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This study employs a mathematical model to analyze and forecast the severe outbreak of SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2), focusing on the socio-economic ramifications within the Thai population and among foreign tourists. Specifically, the model examines the impact of the disease on various population groups, including susceptible (S), exposed (E), infected (I), quarantined (Q), and recovered (R) individuals among tourists visiting the country. The stability theory of differential equations is utilized to validate the mathematical model. This involves assessing the stability of both the disease-free equilibrium and the endemic equilibrium using the basic reproduction number. Emphasis is placed on local stability, the positivity of solutions, and the invariant regions of solutions. Additionally, a sensitivity analysis of the model is conducted. The computation of the basic reproduction number (R0) reveals that the disease-free equilibrium is locally asymptotically stable when R0 is less than 1, whereas the endemic equilibrium is locally asymptotically stable when R0 exceeds 1. Notably, both equilibriums are globally asymptotically stable under the same conditions. Through numerical simulations, the study concludes that the outcome of COVID-19 is most sensitive to reductions in transmission rates. Furthermore, the sensitivity of the model to all parameters is thoroughly considered, informing strategies for disease control through various intervention measures. [ABSTRACT FROM AUTHOR]

This work investigates the stability for the wave equation with damping γ (t , x) (− Δ x) α ∂ t u defined on a bounded domain Ω ⊂ R d , d ≥ 1. The damping coefficient γ (t , x) ≥ 0 may degenerate to zero at some (t , x) ∈ [ τ , + ∞) × Ω. In contrast to the classical geometric control condition (GCC), we give the integral control condition (ICC) which means γ only has a positive lower bound in the sense of integral. [ABSTRACT FROM AUTHOR]

We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension‐one and codimension‐two bifurcation analysis, and chaos control in a predator‐prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior and semitrivial equilibrium solutions under certain model parameter conditions. Furthermore, local stability at trivial, semitrivial, and interior equilibria using the theory of linear stability is investigated. We have also explored the bifurcation sets for trivial, semitrivial, and interior equilibria and proved that flip bifurcation occurs at semitrivial equilibrium. Furthermore, it is also proven that Neimark–Sacker bifurcation as well as flip bifurcation occurs at an interior equilibrium solution, and in addition, at the same equilibrium solution, we also studied codimension‐two 1 : 2 strong resonance bifurcation. Then, OGY and hybrid control strategies are employed to manage chaos in the model under study, which arises from Neimark–Sacker and flip bifurcations, respectively. We have also examined the preservation of the positive solution of the understudied model. Finally, numerical simulations are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, it is considered that the question of adaptive tracking control of nonlinear systems containing unknown time‐varying parameters. To optimize the control effect, a fixed‐time control strategy is adopted, in which the upper bound of the settling time is connected with the designed parameters, but not to the initial conditions. In the design, the unknown time‐varying parameters are treated as the multiplication of known and unknown vectors, and the adaptive laws are constructed to estimate the mean value of the components in the unknown ones, which availably solve the difficulty of unknown control gains. Besides, the application of command filtered technique, which combined with the compensation signals containing the adaptive parameters, effectively avoids the "complexity explosion" problem. Further, Lyapunov stability theory verifies that the tracking error can always be kept within the boundaries of the performance functions, and converges to a designated neighbourhood of the origin within a fixed time, beyond that all signals of the closed‐loop system are bounded. Finally, the simulation results prove the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this article, a fault-tolerant tracking control technique is developed for the ascent of hypersonic vehicles (HSV) experiencing wing damage and time-varying state constraints. The difficulty of control problem lies in handling state constraints associated with both state and time, while determining the unknown control directions of the multi-input multi-output (MIMO) nonlinear system. The presence of constraints in both state and time complicates the design of the control algorithm. This paper proposes the construction of a novel state transition function to establish a new unconstrained system, thereby eliminating the conservative feasibility conditions of Barrier Lyapunov Function (BLF) and integral BLF methods when dealing with time-varying constraints. The fusion of time-varying scaling functions and Nussbaum-type functions not only resolves the issue of unknown control directions in the MIMO nonlinear system but also enhances the transient and steady-state performance of the closed-loop system. Neural Networks are employed to approximate the unknown nonlinear functions. Using Lyapunov stability theory, it is proven that state constraints are not violated, and all signals in the closed-loop system are bounded. Simulation results demonstrate the merits of the designed fault-tolerant control (FTC) algorithm. • A unified fault-tolerant control scheme for the ascent hypersonic vehicle is designed. • Wing damage and function constraints on states are considered. • Nonlinear mapping eliminates the feasibility conditions in barrier Lyapunov functions. • The unknown control direction issue in multivariable nonlinear systems is resolved. [ABSTRACT FROM AUTHOR]

In recent decades, impulse control has been increasingly applied as a discontinuous control method across diverse domains such as satellite orbit transfers, financial market regulation, chaos synchronization, and communication security. This paper investigates an impulse synchronization strategy specifically tailored for chaotic financial systems. We propose a novel strategy grounded in Lyapunov stability theory and the maximum Lyapunov exponent, designed to synchronize chaotic financial systems effectively. Simulation experiments are conducted to validate the efficacy of our proposed approach. [ABSTRACT FROM AUTHOR]

