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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]

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]

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]

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]

We focus on fault-tolerant consensus for heterogeneous dynamics systems with static and dynamic leaders under input saturation in this article. We apply theory of finite-time stability to multiagent system cooperative control. Also, we use integral sliding mode to overcome disturbance. The primary goal is a set of second-order linear and second-order nonlinear agents moving along the leader's trajectory. We use topology graph to describe communication between multiple agents. By using integral sliding mode control way, corresponding controller is introduced to make system stable. Finally, correctness of experiment was confirmed by MATLAB numerical simulation. [ABSTRACT FROM AUTHOR]

Aiming at the problems of slow convergence speed and low tracking accuracy in attitude control and position tracking of quadrotor unmanned aerial vehicles (UAVs). This paper combines the fractional-order calculus theory with the backstepping sliding mode control algorithm, using the backstepping control to compensate for the nonlinearity of the system and the fractional-order theory to eliminate the jitter brought about by the sliding mode control, and proposes a new fractional-order backstepping sliding mode control strategy for the trajectory tracking control of the quadrotor UAV. The proposed fractional-order sliding mode surface increases the control flexibility and improves the robustness and anti-interference ability of the system to some extent. The stability analysis of the system is carried out using the Lyapunov stability theory, and the results prove the stability of the proposed controller. Finally, the effectiveness and feasibility of the proposed method are verified by comparing it with the traditional backstepping sliding mode controller. The simulation results show that the fractional-order reverse-step sliding mode control algorithm proposed in this paper is significantly better than other control algorithms in terms of convergence speed and also has a certain degree of superiority in terms of error elimination. [ABSTRACT FROM AUTHOR]

The equations for the critical height of layered slope were derived by a related researcher, but they lack details and do not agree with the method of limit equilibrium. So this topic was reinvestigated. Considering the possible global or local failure modes of the layered slope, the equations for the critical height of the above modes are derived based on the upper limit theorem by using rotational failure mechanisms or rotational and translational failure mechanisms. Based on the above theory, the stability coefficients of layered slope are investigated. The results show that the presented upper bound approach has better performance than other methods mentioned in the literature and is consistent with the limit equilibrium method. In combination with the strength reduction method, the global and local stability of the layered slope are analyzed using the several examples. The high-calculation accuracy of presented method and the specific measures to improve the smoothness of the sliding surface are reviewed. From the perspective of the combination of sliding surfaces, the dimensionless parameter vector of the layered slope is introduced. The possible limitations of the upper bound limit approach with log spirals are pointed out and the conditions which must be fulfilled in order to achieve a higher computational accuracy are mentioned. [ABSTRACT FROM AUTHOR]

In synchronous machines, electromechanical swinging can be damped by parametric control of the excitation current. This is possible only in case the excitation time constant is much smaller than the mechanical constant of the machine. The method described in this paper is effective for damping oscillations caused by oscillations in the grid frequency, grid voltage, and mechanical torque fluctuations. The method is based on the Lyapunov stability theory and demonstrated on a real synchronous machine. This machine operates as a noninterruptible backup power system. The original power fluctuations were up to 50% of the nominal power of the machine. With the described control, a sevenfold increase in the damping of fluctuations caused by grid frequency variations has been achieved. [ABSTRACT FROM AUTHOR]

This document proposes a control scheme applied to delayed bilateral teleoperation of the forward and turn speed of a biped robot against asymmetric and time-varying delays. This biped robot is modeled as a hybrid dynamic system because it behaves as a continuous system when the leg moves forward and discrete when the foot touches the ground generating an impulsive response. It is proposed to vary online the damping according to the time delay present in the communication channel, and the walking cycle time using an optimization criterion, to decrease the teleoperation system errors. To accomplish this, a three-phase cascade calibration process is used, and their benefits are evidenced in a comparative simulation study. The first phase is an offline calibration of the inverse dynamic compensation and also the parameters of the bilateral controller. The second phase guarantees the bilateral coordination of the delayed teleoperation system, using the Lyapunov–Krasovskii stability theory, by changing the leader damping and the equivalent follower damping together. The third phase assures a stable walk of the hybrid dynamics by controlling the walking cycle time and the real damping to move the eigenvalues of the Poincaré map, numerically computed, to stable limit cycles and link this result with an equivalent continuous system to join both phases. Additionally, a fictitious force was implemented to detect and avoid possible collisions with obstacles. Finally, an intercontinental teleoperation experiment of an NAO robot via the Internet including force and visual feedback is shown. [ABSTRACT FROM AUTHOR]

