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Abstract: This paper studies the general nonautonomous single-species Kolmogorov systems with delays. The sufficient conditions on the persistence and permanence of species, global asymptotic stability and the existence of positive periodic solutions are established. As applications of these results, the permanence, global asymptotic stability and the existence of positive periodic solutions for a series of special single-species growth systems with delays are discussed. [Copyright &y& Elsevier]

In this paper, an anti-unwinding adaptive robust backstepping control law is proposed to solve the attitude control problem of rigid spacecraft with external disturbances and inertia uncertainties. A new variable based on hyperbolic sine functions is designed to prevent the unwinding phenomenon, and then a novel robust backstepping controller is developed. Initially, a nonlinear tracking law is designed to obtain the desired angular velocity and to ensure that the attitude maneuvering system could have two equilibrium points. Subsequently, an adaptive robust control law is devised, which incorporates the adaptive estimation method to update the inertial parameters in real-time. Moreover, the bounded external disturbances are taken into account in the design of the control law, and thus the robustness of the attitude control system is improved. Furthermore, the global asymptotic stability of the attitude control system is verified by the Lyapunov-Krasovskii theorem. Finally, numerical simulations are carried out to demonstrate the effectiveness and robustness of the proposed control law, as well as the anti-unwinding characteristics are perfectly validated during the attitude maneuver of rigid spacecraft. [ABSTRACT FROM AUTHOR]

This paper designs an interval type-2 fuzzy neural network sliding mode robust controller (IT2FNNSMRC) to improve the stability of the vibrational angle of the orbital plane in magnetic rigid spacecraft attitude control. The control system consists of an interval type-2 fuzzy neural network (IT2FNN) controller, a PD controller, and a robust controller in parallel connection. The IT2FNN controller, as a nonlinear regulator, compensates the nonlinearity of the controlled object; the PD controller, as a feedback controller, ensures the global asymptotic stability of the control system; the robust controller inhibits input load disturbance. The IT2FNN controller hereof has a self-organizing function which enables it to automatically determine the network structure and parameters online. At the stage of IT2FNN structure learning, the standard on rule growth is set according to the incentive intensities of IT2FNN rule premises. A new rule is generated when the incentive intensities of rules are all smaller than a certain threshold; next, a significance index is set for each rule. When the significance index of some rule decays to a certain threshold, the corresponding rule shall be deleted to achieve the goals of optimizing IT2FNN structure and reducing system complexity. At the stage of parameter learning, adaptive adjustment of IT2FNN parameters is made via the sliding mode control theory learning algorithm, and the stabilities of the algorithm and control system are proven using Lyapunov function. Finally, the proposed control scheme is used in the control of a magnetic rigid spacecraft, as compared to three other designed control methods. Simulation results show that IT2FNNSMRC has superior control precision and stability. And the IT2FNN which adopts the proposed learning algorithm can address uncertainty satisfactorily, with higher computational implementability. • In the control scheme for the PD controller and IT2FNN parallel operation, a robust controller has been added so that the IT2FNNSMRC can be applied to second-order systems with more complex disturbances. • The self-organizing algorithm based on the incentive intensity of fuzzy rules has been proposed for online optimization of the IT2FNN structure, ensuring the correlation between the input signal and fuzzy rules and determining the optimal structure of the neural network. • The IT2FNN parameters have been optimized using the sliding mode learning algorithm at lower computational cost, which is easier to implement compared to the gradient method. • The computational cost of the IT2FNNSMRC has been analyzed in terms of time complexity, and it has been proven that the computational complexity of IT2FNN in this paper has been reduced below that of traditional fixed structure IT2FNN. • The IT2FNN parameter learning algorithm is tested by Lyapunov stability analysis, and it is further proven that the robust controller can effectively enhance the stability of the system. [ABSTRACT FROM AUTHOR]

In this research paper, we delve into the analysis of a generalized discrete reaction-diffusion system. Our study begins with the discretization of a generalized reaction-diffusion model, achieved through second-order and L 1-difference approximations. We explore the local stability of its unique solution, both in the absence and presence of the diffusion term. To determine the conditions for global asymptotic stability of the steady-state solution, we employ suitable techniques including the direct Lyapunov method. To illustrate the practical application of this theoretical framework, we provide several numerical simulations that examine both the Lengyel-Epstein reaction-diffusion model and the discrete Degn-Harrison reaction-diffusion model. These simulations serve to validate the predictions of asymptotic stability. [ABSTRACT FROM AUTHOR]

This paper addresses the electromagnetic separation problem for mass-unknown spacecraft in elliptical orbits that play a significant role in on-orbit assembly and other future space missions. First, the relative motion dynamics model between the platform (target spacecraft) and module (chaser spacecraft) is presented with the lumped disturbance resulting from external disturbances, elliptical eccentricity and unknown mass, and a compliant reference trajectory is designed by applying the idea of trigonometric-function. Then, an improved sliding mode controller is developed to ensure that the tracking errors of relative motion can converge to near the equilibrium point. In order to avoid adverse impacts, the elliptical eccentricity and unknown mass are fully considered by using the developed control approach, and the global asymptotic stability of the closed-loop system is analyzed by strict theoretical proof. Combined with spacecraft electromagnetic docking technology, the electromagnetic separation scheme can make on-orbit assembly easy to achieve with certain advantages, e.g., it doesn't consume propellant and thus doesn't cause plume contamination, and has reversible, continuous and non-contact characteristics. Finally, numerical simulations are performed to illustrate the effectiveness and feasibility of the developed control approach. [ABSTRACT FROM AUTHOR]