This paper primarily investigates a neural-network-based safe control scheme for solving the optimal control problem of continuous-time (CT) nonlinear systems with asymmetric input constraints under non-zero-sum (NZS) differential game scenarios. Initially, by constructing a novel non-quadratic function, the issue of asymmetric input constraints in the non-zero-sum differential game controllers is addressed. Subsequently, the safe Hamilton-Jacobi-Bellman (HJB) equation is derived from the direct integration of the control barrier function (CBF) into the traditional cost function, ensuring that the system states remain within a safe region. Then, the safe learning control scheme based on single critic neural network (NN) and adaptive dynamic programming (ADP) is proposed to approximate the optimal control strategy, differing from the dual-network update method commonly used in traditional ADP. Based on the constructed neural network weight adjustment rules, the optimal solution to the HJB equation can be derived within the safe learning control framework. Following this, Lyapunov's stability theory demonstrates that the errors in neural network weights and all signals within the closed-loop system are uniformly ultimately bounded (UUB). Finally, the effectiveness of the developed neural-network-based safe learning control method is validated through two simulation results. [ABSTRACT FROM AUTHOR]

A novel controller using fixed‐time sliding mode (FTSM) and fixed‐time disturbance observer (FTDO) is proposed to achieve trajectory tracking control of robotic manipulators. First, the mathematical model is established for robots with dynamic model uncertainties and external disturbances. An FTSM control strategy is presented where the integral terms of position errors are introduced into the existing sliding mode surface (SMS) to reduce the steady‐state error of the system. The exponential form in the integral terms can provide an appropriate control force for tracking systems when the position errors are far from the sliding surface for a long time. Then, an FTDO is designed to obtain a precise estimation of lumped disturbances which can be used to weaken the impact of disturbances on the control accuracy. Finally, the fixed‐time convergence properties of the tracking control system are demonstrated using Lyapunov stability theory. Simulation research is carried out to illustrate that the proposed control strategy has strong robustness and fast‐tracking speed. [ABSTRACT FROM AUTHOR]

Recent years have seen high penetration of renewable energies, which have significantly reduced the inertia of bulk power systems. As a result, the frequency behaviour of power systems is becoming more complex. To resolve this technical challenge, there is a particularly strong interest in developing analytical solutions for frequency dynamics studies. This study first describes a second‐order frequency dynamics model for power systems with renewable energies. A non‐linear perturbation approach is suggested to drive the analytical solution of the model. It is shown that, under many circumstances, frequency dynamics can be effectively approximated using a linear model. Subsequently, the article describes a fourth‐order linear frequency dynamics model that takes into account governor‐turbines. A polynomial eigenvalue method is proposed to identify the dominant and non‐dominant modes of the solution of the four‐order model. It is demonstrated that the dominant mode has a decisive impact on frequency behaviour, while the non‐dominant modes influence the relative frequency oscillations only. Finally, the study derives the analytical expressions of the standard frequency performance metrics and examines the impact of damping and inertia parameters. The introduced results are verified using two test systems, demonstrating the accuracy and effectiveness of the suggested method. [ABSTRACT FROM AUTHOR]

Intersecting disciplines, as an important trend in the development of modern academic research and education, have exerted a profound and positive influence on scientific research activities. Based on control theory and fractional-order theory, this paper presents a novel approach for the speed regulation of a permanent magnet synchronous motor (PMSM) in the presence of uncertainties and external disturbances. The proposed method is a composite control based on a model-free sliding mode and a fractional-order ultra-local model. The model-free sliding mode is a control strategy that utilizes the sliding mode control methodology without explicitly relying on a mathematical model of the system being controlled. The fractional-order ultra-local model is a mathematical representation of a dynamic system that incorporates the concept of fractional-order derivatives. The core of the controller is a new type of fractional-order fast nonsingular terminal sliding mode surface, which ensures high robustness, quick convergence, while preventing singularity. Moreover, a novel fractional-order nonlinear extended state observer is proposed to estimate both internal and external disturbances of the fractional-order ultra-local model. The stability of the system is analyzed using both the Lyapunov stability theory and the Mittag–Leffler stability theory. The analysis confirms the convergence stability of the closed-loop system under the proposed control scheme. The comparison results indicate that the proposed composite control based on the fractional-order ultra-local model is a promising solution for regulating the speed of PMSMs in the presence of uncertainties and disturbances. [ABSTRACT FROM AUTHOR]

This study explores fault-tolerant consensus in leader–following heterogeneous multi-agent systems, focusing on actuator failures in uncrewed aerial vehicles (UAVs) and uncrewed ground vehicles (UGVs). An optimization-based fault-tolerant consensus algorithm is proposed. The algorithm utilizes the Euler–Lagrange formula to ensure system consistency under actuator failures, with the Lyapunov stability theory proving the asymptotic stability of the consistency error. The algorithm is applied to heterogeneous multi-agent systems of UAVs and UGVs to derive optimal fault-tolerant consensus control laws for each vehicle type. Simulation experiments give evidence for the feasibility of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper focuses on the finite‐time synchronization issue for reaction‐diffusion competitive neural networks (RCNNs) with different time scales and time‐varying delays. To reduce the waste of network resources, a periodically intermittent control strategy is presented based on two time scales (short and long memory) and time‐varying delay. By constructing the Lyapunov–Krasovskii functional, with the help of Lyapunov stability theory and auxiliary inequality technique, the finite‐time synchronization can be guaranteed and the settling time is exactly estimated. Finally, an exhaustive numerical analysis is presented to illustrate the effectiveness of the controller and the correctness of theoretical results. [ABSTRACT FROM AUTHOR]