In this study, a very crucial stage of HIV extinction and invisibility stages are considered and a modified mathematical model is developed to describe the dynamics of infection. Moreover, the basic reproduction number R 0 is computed using the next-generation matrix method whereas the stability of disease-free equilibrium is investigated using the eigenvalue matrix stability theory. Furthermore, if R 0 ≤ 1 , the disease-free equilibrium is stable both locally and globally whereas if R 0 > 1 , based on the forward bifurcation behavior, the endemic equilibrium is locally and globally asymptotically stable. Particularly, at the critical point R 0 = 1 , the model exhibits forward bifurcation behavior. On the other hand, the optimal control problem is constructed and Pontryagin's maximum principle is applied to form an optimality system. Further, forward fourth-order Runge–Kutta's method is applied to obtain the solution of state variables whereas Runge–Kutta's fourth-order backward sweep method is applied to obtain solution of adjoint variables. Finally, three control strategies are considered and a cost-effective analysis is performed to identify the better strategies for HIV transmission and progression. In advance, prevention control measure is identified to be the better strategy over treatment control if applied earlier and effectively. Additionally, MATLAB simulations were performed to describe the population's dynamic behavior. [ABSTRACT FROM AUTHOR]

The electro-hydraulic servo system is widely used in industrial automation fields for its merits of the high force to weight ratio, compact size, and fast response. However, the parameter uncertainties and external disturbances of the electro-hydraulic servo system significantly deteriorate the control performance of conventional linear controller in practice. To deal with this problem, sliding mode controller (SMC) that incorporates high gain observer (HGO) is proposed in this paper. HGO is used to obtain the accurate time derivative of position signal for sliding mode controller design. The stability of the control system is guaranteed by Lyapunov stability theory. Comparation simulation is conducted to validate the effectiveness of the presented control scheme. [ABSTRACT FROM AUTHOR]

The traditional design method for narrow foundation pits ignores size effects. Engineering practice shows that this is too conservative and causes large-scale waste. In this study, with the help of ABAQUS finite element software, retaining-structure models in semi-infinite and infinite elastic space are used to simulate the mechanical performances of pile-supported structures under different combinations of excavation depth, retaining pile-embedded depth, and excavation width. Furthermore, based on antioverturning stability theory and circular slip theory, the intrinsic relationship among these variables and their effects on the stability of excavation is analysed. Finally, based on the restraint effect of retaining structures on the soil below the pit bottom under actual working conditions, critical width is determined and used to classify foundation pits. Moreover, the applicability of existing codes is discussed. These results can improve the design and construction of narrow excavations, benefitting the construction industry and society in general. [ABSTRACT FROM AUTHOR]

A novel composite terminal guidance law with impact angle constraints is proposed for supercavitating torpedoes to intercept maneuvering warships. Based on an adaptive super-twisting algorithm and nonsingular terminal sliding mode (NTSM), the proposed guidance law can guarantee the finite-time convergence of line-of-sight (LOS) angle error and the LOS angular rate error. The new guidance law is a combination of finite-time stability theory, sliding mode control (SMC), tracking differentiator (TD), disturbance observer (DO), and dynamic surface control. A high-order sliding mode TD is used for denoising, tracking, and differentiating the measured target heading angle. A novel DO, with its finite-time stability proved, is designed to estimate the target lateral acceleration for feedforward compensation to attenuate chattering in control input. In the case of a first-order-lag autopilot, a new kind of tracking differentiator is adopted to compute the first-order time derivative of the virtual control command, which can improve the accuracy of dynamic surface control and avoid the "explosion of items" problem encountered with the backstepping control. Finally, numerical simulation results are presented to validate the effectiveness and superiority of the proposed TD, DO, and the composite guidance law. [ABSTRACT FROM AUTHOR]

The state estimation problem is a very important and interesting issue in the field of complex dynamical networks. Yet, the constructions of the state estimators in most existing literature studies all need to measure the output information of all nodes. However, the practical situation is that not all nodes could be measured to obtain the output information. Thus, in this paper, the state estimation is realized while only measuring the output data of partial nodes for a complex dynamical network with random data loss existing on its external communication links to the observers, where the lost data are compensated by the corresponding observer data. Depending on whether the network possesses the root strongly connected components that have a perfect matching, the choice problem of measured nodes and the construction problem of specific output matrices are discussed. By applying the Lyapunov stability theory and stochastic analysis method, a sufficient condition for state estimation is given. Through simulation experiments, the effectiveness of the proposed state estimation scheme is demonstrated. [ABSTRACT FROM AUTHOR]

