Perturbation Parameter Research Articles

On the Modified Laplace Homotopy Perturbation Method for Solving Damped Modified Kawahara Equation and Its Application in a Fluid

The manuscript solves a modified Kawahara equation (mKE) within two cases with and without a damping term by applying the Laplace homotopy perturbation method (LHPM). Since the damped mKE is non-integrable (i.e., it does not have analytic integrals) and does not have exact initial conditions, this challenge makes many numerical methods fail to solve non-integrable equations. In this article, we suggested a new modification at LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter and using the initial condition for mKE as the initial condition for non-damped mKE. The results proved that this mathematical approach is an effective method for solving damped mKE. Thus, we believe that the presented method will be helpful for solving many non-integrable equations that describe phenomena in sciences, such as nonlinear symmetrical wave propagation in plasma.

Uniform attractors for nonclassical diffusion equations with perturbed parameter and memory

In this paper, we consider the long-time behavior of the nonclassical diffusion equation with perturbed parameter and memory on a bounded domain Ω⊂Rn(n≥3). The main feature of this model is that the equation contains a dissipative term with perturbation parameters −νΔu and the nonlinearity f satisfies the polynomial growth of arbitrary order. By using the nonclassical operator method and a new analytical method (or technique) (Lemma 2.7), the existence and regularity of uniform attractors generated for this equation are proved. Furthermore, we also get the upper semicontinuity of the uniform attractors when the perturbed parameter ν → 0. It is remarkable that if ν = 0, we can get the same conclusion as in the works of Toan et al. [Acta Appl. Math. 170, 789–822 (2020)] and Conti et al. [Commun. Pure Appl. Anal. 19, 2035–2050 (2020)], but the nonlinearity is critical.

Systems with Perturbations of Parameters

Systems with Perturbations of Parameters

Analysis of Numerical Differential Formulas on a Bakhvalov Mesh in the Presence of a Boundary Layer

The paper considers numerical differentiation of functions with large gradients in the region of an exponential boundary layer. This topic is important, since the application of classical polynomial difference formulas for derivatives to such functions in the case of a uniform mesh leads to unacceptable errors if the perturbation parameter is comparable with the mesh size. The numerical differentiation formula with a given number of nodes in the difference stencil is built on subintervals covering the original interval. The accuracy of numerical differentiation formulas on a Bakhvalov mesh, which is widely used in the construction of difference schemes for singularly perturbed problems, is analyzed. For the original function of one variable, a representation in the form of a sum of regular and boundary-layer components, based on the Shishkin decomposition, is used to solve a singularly perturbed problem. Previously, such a decomposition was used to prove the convergence of difference schemes. An estimate of the error of classical polynomial formulas for numerical differentiation on a Bakhvalov mesh is obtained. The error estimate on a Bakhvalov mesh is obtained in the general case, when a derivative of an arbitrarily given order is calculated and the difference stencil for this derivative contains a given number of nodes. The error estimate depends on the order of the calculated derivative and the number of nodes in difference stencil and takes into account the uniformity in the parameter . The results of numerical experiments are presented, which are consistent with the error estimates obtained.

Composite Observer-Based Optimal Attitude-Tracking Control With Reinforcement Learning for Hypersonic Vehicles.

This article proposes an observer-based reinforcement learning (RL) control approach to address the optimal attitude-tracking problem and application for hypersonic vehicles in the reentry phase. Due to the unknown uncertainty and nonlinearity caused by parameter perturbation and external disturbance, accurate model information of hypersonic vehicles in the reentry phase is generally unavailable. For this reason, a novel synchronous estimation is proposed to construct a composite observer for hypersonic vehicles, which consists of a neural-network (NN)-based Luenberger-type observer and a synchronous disturbance observer. This solves the identification problem of nonlinear dynamics in the reference control and realizes the estimation of the system state when unknown nonlinear dynamics and unknown disturbance exist at the same time. By synthesizing the information from the composite observer, an RL tracking controller is developed to solve the optimal attitude-tracking control problem. To improve the convergence performance of critic network weights, concurrent learning is employed to replace the traditional persistent excitation condition with a historical experience replay manner. In addition, this article proves that the weight estimation error is bounded when the learning rate satisfies the given sufficient condition. Finally, the numerical simulation demonstrates the effectiveness and superiority of the proposed approaches to attitude-tracking control systems for hypersonic vehicles.