Nonholonomic constrained wheeled mobile robot (WMR) trajectory tracking requires the enhancement of the ground adaptation capability of the WMR while ensuring its attitude tracking accuracy, a novel dual closed-loop control structure is developed to implement this motion/force coordinated control objective in this paper. Firstly, the outer-loop motion controller is presented using Laguerre functions modified model predictive control (LMPC). Optimised solution condition is introduced to reduce the number of LMPC solutions. Secondly, an inner-loop force controller based on adaptive integral sliding mode control (AISMC) is constructed to ensure the desired velocity tracking and output driving torques by combining second-order nonlinear extended state observer (ESO) with the estimation of dynamic uncertainties and external disturbances during WMR travelling process. Then, Lyapunov stability theory is utilised to guarantee the consistent final boundedness of the designed controller. Finally, the system is numerically simulated and practically verified. The results show that the double-closed-loop control strategy devised in this paper has better control performance in terms of complex trajectory tracking accuracy, system resistance to strong interference and computational timeliness, and is able to realise effective coordinated control of WMR motion/force. [ABSTRACT FROM AUTHOR]

The purpose of this research is to address the problem of synchronization between two identical biological hyperchaotic snap oscillator systems with unknown parameters at a fixed time, as well as to design a new theory for synchronizing two different chaotic systems. Firstly, we designed an adaptive controller using Lyapunov stability and fixed-time stability theory to achieve synchronization between two identical biological hyperchaotic snap oscillator in fixed time under unknown parameters. Among the results obtained, we found that the synchronization time for system states occurred in a very short time compared to results in previous research. Secondly, we extended and generalized synchronization between non-identical chaotic systems by creating a theory for achieving synchronization in which adaptive control and fixed-time stability are combined. Through the new theory, the unknown parameters in chaotic systems were estimated, and the settling time was determined, which turned out to be very short and independent of the initial conditions of the system states. One of what makes the scheme important is that it can be easily applied to most chaotic and even hyperchaotic systems in the shortest possible time. Finally, we gave examples of different systems to test the feasibility and effectiveness of the scheme that was designed. [ABSTRACT FROM AUTHOR]

This research explores the complex dynamics of a Novel Four-Dimensional Fractional Supply Chain System (NFDFSCS) that integrates a quadratic interaction term involving the actual demand of customers and the inventory level of distributors. The introduction of the quadratic term results in significantly larger maximal Lyapunov exponents (MLE) compared to the original model, indicating increased system complexity. The existence, uniqueness, and Ulam–Hyers stability of the proposed system are verified. Additionally, we establish the global Mittag-Leffler attractive set (MLAS) and Mittag-Leffler positive invariant set (MLPIS) for the system. Numerical simulations and MATLAB phase portraits demonstrate the chaotic nature of the proposed system. Furthermore, a dynamical analysis achieves verification via the Lyapunov exponents, a bifurcation diagram, a 0–1 test, and a complexity analysis. A new numerical approximation method is proposed to solve non-linear fractional differential equations, utilizing fractional differentiation with a non-singular and non-local kernel. These numerical simulations illustrate the primary findings, showing that both external and internal factors can accelerate the process. Furthermore, a robust control scheme is designed to stabilize the system in finite time, effectively suppressing chaotic behaviors. The theoretical findings are supported by the numerical results, highlighting the effectiveness of the control strategy and its potential application in real-world supply chain management (SCM). [ABSTRACT FROM AUTHOR]

The critical lateral buckling load of cantilever beams with IPE cross-section was calculated using analytical closed-form equations and numerical finite element analyses within the scope of the research. The equations suggested in the specifications for simply supported beams were used to calculate the buckling load of cantilever beams. The rationality of the values calculated due to this is not fully known. In the research, a single loading was made to the shear center at the free end of the cantilever beam. Cantilever length and section height were kept variable. As a result, it has been determined that there are partial differences in the analysis result obtained from the elastic stability theory and finite element method. Accordingly, the results obtained from ANSYS and SAP2000 analyses confirm each other. On the other hand, the results obtained using the formulation of Timoshenko and Gere, the calculation results made according to the AISC and DCCPSS regulations, and the results obtained from the LTBeam program confirm each other. However, it differs from the FEA analysis due to the cantilever beam length’s shortening and the section height increase. Thus, to obtain accurate and reliable results in the buckling load calculation of cantilever beams, the equations used in analytical calculations were optimized according to finite element analysis (FEA) results. As a result of the study conducted according to the error criteria, it was determined that the updated equation results gave similar results to the FEA results. [ABSTRACT FROM AUTHOR]

The dynamic vibration absorber with inerter and grounded stiffness (IG-DVA) is used to control a two-scale system subject to a weak periodic perturbation. The vibration suppression effect is remarkable. The amplitude of the main system coupled with absorber is significantly reduced, and the high frequency vibration completely disappears. First, through the slow-fast analysis and stability theory, it is found that the stability of the autonomous system exerts a notable regulating effect on the vibration response of the non-autonomous system. After adding the dynamic vibrator absorber, the center in the autonomous system changes to an asymptotically stable focus, consequently suppressing the vibration in the non-autonomous system. Further research reveals that the parameters of the absorber affect the real parts of the eigenvalues of the autonomous system, thereby regulating the stability of the system. Transitioning from a qualitative standpoint to a quantitative approach, a comparison of the solutions before and after the introduction of the dynamic absorber reveals that, when the grounded stiffness ratio and the mass ratio of the dynamic absorber are not equal, the high-frequency part in the analytical solution disappears. As a result, this leads to a reduction in the amplitude of the trajectory, achieving a vibration reduction effect. [ABSTRACT FROM AUTHOR]

In this investigation, we delve into the influence of throughflow on the phenomenon of bi-disperse convection within Rivlin-Ericksen fluid. In the context of examining bi-disperse convection within this specific type of fluid, the throughflow effect is considered to have a uniform vertical distribution. The primary focus of this study centers on evaluating the system’s linear stability. To achieve this, we employ normal mode analysis to compute the Darcy-Rayleigh number at the onset of convection. This Darcy-Rayleigh number is computed for both stationary and oscillatory convection modes. Furthermore, we conduct a comprehensive analysis and present the results in graphical form to illustrate the impact of various parameters, including Peclet number and kinematic viscoelastic parameter, on both stationary and oscillatory convection. Our research findings demonstrate that when Peclet number Pr1 < 0, it leads to destabilising effect on both stationary and oscillatory convections. Conversely, when Peclet number Pr1 > 0, it induces stabilising effect on both stationary as well as oscillatory convections. [ABSTRACT FROM AUTHOR]