In order to solve the coarse alignment problem of the strapdown inertial navigation system on a rocking base, a fast coarse alignment method using the Special Orthogonal Group optimization has been proposed in this paper. In this method, based on the alignment idea of tracing gravitational apparent motion in inertial frame, the model of coarse alignment on a rocking base has been established using the Special Orthogonal Group directly. A new attitude error function has been proposed on the basis of the cosines between the measurement vector and predictive vector to describe the error between the estimated attitude and the true one. In order to directly reflect the change in the attitude error in the new innovation term and enable the attitude error to converge to zero as fast as possible, the gradient of the new attitude error function has been selected as the new innovation term to compensate for the attitude in the estimation process. Finally, the stability of the proposed optimization estimation method has been proved by employing the Lyapunov stability theory. Simulation and experiment results show that the method presented in this paper exhibits good performance in terms of alignment accuracy and time and can be applied to coarse alignment under a rocking base under different environments. [ABSTRACT FROM AUTHOR]

For a class of uncertain continuously networked Lurie control systems with both sensor-to-controller time-delay and controller-to-actuator time-delay, the problem of codesigning its observer and fault-tolerant controller based on an event-triggered mechanism under actuator failure is investigated. Firstly, considering that the state of the system cannot be measured directly, an observer is constructed on the controller node. Secondly, to reduce the waste of network bandwidth resources and improve the performance of the network control system, a network control system approach based on event-triggered mechanism is proposed. By introducing the event-triggered mechanism and the actuator fault indication matrix, the Lurie networked control system is modeled as a Lurie system with time-delay using the state augmentation technique to obtain a model of the closed-loop system. Finally, based on Lyapunov stability theory, sufficient condition for the stability of the closed-loop system is obtained, and the design method of the fault-tolerant controller and the observer is given. The obtained results are given in the form of linear matrix inequalities, which are easy to be solved by using the linear matrix inequality toolbox. Finally, the feasibility and effectiveness of the method are illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

The local dynamics, chaos, and bifurcations of a discrete Brusselator system are investigated. It is shown that a discrete Brusselator system has an interior fixed point P 1 , r if r > 0. Then, by linear stability theory, local dynamical characteristics are explored at interior fixed point P 1 , r . Furthermore, for the discrete Brusselator system, the existence of periodic points is investigated. The existence of bifurcations around an interior fixed point is also investigated and proved that the discrete Brusselator model undergoes hopf and flip bifurcations if r , h ∈ ℋℬ | P 1 , r = r , h , h = 2 − r and r , h ∈ ℱℬ | P 1 , r = r , h , h = 4 / 2 − r − r 2 − 4 r , respectively. The next feedback control method is utilized to stabilize the chaos that exists in the discrete Brusselator system. Finally, obtained results are verified numerically. [ABSTRACT FROM AUTHOR]

A new fixed-time fuzzy adaptive fault-tolerant control methodology is proposed for the longitudinal dynamics of hypersonic flight vehicles (HFVs) in the presence of actuator faults, uncertain dynamics, and external disturbances. In contrast with the conventional fixed-time control schemes that typically contain the fractional powers of errors in their designs, this work develops a low-complexity control structure in the sense of removing the dependence on the need of abovementioned fractional power terms by means of prescribed performance control (PPC) method. Different from the most existing PPC approaches where the initial conditions of tracking errors are required to be known, the newly proposed prescribed performance function (PPF) can relax such restrictions through choosing properly small initial values of PPF. Fuzzy logic systems (FLSs) are employed to handle unknown dynamics, and minimal learning parameter (MLP) technique is incorporated into the design for the purpose of alleviating computation burden. Closed-loop stability is rigorously proved via Lyapunov stability theory, and simulation results are eventually given to validate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the finite difference scheme of the spatiotemporal fractional convection-diffusion equation is established, and its stability and convergence are proved. Furthermore, this discrete technique is extended to solve nonlinear spatiotemporal fractional convection-diffusion equations. By using the Krylov subspace method to solve the discrete system, the numerical solution of the spatiotemporal fractional convection-diffusion equation can be obtained quickly. In this paper, an efficient optimal control algorithm is proposed to solve the free control problem of a class of nonlinear time-delay systems. We obtained the optimal control law of the system through the Bellman optimality principle, obtained the asymptotic stability criterion of the system in the form of LMI under the optimal control input by using the Lyapunov stability theory, and discussed the effect of the delay parameter on the system stability. Using the principle of intelligent neural network approximation function, the evaluation neural network and the execution neural network are used to approximate the optimal performance index function and optimal control input, respectively, the optimal control strategy of the system is obtained, and the convergence of the weight estimation error is proved to be optimal. On the basis of optimal state adjustment, the optimal tracking control problem is further solved. Numerical example results verify the effectiveness of the proposed method in terms of stability analysis, optimal state control, and optimal tracking control for the nonlinear time-delay system proposed in this paper. We calculate the parameters of the conveyor and select a reasonable transmission and sorting mechanism to realize the speed regulation of the driving motor of each mechanism. Through the work of each part, the design scheme of the automatic transmission system is formed, and the reliability, practicability, and economy of the system are guaranteed. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential synchronization of complex dynamical networks based on the sampled-data control method. The sampled-data control means that the control input remains unchanged for a long time after each sampling, which can reduce the sampling number. By using the stability theory of the dynamical systems, this paper provides a novel sampling controller and estimates the bound of the sampling interval. Finally, a numerical example is given to demonstrate the effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]

