps and the underestimation of energy band gaps are also noticed for the studied compounds by comparing the results obtained from the GGA-PBE functional and HSE06 investigations. The origins of bandgap transformation as well as halide-dependent energy gap modulation are explained by both the partial and total density of states (PDOS and TDOS). The results presented here suggest that all the compounds show low reflectivity, a high absorption coefficient, and also high optical conductivity in the visible and UV regions, making these materials suitable for multijunctional solar cells. Also, these materials have a greater impact on other optoelectronic device applications. Compared to other compounds, the optical investigation reported here demonstrates that AlGeI3 exhibits excellent optical conductivity and absorption in the visible region.

Improved Stability Analysis of Neural Networks with Time Delay Based on Variable Augmented Free Weight Matrix

This article investigates the stability of time-delay neural network system by the free-weighting matrices based on variable-augmentation.In the process of accurately evaluating the stability of delayed neural network systems, the conservative simplification of stability criteria has received widespread attention. In this paper, a variable-augmented-based free-weighting matrix method is applied to time-varying delayed neural network systems, and unnecessary free weighting matrices are removed. Some results with fewer free-weighting matrices are obtained, while maintaining their stability and conservatism. Finally, a specific neural network numerical example was used to demonstrate the effectiveness of this method.

Adaptive quantized tracking control for switched nonlinear systems with hysteresis nonlinearity using a novel predefined‐time stability criterion

AbstractThis article investigates the adaptive tracking control problem for switched nonlinear systems with input quantization and hysteresis nonlinearity. First, the hysteresis nonlinear phenomenon is considered and the Bouc–Wen hysteresis model is employed to address the complexities of controller design. Considering the time‐sampling mechanism may lead to the wastage of communication resources, a hysteresis quantizer is introduced to address this issue. Additionally, a command filter is constructed to relieve complexity explosion issues encountered during the backstepping process. Subsequently, compared with the conventional predefined‐time lemma, a novel predefined‐time lemma is proposed which can effectively adjust system performance even if the predefined‐time parameter is determined. In this case, a novel adaptive predefined‐time control scheme is devised by considering hysteresis properties and input quantization via the application of backstepping, which can track the reference signals within the predefined‐time frame. Finally, the flexibility and effectiveness of the proposed strategy are elaborated through numerical and practical examples.

Stability analysis of damped fractional stochastic differential systems with Poisson jumps: an successive approximation approach

This paper aims to investigate a new class of fractional stochastic differential systems under the influence of damping and Poisson jumps. First, the existence and uniqueness of mild solutions for the proposed system are investigated under the non-Lipschitz conditions. The results are formulated and proved by using the ( β , δ ) -regularised family, Grönwall's inequality, and successive approximation technique, which is different from the fixed point approach. Moreover, novel stability criteria for the considered system are obtained by utilising the corollary of the Bihari inequality. Finally, the correctness of the obtained results is verified by example.

Nonsingular fixed-time K-filter output-feedback control for high-order nonlinear multi-agent systems

This paper investigates the problem of nonsingular fixed-time control for high-order nonlinear multi-agent systems with unmeasurable states and disturbances. To address the unmeasurable states, a K-filter is introduced to reconstruct the system with the input and output only and to facilitate the construction of the observer. To provide an approximation for the unknown nonlinear functions, the fuzzy logic system technique is applied. A novel tracking controller is proposed to ensure that all signals remain bounded for the closed-loop system and that the tracking error converges into a small and adjustable set within a fixed time by utilising the adaptive backstepping recursive technology and the adding power integrator technique. Meanwhile, the singular problems arising from the fixed-time stability criterion can be also avoided. Finally, a simulation experiment verifies the effectiveness of the designed control scheme.

Hardware-in-the-Loop experiments in model ice for analysis of ice-induced vibrations of offshore structures

The study investigated the use of a Hardware-in-the-Loop (HiL) technique applied in model ice experiments to enable the analysis of offshore structures with low natural frequencies under dynamic ice loading. Traditional approaches were limited by facility capacities and ineffective downscaling of the geometry of the offshore structures. The goal of the present study was to overcome these challenges and to enhance the understanding and explore the applicability of a hybrid testing technique in model ice experiments. To achieve the objective, 204 Hardware-in-the-Loop simulations in model Ice (HiLI) were analyzed. Results showed robust behavior and good performance of the HiLI due to minimal variation in measured delay, normalized root mean square error, and peak tracking error and low magnitudes of such parameters despite alterations in factors such as the choice of the numerical structural model, physical prototype, measurement system, and ice type. Notably, the performance of the HiLI was affected when testing with warm model ice or scaling for harsh ice conditions, attributed to a reduced signal-to-noise ratio and instability of the system, respectively. Experimental identification of the critical delay, along with the application of an analytical stability criterion, revealed that the instability observed, was likely induced by reducing the structural stiffness of the numerical structural model to fulfil the scaling requirements when testing for harsh ice conditions. Additionally, the study showed improved HiLI performance when the physical prototype was in contact with the model ice. This observation was further analyzed and is assumed to be caused by the coupling between the ice and physical prototype, causing a coupled and thus increased eigenfrequency of the physical prototype-ice system.