Tracking and Synchronization Control Strategy of Vehicle Dual-Motor Steer-by-Wire System via Active Disturbance Rejection Control

A novel vehicle dual-motor steer-by-wire (SBW) system is proposed to improve the reliability and safety of traditional SBW system. However, the biggest challenge of dual-motor SBW is its tracking and synchronization control issues. In order to solve the problems of poor tracking and synchronization of the vehicle dual-motor SBW system caused by load disturbance, parameter perturbation, and model mismatch, a tracking and synchronization control strategy of the vehicle dual-motor SBW system via the active disturbance rejection control is proposed. First, the driving mechanism of dual-motor SBW system is analyzed, and the system dynamics model is established. Then, considering the system disturbance and parameter uncertainty, a second-order active disturbance rejection controller is designed for the position loop of the steering motor, which is composed of a third-order extended state observer and a state error feedback control law. Next, in order to simplify the adjustment difficulty of the controller, the bandwidth method is introduced to greatly reduce the number of controller parameters and the difficulty of parameter adjustment. Based on this, the disturbance rejection performance and stability of the designed active disturbance rejection controller are proved. Furthermore, the cross-coupling control structure is employed to enhance the synchronization performance of the dual-motor system. Finally, the performance of the controller to suppress the external disturbance and internal parameter perturbation is analyzed in step condition and double lane change condition, respectively, and the effectiveness of the proposed control strategy is verified on the dual-motor experimental platform.

Prescribed-Time Stabilization of Singularly Perturbed Systems

Dear Editor, This letter investigates the prescribed-time stabilization of linear singularly perturbed systems. Due to the numerical issues caused by the small perturbation parameter, the off-the-shelf control design techniques for the prescribed-time stabilization of regular linear systems are typically not suitable here. To solve the problem, the decoupling transformation techniques for time-varying singularly perturbed systems are combined with linear time-varying high gain feedback design techniques. A composite linear time-varying state feedback controller is designed, and the existence of the time-varying Chang transformation matrix for decoupling the slow and fast dynamics is guaranteed. As a result, the prescribed-time stability is ensured. Finally, a numerical example is provided to illustrate the effectiveness of the results.

Trajectory tracking control of tilt-propulsion UAV vertical take-off and landing mode based on NLESO

Aiming at the vertical take-off and landing mode of tilt-propulsion UAV with uncertainties such as external environment disturbance and internal parameter perturbation, this paper studies the trajectory tracking control, and proposes an internal and external double loop sliding mode control scheme based on nonlinear extended state observer (NLESO). Firstly, according to the characteristics of tilt-propulsion UAV, the dynamic model of propulsion system, aerodynamic model of fuselage/wing and yaw rudder, and dynamic equation are established in turn to complete the dynamic modeling work. Then, the internal and external uncertainties are regarded as lumped disturbances, and NLESO is designed to estimate them and compensate the control system. Afterwards, based on NLESO and sliding mode control method, the position and attitude double loop controller of VTOL mode is designed. Finally, the Lyapunov function is designed to analyze the stability of NLESO and the whole control system. Simulation results show that the proposed method significantly improves the trajectory tracking response speed and the ability to suppress uncertainties of vertical take-off and landing mode of tilt dynamic UAV.