In this paper, a general criterion for unidirectionally coupled generalized chaotic synchronization between the response system and the original chaotic system in the form of a desired manifold is presented. The expression of the response system constructed with linear error feedback is given, and the validity of the criterion is proved based on the Lyapunov stability theory. Two numerical examples are used to construct unidirectional coupled chaotic systems in the form of different types of manifolds. Numerical simulation is carried out to verify the feasibility of the construction method and the criterion. [ABSTRACT FROM AUTHOR]

This paper deals with the function projective synchronization of two complex dynamic networks with unknown sector nonlinear input, multiple time-varying delay couplings, model uncertainty, and external interferences. Based on Lyapunov stability theory and inequality transformation method, the robust adaptive synchronization controller is designed, by which the drive and response systems can achieve synchronization according to the function scaling factor. Different from some existing studies on nonlinear system with sector nonlinear input, this paper studies the synchronization of two complex dynamic networks when the boundary of sector nonlinear input is unknown. The controller does not include the boundary value of the sector nonlinear input and the time delay term, so it is more practical and relatively easy to implement. The corresponding simulation examples demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a fixed-time convergence-integrated guidance and control (IGC) method is proposed, which considers terminal line-of-sight (LOS) angle constraint, full-state constraints, and input saturation. Firstly, an IGC design model considering the full coupling of three channels is constructed, and a fixed-time convergence disturbance observer is used to estimate and compensate the unknown disturbances in the model. Secondly, based on the fixed-time stability theory, sliding mode control, and backstepping control, a novel IGC scheme is carried out, and the second-order instruction filter is used to restrict the system states and control instructions. Furthermore, the fixed-time stability of the close-loop system is proved and the expression of convergence time upper bound is given. Finally, comparison simulation and Monte Carlo simulation verify the effectiveness and superiority of the proposed IGC algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time synchronization problem of a class of fuzzy neural networks with hybrid delays and uncertain nonlinear perturbations. By applying the famous finite-time stability theory, combining differential inequality techniques, and the analysis approach, several new algebraic sufficient criteria are obtained to realize finite-time synchronization between the drive system and the response system by designing a state feedback controller and an adaptive controller. Taking discrete delays, distributed delays, and uncertain nonlinear perturbations into account in fuzzy cellular neural networks makes the neural system more general than most existing cellular neural networks. Two different novel types of controllers designed to achieve finite-time synchronization can not only effectively overcome the influence of time delays and perturbations but also change their form according to the change of system state or perturbation to achieve a better control effect. Meanwhile, some algebraic sufficient criteria obtained in this paper can be proved by the parameters of the system itself, and the complex calculation of matrix inequality is avoided. Finally, the validity of our proposed results is confirmed by several examples and simulations. Furthermore, a secure communication problem is presented to further illustrate the fact of the obtained results. [ABSTRACT FROM AUTHOR]

In the biological neural bursting and firing synchronization plays a vital role in all neuronal activities that are utilized for making decisions, executing commands, and sending information by neurons and their complex networks in the biological complexed brain. Understanding how the biological brain functionality comes out from different patterns of neuronal transmission between the large group of neural networks stands as one of the enduring challenges of modern neuroscience. This study investigated a methodology for synchronization of multiple single/dual state gap junctions FitzHugh-Nagumo (FHN) drive and slave networks under the condition of external noise. The theory of control was utilized to propose simple and diverse controllers to examine the synchronization problem of the different single and dual state gap junctions coupled nonnoisy and noisy FHN neurobiological drive and slave networks. Control laws are designed to stabilize the error dynamics without direct cancelation and synchronize all the states of both FHN neurobiological drive and slave networks. Sufficient conditions for achieving synchronization in the multiple single/dual state gap junction FHN noisy and nonnoisy neurobiological drive and slave networks were derived analytically using the theory of Lyapunov stability. Furthermore, the proposed controllers have been verified by using five noisy/nonnoisy FHN neurobiological drive and slave networks through numerical simulations. [ABSTRACT FROM AUTHOR]