In this study, dynamic formation tracking and interception are performed by controlling multi-agent using a Euler-like Lagrangian model. The purpose is to use the distance-based rigid graph method to control multi-agent, and ultimately achieve dynamic formation tracking and target interception of multi-agent. Initially, distance-based graph stiffness and back-stepping techniques were considered to address the formation control challenge. This method helps achieve the initial expected formation and effectively complete the formation mission. Leaders continue to chase the moving target, while followers stick to the expected arrangement. The leader then precisely tracks the moving target and surrounds it within the formation. By using Lyapunov stability theory with adaptive control, it is ensured that the total distance meets finite and consistent error limits. Finally, the numerical simulation of the interception plan was carried out by 6 multi-agents and 1 target at different times to verify the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

To improve the ride comfort and driving stability of automobiles, an optimal sliding mode control (OSMC) strategy based on the enhanced African vultures optimization algorithm (EAVOA) is proposed. Firstly, the structure and operating principle of a semi-active suspension system (SASS) with a magnetorheological damper (MRD) is comprehensively introduced. Secondly, the OSMC is designed based on a quarter-vehicle suspension model with two degrees of freedom (DOF) to meet the Hurwitz stability theory. Simultaneously, the EAVOA is employed to optimize the control coefficients of the sliding mode surface and the control law parameters. Finally, the EAVOA-OSMC control strategy is utilized to construct the simulation model in MATLAB/Simulink (R2018b), providing a comprehensive analysis for passive suspension systems (PSSs) and suspensions with SMC control. The simulation results demonstrate that the EAVOA-OSMC control strategy outperforms SMC controllers, offering a better control performance in real application. [ABSTRACT FROM AUTHOR]

To expand the application prospects of quadrotors in challenging scenes such as those with dense obstacles and narrow corridors, task-driven reconfigurable quadrotors are highly desirable. Aiming to address hazard missions, in this paper, translational reconfigurable quadrotors and rotational reconfigurable quadrotors are proposed with their assumptions and mathematical models. Related motion control laws were designed using model reference adaptive control (MRAC) theory based on Lyapunov stability theory, whose validity was demonstrated by sufficient numerical simulations. The simulation results verify the feasibility of the proposed control laws and reveal the important effect of time delay on the stability of the motion control system. Additionally, the dependence of motion control's stability on the time constant of reference system was discussed. [ABSTRACT FROM AUTHOR]

With the application of the two-tier capital agreement and the introduction of the three-tier capital agreement, the discussion of the role of banks’ capital in the monetary transfer mechanism and banks’ lending decisions has become more important. In this regard, in this research, the effect of the legal requirements of the Basel III Agreement on the lending power and financial stability of the banking sector in Iran has been investigated using the system of simultaneous equations. For this purpose, the data from 19 selected banks and financial institutions were used during the period of 2011-2019. The findings of the research showed that the legal requirements of Basel III had negative and significant effects on bank lending. It was also observed that the legal requirements of Basel III had positive and significant effects on the financial stability of banks. [ABSTRACT FROM AUTHOR]

A H ∞ robust adaptive nonlinear observer for state and parameter estimation of a class of Lipschitz nonlinear systems with disturbances is presented in this work. The objective is to estimate parameters and monitor the performance of nonlinear processes with model uncertainties. The behavior of the observer in the presence of disturbances is analyzed using Lyapunov stability theory and by considering an H ∞ performance criterion. Numerical simulations were carried out to demonstrate the applicability of this observer for a semi-active car suspension. The adaptive observer performed well in estimating the tire rigidity (as an unknown parameter) and induced disturbances representing damage to the damper. The main contribution is the proposal of an alternative methodology for simultaneous parameter and actuator disturbance estimation for a more general class of nonlinear systems. [ABSTRACT FROM AUTHOR]

Malaria is a fever condition that results from Plasmodium parasites, which are transferred to humans by the attacks of infected female Anopheles mosquitos. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. More so, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The reproduction number R o was determined to be an asymptotically stable condition for disease free and endemic equilibria. In this paper, we used various schemes such as Runge–Kutta order 4 (RK-4) and non-standard finite difference (NSFD). All of the schemes produce different results, but the most appropriate scheme is NSFD. This is true for all step sizes. Various criteria are used in the NSFD scheme to assess the local and global stability of disease-free and endemic equilibrium points. The Routh–Hurwitz condition is used to validate the local stability and Lyapunov stability theorem is used to prove the global asymptotic stability. Global asymptotic stability is proven for the disease-free equilibrium when R 0 ≤ 1 . The endemic equilibrium is investigated for stability when R 0 ≥ 1 . All of the aforementioned schemes and their effects are also numerically demonstrated. The comparative analysis demonstrates that NSFD is superior in every way for the analysis of deterministic epidemic models. The theoretical effects and numerical simulations provided in this text may be used to predict the spread of infectious diseases. [ABSTRACT FROM AUTHOR]