Dynamics and control of typhoid fever in Sheno town, Ethiopia: A comprehensive nonlinear model for transmission analysis and effective intervention strategies.

This study presents a reliable mathematical model to explain the spread of typhoid fever, covering stages of susceptibility, infection, carrying, and recovery, specifically in the Sheno town community. A detailed analysis is done to ensure the solutions are positive, stay within certain limits, and are stable for both situations where the disease is absent and where it is consistently present. The Routh-Hurwitz stability criterion has been used and applied for the purpose of stability analysis. Using the next-generation matrix, we determined the intrinsic potential for disease transmission. It showing that typhoid fever is spreading actively in Sheno town, with cases above a critical level. Our findings reveal the instability of the disease-free equilibrium point alongside the stability of the endemic equilibrium point. We identified two pivotal factors for transmission of the disease: the infectious rate, representing the speed of disease transmission, and the recruitment rate, indicating the rate at which new individuals enter the susceptible population. These parameters are indispensable for devising effective control measures. It is imperative to keep these parameters below specific thresholds to maintain a basic reproduction number favorable for disease control. Additionally, the study carefully examines how different factors affect the spread of typhoid fever, giving a detailed understanding of its dynamics. At the end, this study provides valuable insights and specific strategies for managing the disease in the Sheno town community.

Delay-dependent exponential stability of highly nonlinear stochastic functional switched systems: an average dwell time approach

The delay-dependent exponential stability of stochastic functional switched systems (SFSSs) with highly nonlinear coefficients is investigated in this paper. By virtue of the mode-dependent average dwell time (MDADT) technique, the existence of global solution and qth moment exponential stability is studied without linear growth condition (LGC). Both of drift and diffusion coefficients have functional terms which can embody many existing delay cases, e.g. constant delay, time-varying delay and distributed delay, etc. By employing common/multiple Lyapunov function method, sufficient delay-dependent stability criteria of qth moment exponential stability are proposed. The MDADT condition reveals the positive role of switching signal in the delay-dependent stability analysis. Finally, an example is given to validate our theoretical results.

Resilient sampled-data control for fractional-order PMVG-based WTS with actuator saturation and probabilistic faults using fuzzy Lyapunov function method

The goal of this study is to present a new fuzzy Lyapunov function-based resilient sampled-data control method for a fractional-order permanent magnet vernier generator (PMVG)-based wind turbine system (WTS) that addresses actuator saturation and probabilistic faults. To achieve this, we first model the dynamical fractional model of the PMVG-based WTS as a T-S fuzzy model. Next, we introduce a fuzzy Lyapunov function within a unified framework that incorporates actuator saturation, probabilistic faults, and uncertainty information from control gain matrices. We then present an actuator fault model that represents actuator faults as stochastic variables with a specific probability distribution. Subsequently, we formulate a robust asymptotic stability criterion for closed-loop systems using linear matrix inequality (LMI), which integrates the fuzzy Lyapunov function and membership function information with fractional integral inequality techniques based on sampling time. We also propose an LMI approach to identify the domain of attraction that meets the necessary actuator saturation criteria. Finally, we apply the proposed method to a PMVG-based WTS, demonstrating its superiority and practical applicability through a comparison with existing methods using a numerical example of a nonlinear truck trailer system.

Robust dynamic output feedback predictive fault‐tolerant control for discrete uncertain systems

AbstractA robust predictive fault‐tolerance control method integrating dynamic output feedback is proposed for discrete industrial processes with unmeasurable states, actuator faults, uncertainties, and external disturbances. First, a new iterative error model is developed, which extends the output tracking error to increase the freedom of controller regulation and ensure the tracking performance of the system. Second, a robust dynamic output feedback predictive fault‐tolerant controller is designed based on the preceding model. According to the Lyapunov stability theory, the robust stability criterion of the system is performed in the case of actuator faults, and the stability conditions of the system in the form of linear matrix inequality are given. The real‐time optimal control law gains are obtained by solving the stability conditions online. This method can effectively suppress the effects of actuator faults, uncertainties and external disturbances on the system with unmeasurable states, which can guarantee the tracking performance and stability of the system. The effectiveness of the proposed method is finally verified by using an injection molding process as an example.