In the terminal guidance phase of intercepting aerial target, a guidance law, satisfying impact angle constraint, acceleration constraint, and second-order dynamic characteristic of interceptor autopilot, is designed based on the prescribed performance control and dynamic surface control method. Firstly, a two-dimensional plane interception model considering the dynamic characteristics of autopilot and input constraints is established. Furthermore, for the nonconstrained system, based on the dynamic surface control, the prescribed performance reaching law is used to ensure that the line-of-sight angle and the line-of-sight angle rate can converge to the prescribed range in finite time. At the same time, an adaptive law is used to estimate the uncertainty caused by target maneuver and autopilot. Then, aiming at the acceleration constraint, an auxiliary system is established to convert the restricted system into a nonrestricted system. The finite-time convergence of the terminal line-of-sight tracking error, the line-of-sight rate, and the uniform ultimate boundedness of the system are rigorously proved by Lyapunov stability theory. Finally, the simulation results show that the proposed guidance law can make the interceptor have better interception performance when attacking targets with different maneuvering forms. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for synchronizing noisy and nonnoisy multiple coupled neurobiological FitzHugh–Nagumo (FHN) drive and slave neural networks with and without delayed coupling, under external electrical stimulation (EES), external disturbance, and variable parameters for each state of both FHN networks. Each network of neurons was configured by considering all aspects of real neurons communications in the brain, i.e., synapse and gap junctions. Novel adaptive control laws were developed and proposed that guarantee the synchronization of FHN neural networks in different configurations. The Lyapunov stability theory was utilized to analytically derive the sufficient conditions that ensure the synchronization of the FHN networks. The effectiveness and robustness of the proposed control laws were shown through different numerical simulations. [ABSTRACT FROM AUTHOR]

A diffusive predator-prey system with both the additive Allee effect and the fear effect in the prey subject to Neumann boundary conditions is considered in this paper. Firstly, non-negative and non-trivial solution a priori estimations are shown. Furthermore, for specific parameter ranges, the absence of non-constant positive solutions is demonstrated. Secondly, we use the linearized theory to investigate the stability of non-negative constant solutions. The spatially homogeneous and non-homogeneous periodic solutions, as well as non-constant steady state solutions, are next investigated by using Allee effect parameters as the bifurcation parameter. Finally, numerical simulation is used to illustrate some theoretical results. [ABSTRACT FROM AUTHOR]

The finite-time pinning synchronization control problem is studied for coupled complex networks with time-varying delays. Based on the finite-time stability theorem, a finite-time tractive synchronous controller is designed. In addition, the selection process of tractive nodes is developed to control as few nodes as possible such that all nodes are synchronized in the network in finite time. At the same time, sufficient conditions of the finite-time constraint synchronization of the drive-response network are obtained using the Lyapunov stability theory and the matrix inequality method. The effectiveness of the proposed controller is verified by numerical simulation. This approach can be applied to large-scale complex networks with time-varying delays. [ABSTRACT FROM AUTHOR]

Differential equations with fractional derivative are being extensively used in the modelling of the transmission of many infective diseases like HIV, Ebola, and COVID-19. Analytical solutions are unreachable for a wide range of such kind of equations. Stability theory in the sense of Ulam is essential as it provides approximate analytical solutions. In this article, we utilize some fixed point theorem (FPT) to investigate the stability of fractional neutral integrodifferential equations with delay in the sense of Ulam-Hyers-Rassias (UHR). This work is a generalized version of recent interesting works. Finally, two examples are given to prove the applicability of our results. [ABSTRACT FROM AUTHOR]

Aimed at the flight control problem of a near-space vehicle (NSV) with uncertainties such as parameter perturbation and external disturbance, a novel dynamic surface control (DSC) method with high-order linear extended state observer (HLESO) compensation is proposed in this paper. In the proposed method, a tracking differentiator (TD) based on an inverse hyperbolic sine function is firstly designed, and the convergence of TD is also analysed with the Lyapunov stability theory. Furthermore, the numerical simulations are detailed to demonstrate the superiority of the proposed TD compared with others. Then, a dynamic surface controller based on the traditional backstepping control technique is designed, where the TD is adopted to obtain the differential signal of the virtual control law, in order to solve the "differential expansion," and the HLESO is adopted to accurately estimate the "lumped disturbance" so as to realize the dynamic compensation of the controller and enhance the disturbance suppression ability of the system. The simulation results demonstrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Recently, to balance the increased electricity demands and total generated power, the multiarea power system (MAPS) has been introduced with multipower sources such as gas, nuclear, hydro, and thermal, which will impact the load frequency control (LFC). Therefore, the LFC of the two-area gas-hydro-thermal power system (TAGHTPS) is introduced by applying the single-phase sliding mode control-based state observer (SPSMCBSO). In this scheme, the TAGHTPS is the first model that considers the uncertainties of the parameters in the state and the interconnected matrix. Second, the state observer is employed to estimate the state variables for the feedback control. Third, the SPSMCBSO is developed to modify the basic sliding mode control to improve the performance of TAGHTPS in terms of overshoot and settling time. In addition, the SPSMCBSO is established to rely fully on the state observer so that the difficulty in the state variable measurement is solved. Fourth, the TAGHTPS stability analysis is performed using a new linear matrix inequality (LMI) scheme—Lyapunov stability theory. Lastly, the simulation results are shown and compared to recently established classical control methods to validate the SPSMCBSO choice of application for the LFC of the multiarea multisource power system (MAMSPS). [ABSTRACT FROM AUTHOR]