This work deals with designing an advanced integral sliding mode controller (AISMC) for residual current compensation (RCC) inverters connected with arc suppression coils to compensate for power distribution networks where the main idea is to alleviate hazardous circumstances caused by electric faults on powerlines. The key advancement in the proposed AISMC over traditional sliding mode controllers is the utilization of an improved exponential reaching law which ensures the faster convergence of the desired control objective that is the fault current compensation in this particular application. An improved exponential reaching law (IERL) used in this work is a combination of the exponential and constant‐proportional reaching laws (while existing approaches use constant reaching laws) which assists to minimize the current injection error through the RCC inverter in the steady‐state. The integral action in conjunction with the exponential function in the sliding surface, based on which the proposed controller is designed, helps to eliminate the chattering effects in a quickest way that can be evidenced from the settling time and percentage overshoot. The feasibility of the proposed AISMC is theoretically assessed by analyzing the stability using the Lyapunov stability theory. Simulation and processor‐in‐loop results further justify the theoretical foundation by confirming the desired current injection and compensating voltage and current due to the fault. Finally, results are compared with a TIMSC for demonstrating the superiority of the AISMC. [ABSTRACT FROM AUTHOR]

This paper explores resilient control problems for discrete-time nonlinear semi-Markov jump systems characterized by incremental quadratic constraints. Considering the system's uncertainties and external environmental factors, mode-dependent resilient controllers are developed to ensure the system's mean-square stability. A proposed event-triggering mechanism is suggested to alleviate the communication burden within the system. Additionally, the system's nonlinearity is characterized by using incremental quadratic constraints to derive a less conservative feasible solution. Sufficient conditions for the system's mean-square stability are established by employing the Lyapunov stability theory. Finally, a numerical simulation example is given to prove the conclusion's validity. [ABSTRACT FROM AUTHOR]

The issues of state estimations based on distributed observers for linear time-invariant (LTI) systems with multiple sensors are discussed in this paper. We deal with the scenario when the information exchange has known time delays, and aim at designing a distributed observer for each subsystem such that each distributed observer can estimate the system state asymptotically by rejecting the time delay. To begin with, by rewriting the target system in a connecting form, a subsystem which is affected by the time-delay states of other nodes is established. And then, for this subsystem, a distributed observer with time delay is constructed. Moreover, an equivalent state transformation is made for the observer error dynamic system based on the observable canonic decomposition theorem. Further, in order to ensure that the distributed observer error dynamic system is asymptotically stable even if there exists a time delay, a linear matrix inequality (LMI) which is relative to the Laplace matrix is elaborately set up, and a special Lyapunov function candidate based on the LMI is considered. Next, based on the Lyapunov function and Lyapunov stability theory, we prove that the error dynamic system of the distributed observer is asymptotically stable, and the observer gain is determined by a feasible solution of the LMI. Finally, a simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new 4 - D hyperchaotic system with a nonlinear term in the form of an exponential function. The system is derived from a modified 3 - D Lü system. Firstly, we discuss the qualitative properties of the proposed system, using tools such as hyperchaotic attractors, symmetry, dissipation, equilibrium points, and Lyapunov spectrum for analysis. Next, we present an adaptive controller for stability analysis of the system. An active controller is designed to achieve complete synchronization between two identical systems. All stability results are established using Lyapunov stability theory. Finally, numerical examples and computer simulations are provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper explored a delayed diffusive prey-predator model with prey-taxis involving the volume-filling mechanism subject to homogeneous Neumann boundary condition. To figure out the impact on the dynamic of the prey-predator model due to prey-taxis and time delay, we treated the prey-tactic coefficient χ and time delay τ as the bifurcating parameters and did stability and bifurcation analysis. It showed that the time delay will induce Hopf bifurcations in the absence of prey-taxis, and the bifurcation periodic solution at the first critical value of τ was spatially homogeneous. Hopf bifurcations occurred in the model when the prey-taxis and time delay coexisted, and at the first critical value of τ , spatially homogeneous or nonhomogeneous periodic solutions might emerge. It was also discovered that the bifurcation curves will intersect, which implied that Hopf-Hopf bifurcations can occur. Finally, we did numerical simulations to validate our outcomes. [ABSTRACT FROM AUTHOR]

This paper investigates the performance of Neural Network (NN) based PI Controller (NNC) and Fractional Order Sliding Mode Controller (FOSMC) for sensorless speed control of Interior Permanent Magnet Synchronous Motor (IPMSM). It proposed new method of NN based PI sensorless speed control based on offline learning using look up table obtained from analysis of the PI controller. The FOSMC was designed, analysed and its stability was guaranteed using Lyapunov stability theory to validate its higher performance. This paper proposes novel speed observer as low pass filter of motor currents and load torque in the time domain to increase the reliability of the closed loop system. Simulations results using MATLAB/SIMULINK proved the improved performance of the two controllers and the strong robust performance of FOSMC compared to Neural Network based PI sensorless speed Controller (NNC) against large ranges of uncertainties and external load disturbances in field-oriented Vector Control (VC) scheme. Analysis study of the effect of fractional order differentiator was presented to show that as its value decreases, the transient and steady state performance of the motor is improved. [ABSTRACT FROM AUTHOR]

In the present work, we developed a deterministic SHATR (Susceptible - HIV infected -AIDS infected - Antiretroviral Treatment - Recovered) compartment model for HIV/AIDS. This model considers the disease outbreak due to a lack of awareness and treatment. The steady states of the proposed model system are obtained and analyzed by using the nonlinear stability theory of differential equations. The basic reproduction number is derived and explored to determine the stability and sensitivity index of some important relative parameters. Further, to know the global behavior of the model one parameter bifurcation study is discussed. Moreover, the optimal control theory has been applied to identify the optimal strategy by taking treatment and awareness for safe intercourse as control parameters. The control problem is solved analytically by using Pontryagin's maximum principle. Finally, the model is simulated to describe the optimality under various assumptions and the stability of equilibrium points. [ABSTRACT FROM AUTHOR]