Improved Grey Wolf Optimizer Tuned Active Disturbance Rejection Control for Ship Heading

The ship heading control is very important to the shipping industry. The Active Disturbance Rejection Control (ADRC) method is ideal for ship heading control, but it is highly correlated with parameters. In this brief, we employed the chaotic mapping and fractional derivative update method to enhance the Grey Wolf Optimizer (GWO), namely Improved GWO (IGWO). The IGWO is proposed to tune the parameters of ADRC adaptively, then the IGWO-tuned ADRC is utilized to control the ship heading. As the comparison, four other optimizers are also employed to tune the parameters of ADRC. Five different disturbance situations are considered to validate the stability of these tuning methods. The robustness of the proposed method for ship parameters perturbation is also analyzed by Monte Carlo experiments. The results indicate that the performance of proposed methods is superior to others.

Effects of Oral Levodopa on Balance in People with Idiopathic Parkinson's Disease.

Balance impairment is a frequent cause of morbidity and mortality in people with Parkinson's disease (PD). As opposed to the effects of appendicular motor symptoms, the effects of Levodopa on balance impairment in idiopathic PD are less clear. To review the literature on the effects of oral Levodopa on clinical balance test performance, posturography, step initiation, and responses to perturbation in people with idiopathic PD (PwPD). A systematic search of three scientific databases (Pubmed, Embase, and Web of Science) was conducted in accordance with PRISMA guidelines. For the pilot meta-analysis, standardized mean differences with 95% confidence intervals were calculated using an inverse variance random effects model. Data not suitable for implementation in the meta-analysis (missing means or standard deviations, and non-independent outcomes) were analyzed narratively. A total of 2772 unique studies were retrieved, of which 18 met the eligibility criteria and were analyzed, including data of 710 idiopathic PwPD. Levodopa had a significant positive effect on the Berg Balance Scale, the Push and Release test, and jerk and frequency parameters during posturography. In contrast, some significant negative effects on velocity-based sway parameters were found during posturography and step initiation. However, Levodopa had no significant effect on most step initiation- and all perturbation parameters. The effects of Levodopa on balance in PwPD vary depending on the outcome parameters and patient inclusion criteria. A systematic approach with well-defined outcome parameters, and prespecified, sensitive and reliable tests is needed in future studies to unravel the effects of oral Levodopa on balance.

Uniformly convergent scheme for fourth-order singularly perturbed convection-diffusion ODE

This paper contemplates a numerical investigation of the convection-diffusion type's fourth-order singularly perturbed linear and nonlinear boundary value problems. First, the considered linear fourth-order differential equation is converted into a strongly/weakly coupled singularly perturbed system (depending on the coefficient of the first-order derivative) of two ordinary differential equations with Dirichlet boundary conditions to solve the problem numerically. One of the equations is free from the perturbation parameter in the system. To obtain the solution for this system, we propose a numerical method of quadratic B-splines on an exponentially graded mesh. Convergence analysis shows that the proposed numerical scheme is second-order uniformly convergent in the discrete maximum norm. The nonlinear differential equation is linearized using the quasilinearization technique, and then the proposed approach is applied to the linearized problem. The theoretical outcomes are validated by executing the proposed method on three test problems.

High-fidelity multi-level efficiency optimization of propeller for high altitude long endurance UAV

This paper describes the development of a high-fidelity multi-level optimization framework to maximize the efficiency of a propeller. Specifically, the discrete adjoint method optimizes the airfoil cluster in a three-dimensional state. Subsequently, parametric perturbation and flow pattern reconstruction methods are applied to the optimization of the twist angle and chord length distribution. Additionally, we use the concepts of perturbation loss and additional efficiency to quantify the influence of the viscosity loss on the efficiency and the potential chord length optimization at each blade section. The precision during the optimization is consistent with that of Computational Fluid Dynamics (CFD), which agrees well with the experimental data. The results indicate that the proposed optimization framework can efficiently combine high fidelity and low computational costs and accurately quantify the influence of complex three-dimensional flow characteristics on the optimal shape of the propeller. With the aid of the proposed optimization criterion, the three-dimensional flow can reach the state that is most conducive to improving the propeller efficiency by adjusting the shape parameters. Overall, this research's methodology and general rules provide a reference for the propeller design of a high altitude long endurance UAV.