This research paper is devoted to investigating two classes of boundary value problems for nonlinear Atangana–Baleanu-type fractional differential equations with Atangana–Baleanu fractional integral conditions. The applied fractional derivatives work as the nonlocal and nonsingular kernel. Upon using Krasnoselskii's and Banach's fixed point techniques, we establish the existence and uniqueness of solutions for proposed problems. Moreover, the Ulam–Hyers stability theory is constructed by using nonlinear analysis. Eventually, we provide two interesting examples to illustrate the effectiveness of our acquired results. [ABSTRACT FROM AUTHOR]

This study addresses the observer-based proportional-integral-derivative (PID) security control problem for nonlinear discrete-time fuzzy systems subject to deception attacks. In order to reduce the burden of communication, a distributed dynamic event-triggered mechanism (DETM) is proposed, and each sensor node is equipped with an event-trigger generator. A new discrete-time Takagi–Sugeno (T-S) fuzzy model is established, in which both DETM and deception attacks are taken into consideration. Then, based on Lyapunov stability theory, the sufficient conditions for the input-to-state stability (ISS) are proposed, and the desired fuzzy PID controllers are given. Finally, a simulation example is provided to show the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

Fractional derivatives are used to model the transmission of many real world problems like COVID-19. It is always hard to find analytical solutions for such models. Thus, approximate solutions are of interest in many interesting applications. Stability theory introduces such approximate solutions using some conditions. This article is devoted to the investigation of the stability of nonlinear differential equations with Riemann-Liouville fractional derivative. We employed a version of Banach fixed point theory to study the stability in the sense of Ulam-Hyers-Rassias (UHR). In the end, we provide a couple of examples to illustrate our results. In this way, we extend several earlier outcomes. [ABSTRACT FROM AUTHOR]

In recent years, the technology of Internet of Vehicles has developed rapidly, among which vehicle to everything (V2X) technology is provided with a quite important promotion value in the intelligent transportation field. In V2X environment, the driver can receive real-time information of the motion status of adjacent vehicles and the signal duration of the intersection, and take the decision-making action of manipulating the vehicle in advance, which has a certain impact on the evolution process of queue dissipation. This paper studies the improved OV model based on V2X environment and considering the driver's early response time selects the intersection queue dissipation efficiency as the index to analyze the intersection traffic efficiency and studies the impact of different initial headway, maximum speed, and safety distance on the intersection traffic flow. The simulation results show that compared with the traditional OV model and the OV model considering driver's reaction delay, the model proposed in this paper greatly improves the efficiency of traffic flow recovery after green light, so the model proposed in this paper can promote the stability of traffic flow. The linear stability of the proposed model was analyzed by using the linear stability theory to obtain the stability conditions of the improved model. Furthermore, a simulation environment was established to analyze the vehicle queue dissipation at intersections and to simulate the improved V2X car-following model as well as the platoon dissipation state under different traffic parameters. The research results show that vehicle drivers can obtain traffic flow operation status in real-time through V2X equipment and change the operation of the vehicle itself in a targeted manner, which can significantly improve the safety and stability of traffic flow operation, and greatly raise the dissipation efficiency of the platoon. The method proposed in this paper can increase the queue dissipation rate and shorten the recovery time of the traffic system, respectively. [ABSTRACT FROM AUTHOR]

This study focuses on hybrid synchronization, a new synchronization phenomenon in which one element of the system is synced with another part of the system that is not allowing full synchronization and nonsynchronization to coexist in the system. When lim t ⟶ ∞ Y − α X = 0 , where Y and X are the state vectors of the drive and response systems, respectively, and Wan (α = ∓ 1)), the two systems' hybrid synchronization phenomena are realized mathematically. Nonlinear control is used to create four alternative error stabilization controllers that are based on two basic tools: Lyapunov stability theory and the linearization approach. [ABSTRACT FROM AUTHOR]

With the aim to improve the antidisturbance ability of the islanded distributed energy resource (DER) systems, a disturbance-observer-based adaptive fuzzy sliding mode control (DAFSC) voltage controller is designed based on indirect vector control, which implements the voltage tracking and improves the self-regulation ability of the islanded DER systems. Firstly, the circuit diagram and the mathematical model of the DER system are presented. Then, the second-order sliding mode differentiator is designed to solve the problem of calculation expansion in the backstepping control method. To solve the influence of lumped disturbance on the system, a disturbance-observer is proposed to observe the unknown disturbance and compensate the controller feed-forward. Moreover, fuzzy control is proposed to reduce the dependence of the control effect on model accuracy. Finally, the stability of the controller is verified by Lyapunov stability theory, and the hardware in the loop results is given to verify that the control effect of the proposed DAFC controller has better dynamic performance compared with proportion-integral (PI) and the backstepping control strategy. [ABSTRACT FROM AUTHOR]