In this paper, we have delved into the intricate dynamics of a discrete-time Hepatitis B virus (HBV) model, shedding light on its local dynamics, topological classifications at equilibrium states, and pivotal epidemiological parameters such as the basic reproduction number. Our analysis extended to exploring convergence rates, control strategies, and bifurcation phenomena crucial for understanding the behavior of the HBV system. Employing linear stability theory, we meticulously examined the local dynamics of the HBV model, discerning various equilibrium states and their topological classifications. Subsequently, we identified bifurcation sets at these equilibrium points, providing insights into the system’s stability and potential transitions. Further, through the lens of bifurcation theory, we conducted a comprehensive bifurcation analysis, unraveling the intricate interplay of parameters that govern the HBV model’s behavior. Our investigation extended beyond traditional stability analysis to explore chaos and convergence rates, enriching our understanding of the dynamics of the understudied HBV model. Finally, we validated our theoretical findings through numerical simulations, confirming the robustness and applicability of our analysis in real-world scenarios. By integrating biological and epidemiological insights into our mathematical framework, we offered a holistic understanding of the dynamics of HBV transmission dynamics, with implications for public health interventions and disease control strategies. [ABSTRACT FROM AUTHOR]

Stoichiometric homeostasis is an important mechanism in maintaining ecosystem structure, function, and stability. Phyllostachys edulis (moso bamboo) is a typical clone plant, forming pure bamboo forests or bamboo–wood mixed forests by expanding rhizomes around. Studying the stoichiometric homeostasis characteristics of moso bamboo at different ages after expansion contributes to a deeper understanding of the stability of bamboo forest ecosystems, and is of great significance for expanding the research scope of ecological stoichiometry. Based on the stoichiometric internal stability theory, the nitrogen (N) and phosphorus (P) elements in the soil and plants of typical moso bamboo forests in Tianbaoyan National Nature Reserve of Fujian Province were determined, and the internal stability index (H) of bamboo leaves of different ages (I-du, II-du, III-du, and IV-du bamboos) was calculated. The results showed that the dependence of moso bamboo on soil nutrients and the ability of moso bamboo to regulate nutrient elements were both significantly affected by the plant's age. Under the condition of the same soil nutrients (N, P), the content of N and P in bamboo leaves decreased significantly with the increase in bamboo age. The limiting effect of phosphorus on the growth and development of moso bamboo was greater than that of nitrogen, and the limiting effect of phosphorus on aged bamboo was greater than that of young bamboo. The stoichiometric internal stability index of N and P in bamboo leaves is HN:P > HN > HP, which means that the internal stability of moso bamboo is closely related to the limiting elements. Therefore, the regulation ability of the internal stability of moso bamboo of different ages makes it grow well in the changeable environment, has stronger adaptability and competitiveness, and the leaf internal stability of I-du bamboo was higher than that of other ages, which may be one of the reasons for its successful expansion to form a stable bamboo stand structure. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with some of the theoretical aspects of equitable multi-objective optimization. By using the equitability preference structure, we discuss some properties of the equitably nondominated set, such as nonemptiness, external stability and connectedness. Also, we introduce the concept of proper equitable nondominance, and show that these solutions can be obtained by minimizing a weighted sum of the sort of objective functions where all weights are positive and decreasing. Moreover, we present a hybrid scalarization problem to generate equitably nondominated solutions. This method also provides a necessary condition for the existence of properly equitable nondominated solutions. [ABSTRACT FROM AUTHOR]

The ultra-high-speed aerodynamically alleviated marine vehicle (AAMV) is a high-performance vessel that combines a hydrodynamic configuration and an aerodynamic wing to reduce wave-making resistance during the high-speed planing phase. The forces of the AAMV exhibit strong nonlinear and water–air coupling characteristics, resulting in particularly complex motion characteristics. This paper presents a longitudinal and lateral stability model of the AAMV, which considers the effects of aerodynamic alleviation. Additionally, a numerical model of wind and wave turbulence forces is established, which considers viscous correction based on the potential theory. Finally, the effect of wind and wave turbulence forces on the motion stability of the AAMV under regular and irregular waves is analyzed by numerical solution. The simulation results demonstrate the influence of these disturbance forces on the stability of the AAMV under different sea states. The motion parameters of the AAMV exhibit a pronounced response to changes in sea state level. The aerodynamically alleviated effect is enhanced as speed increases, and the influence of winds and waves on the AAMV is greatly weakened, reducing the possibility of instability. During the cruising phase under class V sea state, the pitch, roll, and heave response are 0.210°, 0.0229°, and 0.0734 m, respectively. This effect can effectively improve the motion stability of the AAMV in winds and waves. [ABSTRACT FROM AUTHOR]

This article addresses the containment control issue for multi-AUV systems with the intervention of both external disturbance and input saturation. Firstly, a distributed estimator is established for the sake of acquiring precise estimation information of the desired position and its derivative for each follower AUV in the system. Next, on the basis of the proposed distributed estimator, a virtual control law is designed for each follower AUV. Then, due to the difficulty in obtaining accurate information about the derivative of the virtual control law, a linear tracking differentiator is introduced. Additionally, a disturbance observer is employed to tackle the composite disturbance, which mainly contains the internal model uncertainties and external bounded disturbances. Meanwhile, the issue of input saturation is handled by constructing the auxiliary system. Furthermore, a containment control law is designed with the assistance of the introduced linear tracking differentiator, the established disturbance observer, and the constructed auxiliary system. Additionally, the Lyapunov stability theory is applied to analyze the stability of the multi-AUV system. Finally, simulation results are given to confirm the feasibility of the proposed containment control scheme. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the stability analysis for a contaminant convection-reaction-diffusion model of the recovered fracturing fluid (RFFM, for short), which couples a nonlinear and non-smooth stationary incompressible Navier-Stokes equation with a multivalued frictional boundary condition, and a nonlinear reaction-diffusion equation with mixed Neumann boundary conditions. First, we introduce a family of perturbation problems corresponding to (RFFM), and present the variational formulation of perturbation problem which is a perturbation elliptic hemivariational inequality driven by a perturbation nonlinear variational equation. Then, the existence of solutions and the uniform bound of the solution set to the perturbation problem are obtained. Finally, it is established that, as the perturbation parameter tends to zero, the solution set of the perturbation problems converge to the solution set of (RFFM) in the sense of the Kuratowski upper limit. This shows that (RFFM) is stable with respect to the perturbation data. [ABSTRACT FROM AUTHOR]