Nonzero θ13, CP-violation and neutrinoless double beta decay for neutrino mixing in the A4×Z2×Z3 flavor symmetry model

In this paper, we study the modification of the Altarelli–Feruglio [Formula: see text] flavor symmetry model by adding three singlet flavons [Formula: see text], [Formula: see text] and [Formula: see text] and the model is augmented with extra [Formula: see text] symmetry to prevent the unwanted terms in our study. The addition of these three flavons leads to two higher order corrections in the form of two perturbation parameters [Formula: see text] and [Formula: see text]. These corrections yield the deviation from exact tri-bimaximal (TBM) neutrino mixing pattern by producing a nonzero [Formula: see text] and other neutrino oscillation parameters which are consistent with the latest experimental data. In both the corrections, the neutrino masses are generated via Weinberg operator. The analysis of the perturbation parameters [Formula: see text] and [Formula: see text], shows that normal hierarchy (NH) and inverted hierarchy (IH) for [Formula: see text] do not change much. However, as the values of [Formula: see text] increase, [Formula: see text] occupies the lower octant for NH case. We further investigate the neutrinoless double beta decay parameter [Formula: see text] using the parameter space of the model for both normal and inverted hierarchies of neutrino masses.

Reconstruction of Scalar-Torsion Gravity Theories from the Physical Potential of a Scalar Field

We consider scalar-torsion gravity theories based on the exact solutions of a physical type of potential for cosmological inflationary models based on the non-minimal coupling of a scalar field and torsion. We analyzed the inflationary models with different types of inflationary dynamics and corresponding scalar field parameters. Such an approach allows us to consider different physical potentials and types of scalar-torsion gravity theories in the context of the realization of both stages of accelerated expansion of the universe. We also considered the correspondence surrounding the proposed inflationary models and the observational constraints on the parameters of cosmological perturbations.

DDPG based LADRC trajectory tracking control for underactuated unmanned ship under environmental disturbances

Realizing trajectory tracking control of underactuated unmanned ships is critical for safe and stable navigation during offshore operations. The principal difficulties of this task lie in the coupling problem caused by the underactuated system and the uncertainty caused by the modeling error, internal parameter perturbations, and external environment. In this paper, a three-degree-of-freedom ship model is first built based on the manipulative modeling group equation. Then, a trajectory tracking line-of-sight guidance law is proposed to achieve the desired heading angle and forward speed during trajectory tracking, and the Lyapunov function is used to analyze its stability. Furthermore, the heading angle controller and forward speed controller are designed based on the linear active disturbance rejection control framework. In addition, to solve the challenging problem of controller parameter tuning and further improve the controller’s robustness, the Deep Deterministic Policy Gradient algorithm is applied to adjust the controller parameters. Finally, the effectiveness of the proposed method is verified by the simulation results of sinusoidal, circular, and square trajectories with wind and current disturbances.

A SEMI-ANALYTIC METHOD FOR SOLVING SINGULARLY PERTURBED TWIN-LAYER PROBLEMS WITH A TURNING POINT

This computational study investigates a class of singularly perturbed second-order boundary-value problems having dual (twin) boundary layers and simple turning points. It is well-known that the classical discretization methods fail to resolve sharp gradients arising in solving singularly perturbed differential equations as the perturbation (diffusion) parameter decreases, i.e., ε → 0+. To this end, this paper proposes a semi-analytic hybrid method consisting of a numerical procedure based on finite differences and an asymptotic method called the Successive Complementary Expansion Method (SCEM) to approximate the solution of such problems. Two numerical experiments are provided to demonstrate the method’s implementation and to evaluate its computational performance. Several comparisons with the numerical results existing in the literature are also made. The numerical observations reveal that the hybrid method leads to good solution profiles and achieves this in only a few iterations.