Compared with previous studies, this paper focuses on the time delay phenomenon in the consensus state between the leader and followers and considers that the DoS attack occurs nonperiodically. First, a new event-triggered mechanism and lag consensus control strategy are proposed. Then, through the Lyapunov stability theory, algebraic knowledge, and graph theory, it is proved that followers and leader can achieve lag consistent under the DoS attack, and the trigger interval is designed to ensure that Zeno behavior does not occur. Finally, the correctness and effectiveness of the proposed theory and method are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

In this study, a novel 7D hyperchaotic model is constructed from the 6D Lorenz model via the nonlinear feedback control technique. The proposed model has an only unstable origin point. Thus, it is categorized as a model with self-excited attractors. And it has seven equations which include 19 terms, four of which are quadratic nonlinearities. Various important features of the novel model are analyzed, including equilibria points, stability, and Lyapunov exponents. The numerical simulation shows that the new class exhibits dynamical behaviors such as chaotic and hyperchaotic. This paper also presents the hybrid synchronization for a novel model via Lyapunov stability theory. [ABSTRACT FROM AUTHOR]

Chaotic systems are one of the most significant systems of the technological period because their qualities must be updated on a regular basis in order for the speed of security and information transfer to rise, as well as the system's stability. The purpose of this research is to look at the special features of the nine-dimensional, difficult, and highly nonlinear hyperchaotic model, with a particular focus on synchronization. Furthermore, several criteria for such models have been examined; Hamiltonian, synchronizing, Lyapunov expansions, and stability are some of the terms used. The geometrical requirements, which play an important part in the analysis of dynamic systems, are also included in this research due to their importance. The synchronization and control of complicated networks' most nonlinear control is important to use and is based on two major techniques. The linearization approach and the Lyapunov stability theory are the foundation for attaining system synchronization in these two ways. [ABSTRACT FROM AUTHOR]

Given the resolution of the guidance for intercepting highly maneuvering targets, a novel finite-time convergent guidance law is proposed, which takes the following conditions into consideration, including the impact angle constraint, the guidance command input saturation constraint, and the autopilot second-order dynamic characteristics. Firstly, based on the nonsingular terminal sliding mode control theory, a finite-time convergent nonsingular terminal sliding mode surface is designed. On the back of the backstepping control method, the virtual control law appears. A nonlinear first-order filter is constructed so as to address the "differential expansion" problem in traditional backstepping control. By designing an adaptive auxiliary system, the guidance command input saturation problem is dealt with. The RBF neural network disturbance observer is used for estimating the unknown boundary external disturbances of the guidance system caused by the target acceleration. The parameters of the RBF neural network are adjusted online in real time, for the purpose of improving the estimation accuracy of the RBF neural network disturbance observer and accelerating its convergence characteristics. At the same time, an adaptive law is designed to compensate the estimation error of the RBF neural network disturbance observer. Then, the Lyapunov stability theory is used to prove the finite-time stability of the guidance law. Finally, numerical simulations verify the effectiveness and superiority of the proposed guidance law. [ABSTRACT FROM AUTHOR]

Considering recurrent optimization process in model predictive control (MPC), the model uncertainties and disturbances terms in the missile's guidance and control model can degrade recursive feasibility, and there are control mutation problems in common MPC algorithm. This paper presents a disturbance rejection model predictive control algorithm for missile integrated guidance and control (IGC). Firstly, a sliding mode observer (SMDO) is designed to estimate the unknown disturbances caused by target maneuvering. Secondly, the method of optimizing control increment is adopted in MPC to avoid the phenomenon of control mutation in the model calculation. By limiting the control increment in each cycle, it ensures the continuity of the control input. Thirdly, by combining the SMDO and MPC, an IGC algorithm is presented, and the stability of the algorithm is proved by using Lyapunov stability theory. Finally, the simulation results with different impact angles verify the effectiveness of the proposed algorithm for intercepting maneuver target. [ABSTRACT FROM AUTHOR]

In this paper, the inherent stability problem for multibody systems with variable-stiffness springs (VSSs) is studied. Since multibody systems with VSSs may consume energy during the variation of stiffness, the inherent stability is not always ensured. The motivation of this paper is to present sufficient conditions that ensure the inherent stability of multibody systems with VSSs. The absolute stability theory is adopted, and N-degree-of-freedom (DOF) systems with VSSs are formulated as a Lur'e form. Furthermore, based on the circle criterion, sufficient conditions for the inherent stability of the systems are obtained. In order to verify these conditions, both frequency-domain and time-domain numerical simulations are conducted for several typical low-DOF systems. [ABSTRACT FROM AUTHOR]