We consider a Schrödinger equation with a nonlinearity which is a general perturbation of a power nonlinearity. We construct a profile decomposition adapted to this nonlinearity. We also prove global existence and scattering in a general defocusing setting, assuming that the critical Sobolev norm is bounded in the energy-supercritical case. This generalizes several previous works on double-power nonlinearities. [ABSTRACT FROM AUTHOR]

The fast finite-time output bipartite tracking of networked heterogeneous robotic systems with matrix-weighted digraphs, parametric uncertainties and external disturbances is studied in this article. Besides, solving the fast finite-time bipartite tracking problem in this paper implies that the system states are forced to reach the employed nonsingular finite-time sliding surface in a predefined time, which thus called fast finite-time control. To address the aforementioned issues, a fast finite time hierarchical control algorithm utilizing estimator methodologies are proposed. The Lyapunov stability theory is used to derive some sufficient requirements for performing output bipartite tracking in a fast finite time manner. To verify that the theoretical results are valid, numerical simulation examples are given. [ABSTRACT FROM AUTHOR]

Photovoltaic inverters are widely utilized in microgrid systems working as the key equipment for converting solar energy into usable electricity. This paper presents a fuzzy sliding mode control (FSMC) method for the photovoltaic inverter in a microgrid. The inverter module uses voltage control to achieve stable AC output voltage. Moreover, to deal with system uncertainty and non-linearity in the photovoltaic inverter, a fuzzy controller was designed to realize real-time adaptation of the gains of the constant term and the reaching term in the sliding mode control law, which serves as a compensating controller for traditional sliding mode control. The gains of the exponential reaching law can be adjusted according to the system state instead of fixed gains, which can effectively reduce the chattering phenomenon and improve the robustness of the photovoltaic microgrid. Finally, the Lyapunov stability theory was used to ensure the stability of the entire control system, achieving a high-performance independent power supply for loads in a microgrid. Simulation results show that the designed control system is more robust to load disturbances and has superior dynamic performance. [ABSTRACT FROM AUTHOR]

In this paper, a fractional‐order unified system with complex variables is proposed. Firstly, the basic properties of the system including the equilibrium points and symmetry are analyzed. Bifurcations of the system in commensurate‐order and incommensurate‐order cases are studied. Tangent and period‐doubling bifurcations can be observed when a derivative order or a parameter is varied. The stabilization the system is investigated via the predict feedback method. Based on the stability theory of fractional‐order systems, a projective synchronization for the fractional‐order unified complex system is proposed by designing an appropriate controller. Numerical simulations are applied to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This article proposes a new nonlinear processing method combined with model predictive control (MPC) to study the demagnetization vibration problem of permanent magnet synchronous motors (PMSMs). First, based on the theory of rotor dynamics, a demagnetized rotor vibration dynamics model considering the unbalanced magnetic pulling (UMP) caused by demagnetization of PMSM was constructed. Accurately modeling the nonlinear UMP function is difficult in practical engineering, thereby increasing the complexity of accurately constructing the parameters of the demagnetized rotor vibration dynamics model. Thus, this article innovatively constructs an empirical function model for UMP based on practical experience and then establishes a system observer model. Sufficient conditions are obtained for the system observer model based on Lyapunov stability theory to effectively observe the demagnetization vibration dynamics model. Then, an MPC scheme is proposed based on the constructed demagnetization vibration observer model. Finally, numerical simulation was conducted to verify the effectiveness of the system observer model in tracking the system model and predicting the effectiveness of system vibration control. [ABSTRACT FROM AUTHOR]

This paper presents a new control approach of trajectory tracking for quadrotor unmanned aerial vehicle (UAV) systems under external disturbances and parameter uncertainties. The integral fast terminal sliding mode control (IFTSMC) approach applying state-dependent Riccati equation (SDRE) observer is presented for this purpose. As a result, the nonlinear SDRE observer is designed to estimate the non-measurable states. Afterward, employing the estimated states of the SDRE observer, the proposed IFTSMC controller is designed for trajectory tracking of the perturbed quadrotor UAV. Besides, applying Lyapunov's stability theory, the finite-time convergence and robustness of the closed-loop UAV system are assured. Based on the numerical simulation results, the proposed controller successfully tracked various reference trajectories of quadrotor UAVs despite external disturbances and parametric uncertainty. [ABSTRACT FROM AUTHOR]

In this work, we are interested in studying bending, buckling stability, and dynamic behaviors of functionally graded nanobeams reinforced by carbon nanotubes (FG-CNTRC) by a novel shear deformation theory. This model is simple and efficient based on the new polynomial-exponential integral shear deformation theory including the effect of size taking into account the effects of the Winkler–Pasternak elastic foundations. The polynomial-exponential transverse shear function is incorporated to better represent a new displacement field that includes indeterminate integral terms. It is presumed that the material possessions of FG-CNTRC are diverse along the thickness direction employing distinct four distributions of carbon nanotubes (NT-CNTs). The nonlocal elasticity offered by Eringen is used to involve size effects in this approach. The impacts of numerous factors such as the volume fraction of CNTs, the nonlocality, and the impacts of the elastic foundation on the response of the FG-CNTRC beams are examined. [ABSTRACT FROM AUTHOR]