Inspection of the nonlinear instability of electrified Casson fluids: a novel approach

The nonlinear electrohydrodynamic (EHD) instability of a circular cylindrical interface, separating two Casson prototypes is the aim of the present inspection. The motivation for the issue is owing to the increasing significance of several engineering and practicle physics. Because of the complicated mathematical processes, the contribution is performed through the viscous potential theory (VPT). The methodology resulted in a nonlinear characteristic equation of the interface displacement. This equation is transformed to simulate a hybrid Rayleigh-Helmholtz Duffing oscillator (HRDO) with complex coefficients. Guaranteeing the stability of fluid interfaces is crucial in industrial coating operations to provide consistent and even coatings. Gaining comprehension of the nonlinear stability criterion helps to enhance the management of coating thickness and uniformity. A novel methodology via the Non-perturbative approach (NPA) is employed. Through the case of the real coefficients, the later form is validated using a numerical solution (NS). It is concluded that the Ohnesorge contribution has a destabilizing effect on the stability zone in contrast with permeability factor. The electrical coefficients are found to be decaying factors in the stability configuration. It is also established that the viscosity decays the nonlinear steadiness requirement of the structure. The approach is a simple, promising, effective, and interesting.

Mode transitions in a magnetically shielded Hall thruster. II. Stability criterion

Mode transitions in a magnetically shielded Hall thruster. II. Stability criterion

Adaptive conservative time integration for unsteady compressible flow

Unsteady flow computations typically rely on time integration schemes which employ the same step size everywhere. However, in cases with strong variations of wave speed and/or spatial resolution, local stability criteria and truncation errors would allow for much larger time steps in parts of the domain. To exploit this potential of improving the computational efficiency, adaptive time-stepping methods have been developed. Recently, an adaptive conservative time integration (ACTI) scheme for explicit finite volume methods was devised. Opposed to previous methods, ACTI guarantees exact conservation and periodic synchronization. Both are achieved by splitting a global time step into 2L (L≥0 is a cell dependent level) sub-steps, whereas the order of cell updates is critical. It has been demonstrated for flows in fractured porous media and for the Euler equations that ACTI can reduce the computational cost dramatically while preserving second order accuracy in space and time. In this paper, the ACTI scheme is extended to the compressible Navier-Stokes-Fourier system, and special attention is required for the spatio-temporal discretization of the convective and viscous fluxes. Numerical studies of unsteady flows involving shock boundary layer interaction demonstrate that the same accuracy is achieved with the new compressible ACTI flow solver as with classical time integration, but at much lower cost. Moreover, since the method is explicit, it has the potential for efficient computations on multiple CPUs and GPUs.

Position Control of Electro-hydraulic Servo System Based on Repetitive Control Strategy

Background: When performing repetitive work in an electro-hydraulic servo system, the expected tracking signals are often periodic signals, such as trigonometric functions. For this kind of electro-hydraulic servo system, repetitive control is one of the most ideal control strategies. Objective: The objective of this patent technology is to improve the position-tracking performance of the electro-hydraulic servo system and minimize tracking errors by designing and implementing a repetitive control strategy. Methods: The study models an electro-hydraulic servo system, designs a stabilizing controller, and develops a plug-in repetitive controller to enhance EHSS tracking. The regeneration spectrum is used as a stability criterion, and performance is evaluated using statistical metrics like Mean Square Error (MSE), Root Mean Square Error (RMSE), and standard deviation of the tracking error along with tracking performance and steady-state error. Results: The developed controller, validated through simulation analysis and real-time experiments, significantly reduces tracking error and enhances system position tracking accuracy, demonstrating its effectiveness. For instance, the repetitive control strategy outperforms PID and backstepping controllers at 30 mm with 0.5 Hz, achieving an error of 0.2 with an RMSE of 0.0924 and σ of 0.0878. Similar trends are observed at various test conditions, highlighting the consistent and robust performance of the designed repetitive controller. Additionally, the designed repetitive controller demonstrates an average improvement of 75.175% and 62.97% compared to the proportional- integral-derivative and backstepping controllers, respectively. Conclusion: The designed controller provides technical support for position control of the electrohydraulic servo system, achieves position control requirements, and significantly improves positioning accuracy and response.

Inverse Optimal Adaptive Neural Control for State-Constrained Nonlinear Systems.

Optimizing a performance objective during control operation while also ensuring constraint satisfactions at all times is important in practical applications. Existing works on solving this problem usually require a complicated and time-consuming learning procedure by employing neural networks, and the results are only applicable for simple or time-invariant constraints. In this work, these restrictions are removed by a newly proposed adaptive neural inverse approach. In our approach, a new universal barrier function, which is able to handle various dynamic constraints in a unified manner, is proposed to transform the constrained system into an equivalent one with no constraint. Based on this transformation, a switched-type auxiliary controller and a modified criterion for inverse optimal stabilization are proposed to design an adaptive neural inverse optimal controller. It is proven that optimal performance is achieved with a computationally attractive learning mechanism, and all the constraints are never violated. Besides, improved transient performance is obtained in the sense that the bound of the tracking error could be explicitly designed by users. An illustrative example verifies the proposed methods.