The local behavior with topological classifications, bifurcation analysis, chaos control, boundedness, and global attractivity of the discrete-time Kolmogorov model with piecewise-constant argument are investigated. It is explored that Kolmogorov model has trivial and two semitrival fixed points for all involved parameters, but it has an interior fixed point under definite parametric condition. Then, by linear stability theory, local dynamics with different topological classifications are investigated around trivial, semitrival, and interior fixed points. Further for the discrete Kolmogorov model, existence of periodic points is also investigated. It is also investigated the occurrence of bifurcations at interior fixed point and proved that at interior fixed point, there exists no bifurcation, except flip bifurcation by bifurcation theory. Next, feedback control method is utilized to stabilize chaos existing in discrete Kolmogorov model. Boundedness and global attractivity of the discrete Kolmogorov model are also investigated. Finally, obtained results are numerically verified. [ABSTRACT FROM AUTHOR]

In this study, the mathematical model of the cholera epidemic is formulated and analyzed to show the impact of Vibrio cholerae in reserved freshwater. Moreover, the results obtained from applying the new fractional derivative method show that, as the order of the fractional derivative increases, cholera-preventing behaviors also increase. Also, the finding of our study shows that the dynamics of Vibrio cholerae can be controlled if continuous treatment is applied in reserved freshwater used for drinking purposes so that the intrinsic growth rate of Vibrio cholerae in water is less than the natural death of Vibrio cholerae. We have applied the stability theory of differential equations and proved that the disease-free equilibrium is asymptotically stable if R 0 < 1 , and the intrinsic growth rate of the Vibrio cholerae bacterium population is less than its natural death rate. The center manifold theory is applied to show the existence of forward bifurcation at the point R 0 = 1 and the local stability of endemic equilibrium if R 0 > 1. Furthermore, the performed numerical simulation results show that, as the rank of control measures applied increases from no control, weak control, and strong control measures, the recovered individuals are 55.02, 67.47, and 674.7, respectively. Numerical simulations are plotted using MATLAB software package. [ABSTRACT FROM AUTHOR]

Summary: A nonlinear backstepping control scheme is proposed in this work for a bridge type fault current limiter (BFCL) in a hybrid power system for enhancing its transient performance. The hybrid power system has the provision to supply AC loads connected to the main grid and local DC loads. The DC‐side of that system is coupled with AC‐side through a bidirectional converter having power exchange capability between both AC‐ and DC‐sides. The AC‐side is coupled with the main grid through transmission lines and the BFCL is placed on the transmission line, where the faults are considered, as the transmission line is the most vulnerable point. The dynamical model of the BFCL is used to design the nonlinear backstepping controller (BSC) where the control input is derived in a way that it can ensure as well as enhance the transient performance of that hybrid power system. Lyapunov stability theory is used to theoretically demonstrate the stability of the BFCL using the proposed BSC. Theoretical findings guarantee the system stability, and simulation studies clearly indicate the superiority of the proposed BSC based BFCL (BSC‐BFCL), both graphically and numerically over an existing nonlinear sliding mode controller (SMC) for the BFCL (SMC‐BFCL), for symmetrical and unsymmetrical fault scenarios (both temporary and permanent type). In addition, percentage overshoot and settling time analyses suggest the lesser deviation of system responses during transients from their ideal values and quicker stability, respectively. Moreover, the astonishing total harmonic distortion (THD) values with the proposed technique signify the excellency over its competitors in every aspect. [ABSTRACT FROM AUTHOR]

We investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system (BVS) of FDE. We use Krasnoselskii's and Banach's fixed point theorems to obtain the desired results for the existence of solution. Stability is an important aspect from a numerical point of view we investigate here. To justify the main work, relevant examples are provided. [ABSTRACT FROM AUTHOR]

An antisaturation backstepping control scheme based on constrained command filter for hypersonic flight vehicle (HFV) is proposed with the consideration of angle of attack (AOA) constraint and actuator constraints of amplitude and rate. Firstly, the HFV system model is divided into velocity subsystem and height subsystem. Secondly, to handle AOA constraint, a constrained command filter is constructed to limit the amplitude of the AOA command and retain its differentiability. And the constraint range is set in advance via a prescribed performance method to guarantee that the tracking error of the AOA meets the constraint conditions and transient and steady performance. Thirdly, the proposed constrained command filter is combined with the auxiliary system for actuator constraints, which ensures that the control input meets the limited requirements of amplitude and rate, and the system is stable. In addition, the tracking errors of the system are proved to be ultimately uniformly bounded based on the Lyapunov stability theory. Finally, the effectiveness of the proposed method is verified by simulation. [ABSTRACT FROM AUTHOR]