Currently, cranes used at sea are insufficient in efficiency. Accordingly, a floating multi-robot coordinated towing system is proposed to meet offshore towing needs. However, the towing robot is prone to overturning because of the system's utilization of rope-driven robot flexibility and its floating attributes in fluid environments. First, the kinematics and dynamics of the towing system are analyzed through coordinate transformations and hydrodynamic theory. Subsequently, physical modeling of the towing system is conducted, with an emphasis on analyzing the system's fluid-structure coupling properties, supplemented by illustrative examples. Finally, the stability of the floating robot is assessed based on ship stability theory, encompassing analyses of the rope tension effects, size and shape of the floating base, and external environmental factors influencing system stability. Results show that the special shape of the floating base is beneficial in reducing water resistance and improving the stability of the floating robot in the flow field. The results provide a good basis for the system structural design and application. [ABSTRACT FROM AUTHOR]

Lag consensus is an essential dynamic behavior in nature and practical systems, which means that the trajectory of followers lags behind the leader owing to a track time-delay. In this paper, the lag consensus problem under event-triggered control is investigated for leader-following multi-agent systems with nonlinear dynamics. A novel static event-triggered control strategy based on combined measurement is presented to avoid continuous information interaction between agents by introducing a track time-delay. It should be emphasized that this control protocol is fully distributed, that is, the global information in the network is not involved. In addition, for each agent, the information transmission and the updates of control protocol only arise at its own triggering instants. Based on stability theory, a sufficient condition is derived for leader-following multi-agent systems with nonlinear dynamics to achieve lag consensus. Moreover, it is exhibited that Zeno behavior is excluded by proving the existence of a positive lower bound for the triggering interval. Finally, the correctness of theoretical results is verified via numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of the SIR infectious disease model, with a specific emphasis on utilizing a harmonic mean-type incidence rate. It thoroughly analyzes the model's equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. A sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V-L) matrices, is developed to examine the overall trajectory of the model globally. In addition to that, we describe the transmission of infectious disease through a mathematical model using fractal-fractional differential operators. We prove the existence and uniqueness of solutions in the SIR model framework with a harmonic mean-type incidence rate by using the Banach contraction approach. Functional analysis is used together with the Ulam–Hyers (UH) stability approach to perform stability analysis. We simulate the numerical results by using a computational scheme with the help of MATLAB. This study advances our knowledge of the dynamics of epidemic dissemination and facilitates the development of disease prevention and mitigation tactics. [ABSTRACT FROM AUTHOR]

In multilayer complex networks, the uncertainty in node states leads to intricate behaviors. It is, therefore, of great importance to be able to estimate the states of target nodes in these systems, both for theoretical advancements and practical applications. This paper introduces a state observer-based approach for the state estimation of such networks, focusing specifically on a class of complex dynamic networks with nodes that correspond one-to-one. Initially, a chaotic system is employed to model the dynamics of each node and highlight the essential state components for analysis and derivation. A network state observer is then constructed using a unique diagonal matrix, which underpins the driver and response-layer networks. By integrating control theory and stability function analysis, the effectiveness of the observer in achieving synchronization between complex dynamic networks and target systems is confirmed. Additionally, the efficacy and precision of the proposed method are validated through simulation. [ABSTRACT FROM AUTHOR]

This paper is devoted to dealing with the issue of the estimation of the domain of attraction (DOA) for highly nonlinear neutral complex networks (HNNCNs) with time delays. Firstly, by the Razumikhin approach, we establish several novel lemmas on the estimation of DOA for highly nonlinear neutral differential systems. The cases of bounded non-differentiable delays and unbounded proportional delays are discussed, respectively. Subsequently, by utilizing the proposed lemmas, combining the Lyapunov stability theory and inequality technique, the estimation of DOA on HNNCNs with bounded delays or proportional delays is derived when the chosen control gain is sufficiently large. If initial values start from DOA, then the states of systems will exponentially or polynomially converge to the equilibrium point, which means that the local exponential or polynomial synchronization of HNNCNs is realized. Additionally, the weighted outer-coupling matrix of complex networks is not required to be symmetric, which means that the derived results can be applied to both the undirected networks and directed networks. Finally, several numerical examples are provided to illustrate the feasibility of theoretical findings. [ABSTRACT FROM AUTHOR]

Due to the Jacobian matrix rank reduction near singularities, applying numerical methods to study PMs' motion stability at singularities is quite difficult. As a result, there is a scarcity of literature on the investigation of PMs' dynamic behaviors near singularities and the influence of kinematic parameters on the motion stability of PMs. To address the research gap related to the above issues, based on the Gerschgorin perturbation method, Hurwitz exact approach, and the Lyapunov dynamic stability theory, the influence of kinematic parameters and external loads on a PM's motion stability at singularities is studied for the first time. The theoretical analysis results reported in this paper reveal many previously undiscovered features beyond those derived from previous numerical methods, and indicate the limitations of some widely accepted statements. For example, increasing the angular speed of the movable platform can expand the range of the external loads that meet the motion stability at singular configurations. The prevailing notion in prior research that PMs are unable to support external loads in the direction of the gained DoF at singular configurations is only partially accurate. This pioneering research establishes a theoretical foundation for exploring a new real-time approach to avoid dynamic singularities by fully exploiting the influence mechanisms of kinematic parameters on PMs' dynamic stability at singularities. [ABSTRACT FROM AUTHOR]