Membership-Functions-Derivative-Dependent Stability Criteria for Delayed Takagi–Sugeno Fuzzy Systems

Membership-Functions-Derivative-Dependent Stability Criteria for Delayed Takagi–Sugeno Fuzzy Systems

Hydrodynamic instability of shear imposed falling film over a uniformly heated inclined undulated substrate

Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single nonlinear free surface deflection equation. The linear stability criteria for the onset of instability are derived using the normal mode form in the linearized portion of the surface deformation equation. Linear stability theory reveals that the flow-directed sturdy external shear grows the surface wave instability by increasing the net driving force. On the contrary, the upstream-directed imposed shear may reduce the surface mode instability by restricting the gravity-driving force, which has the consequence of weakening the bulk velocity of the liquid film. However, the surface mode can be stabilized/destabilized by increasing the temperature-dependent density/surface-tension variation. Furthermore, the bottom steepness shows dual behavior on the surface instability depending upon the wavy wall's portion (uphill/downhill). At the downhill portion, the surface wave becomes more unstable than at the bottom substrate's uphill portion. Moreover, the multi-scale method is incorporated to obtain the complex Ginzburg–Landau equation in order to study the weakly nonlinear stability, confirming the existence of various flow regions of the liquid film. At any bottom portion (uphill/downhill), the flow-directed external shear expands the supercritical stable zones, which causes an amplification in the nonlinear wave amplitude, and the backflow-directed shear plays a counterproductive role. On the other hand, the supercritical stable region decreases or increases as long as the linear variation of density or surface tension increases with respect to the temperature, whereas the sub-critical unstable region exhibits an inverse trend.

Dynamics of axially moving spinning microbeams composed of tri-directional graded porous materials with axisymmetric cross-sections and piezoelectric layers in complex fields

The current article appraises the vibration and stability of tri-directional functionally graded porous microscale beams with rectangular cross-sections integrated with piezoelectric layers under spinning and axial movements in complex environments. The microbeam is surrounded by a three-parameter Winkler-Pasternak-Hetenyi medium, and its material characteristics are graded in thickness, width, and longitudinal spatial directions by considering non-uniform and uniform porosity models. Dynamic equations, vibration frequencies, and stability criteria of the system are determined with the aid of the Galerkin approach and Laplace transform. The Campbell diagram and stability maps are drawn. Frequency and stability analyses, as well as comparison and parametric analyses, are conducted. The impacts of piezoelectric voltage, magneto-hygro-thermal fields, axial and tangential distributed follower forces, substrate characteristics, scale parameter, aspect ratio, porosity factor, and material gradation on flutter and divergence instability boundaries are assessed in detail. It is deduced that instability regions are condensed, and the instability threshold is enhanced by fine-adjusting the porosity and material gradient. It is discovered that destructive environmental effects can be alleviated by regulating the piezoelectric voltage. In addition, compared with the case of a square cross-section, the divergence/flutter instability region of the microbeam with a rectangular cross-section is smaller/larger. The outcomes of the present research can be helpful in the design of next-generation bi-gyroscopic systems.

Enhanced Results on Sampled-Data Synchronization for Chaotic Neural Networks With Actuator Saturation Using Parameterized Control.

This article investigates a novel sampled-data synchronization controller design method for chaotic neural networks (CNNs) with actuator saturation. The proposed method is based on a parameterization approach which reformulates the activation function as the weighted sum of matrices with the weighting functions. Also, controller gain matrices are combined by affinely transformed weighting functions. The enhanced stabilization criterion is formulated in terms of linear matrix inequalities (LMIs) based on the Lyapunov stability theory and weighting function's information. As shown in the comparison results of the bench marking example, the presented method much outperforms previous methods, and thus the enhancement of the proposed parameterized control is verified.

Stability criteria and calculus rules via conic contingent coderivatives in Banach spaces

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between Banach spaces important in optimization theory and its applications. Our tools of generalized differentiation revolve around the newly introduced concept of ε-regular normal cone to sets and associated coderivative notions for set-valued mappings. Based on these constructions, we establish several characterizations of the central stability notion known as the relative Lipschitz-like property of set-valued mappings in infinite dimensions. Applying a new version of the constrained extremal principle of variational analysis, we develop comprehensive sum and chain rules for our major constructions of conic contingent coderivatives for multifunctions between appropriate classes of Banach spaces.