Instability Problems and Density-Driven Convection in Saturated Porous Media Linking to Hydrogeology: A Review

Investigations of fluid instability and density-driven convection in soils and rocks are motivated by both natural phenomena giving rise to ecological problems, and human activities. Knowledge about the admixture transportation by underground fluid flows driven by the gravity force is relevant, for example, to succeed in preventing degradation of soil quality or to improve the efficiency of carbon capture and sequestration technologies. We focus on fully saturated porous media containing two-component miscible fluid systems and consider the dynamic processes, which can be reduced to one of three principal problems, namely one-sided convection, two-sided convection, or convection caused by evaporation. This work reviews the main achievements in the field with more attention to the recent literature. Dependence of the convection onset on perturbations of physical parameters, asymmetric development of the Rayleigh–Taylor instability, appearance of salt drops under the evaporation surface, and other important findings are reported in the review.

Robustness of 3D Navier–Stokes System with Increasing Damping

The principal objective of the paper is the study of the three-dimensional Navier–Stokes system with non-autonomous perturbation force term and increasing damping term, which often appears in the fluid system within saturated porous media and other complex media. With some suitable assumptions on the system parameters and external force term, based on the known result on global well-posedness, the existence of pullback attractors is educed, and the system robustness is shown via the upper semicontinuity of system attractors as the perturbation parameter approaches a certain value.

Fractional order internal model control of non‐minimum phase and time‐delayed plants

AbstractSeveral applications on fractional order (FO) control have gained considerable significance in the recent years, which led to the evolution of novel tuning strategies of the generalized order FO controllers. Some of the methods in available literatures are based on constrained minimization optimization techniques or analytical method defined only for specific plants. They are valid only for some special model cases. On the contrary, in this technical note, a generalized non‐integer order internal model control (IMC) framework is realized for any order non‐minimum phase (NMP) plants with right half plane (RHP) zero as well as time delayed plants having any finite relative order. Its parameters are graphically interpreted satisfying the frequency domain design stipulations for single input and single output (SISO) higher order linear time invariant (LTI) plants. The performance of the same on a bioreactor fermentation process for its temperature control is found to have outperformed in contrast to its integer order (IO)‐IMC. It is therefore inferred here that this new approach pledges to impart unique solution of the controller parameters, formulating a highly efficient tool outperforming the existing paradigms. Simulation and real time experimentation are presented to validate the method put forward providing satisfactory performance in reference tracking, disturbance rejection, and robustness to various plant parameter perturbations.

On the adoption of nonpharmaceutical interventions during the pandemic: An evolutionary game model.

The adoption of behavioral nonpharmaceutical interventions (NPIs) among the public is essential for tackling the COVID-19 pandemic, yet presents challenges due to the complexity of human behaviors. A large body of literature has utilized classic game theory to investigate the population's decisions regarding the adoption of interventions, where the static solution concept such as the Nash equilibrium is studied. However, individual adoption behavior is not static, instead it is a dynamic process that involves the strategic interactions with other counterparts over time. The study of quantitatively analyzing the dynamics on precautionary behavior during an outbreak is rather scarce. This article fills the research gap by developing an evolutionary game-theoretic framework to model the dynamics of population behavior on the adoption of NPI. We construct the two-group asymmetric game, where behavioral change for each group is characterized by replicator equations. Sensitivity analyses are performed to examine the long-term stability of equilibrium points with respect to perturbation of model parameters. We found that the limiting behavior of intervention adoption in the population consists of only pure strategies in a game setting, indicating that the evolutionary outcome is that everyone either takes up the preventive measure or not. We also applied the framework to examine the mask-wearing behavior, and validated with actual data. Overall, this article provides insights into population dynamics on the adoption of intervention strategy during the outbreak, which can be beneficial for policy makers to better understand the evolutionary trajectory of populationbehavior.