• A new criterion for the boundedness and asymptotic stability of NCN on time scales under impulsive control is proposed. • The results show that constrained nonlinearity plays an important role in the global boundedness of nonautonomous complex networks under impulsive control. • An application is given for the bounded driving of unmanned vehicles. This paper discusses time-scale type global boundedness of nonautonomous complex networks (NCNs) under impulsive control. By using constraint nonlinearity of NCNs, properties of exponential function and impulsive inequalities, we establish new sufficient conditions for global boundedness and asymptotic stability of NCNs on time scales, and the upper bound of the system can be calculated easily. It is shown that the constraint nonlinearity and impulse interval length will affect the estimation of state bound of NCNs under different network size. It provides a unified criteria for global boundedness of NCNs on continuous, discrete and mixed-time domains and hence improves corresponding existing ones. The nonlinear constraints studied in this paper are widely applied to Lurie systems, ball motion models and so on. Numerical examples are given to illustrate the correctness of the results. Finally, the theoretical results are applied to Lurie systems and bounded driving of unmanned vehicles. [ABSTRACT FROM AUTHOR]

The paper considers multi-agreements that may exist in social networks that do not have connectivity across the network, and where each agent can decide on how an opinion from an influencing agent is accepted or not. The opinion dynamics considered in this paper are therefore nonlinear. Because of this nonlinearity, and because general directed graphs are considered, the first contribution is using a decomposition of the directed graph, which identifies the key influencers (with strong connectivity) and the pure followers in the graph, to partition the dynamics into two cascaded subsystems. Based on a LaSalle invariance principle and a max–min Lyapunov function, global asymptotic stability of "agreements" can then be established under very weak, nearly necessary conditions. The result generalizes a number of results for consensus networks with first-order multi-agent systems, as well as three important models, namely, stubborn extremists, stubborn positives, and stubborn neutrals. A Gaussian elimination based algorithm is introduced to simultaneously identify the key influencers and a particular basis of the left kernel space of the Laplacian matrix. To compute a special basis of the right kernel space of the Laplacian matrix, an effective algorithm is then proposed based on the Cramer's rule. These algorithms are closely related to the prediction of final agreement values. Simulation studies complement the theoretical results, hinting toward agreement design. [ABSTRACT FROM AUTHOR]

In this paper, the stability problem for a class of nonlinear systems in the form of strict-feedback with applying input quantization has been addressed. By considering a sector-bounded hysteresis quantizer, signal quantization has been achieved. The employed quantizer can reduce the potential chattering which can occur in some approaches. By using a common Lyapunov function (CLF) and the backstepping method, a control scheme has been introduced to stabilize the uncertain nonlinear system. Compared with the recent papers, in order to handle the quantization error, one of the sector-bounding features has been utilized straightly instead of decomposing the quantized input into linear and nonlinear parts, in this case, the possible disturbance-like term has been ignored. The designed control scheme does not need the global Lipschitz assumption over the system mismatched nonlinearities. Besides, the asymptotic stability of system trajectories to the origin is guaranteed and the imposed restrictions over quantization design parameters such as quantization density have been eliminated. Finally, in the simulation results, the accuracy and efficiency of the this control scheme are shown. • Stability of a strict-feedback form with hysteresis quantization is considered. • A more general form of the strict-feedback system has been investigated. • Restrictions on choosing parameters in the design procedure have been relaxed. • Global asymptotic stability in the presence of quantized input has been guaranteed. • The superiority and efficiency of the proposed method have been illustrated. [ABSTRACT FROM AUTHOR]

This paper provided a novel control technique for generating a switching sequence for a six-step commutation of BLDC motor utilizing a Hall Effect sensor. The strategy combines hybrid control with a model predictive current control (MPCC), namely Hybrid-MPCC. The purpose of implementing Hybrid-MPCC is to obtain a simple commutation scheme, make step commutation works automatically, and reduces torque ripple. The framework of Hybrid-MPCC is a control system that is composed of an interacting continuous and discrete system that influences each other's behavior, kept the constant of the non-commutation phase current, predicted the phase current based on the output phase currents over a specified interval, controlled the three-phase currents separately by varying the motor speed and set the active PWM modulation. Desired properties of Hybrid-MPCC include global asymptotic stability of an equilibrium point and the close-loop system takes on safe values variables. The simulation and practical findings show that the proposed unique method in this work may successfully decrease torque ripple when compared to classic driving methods. [ABSTRACT FROM AUTHOR]

This paper disseminated two formation control strategies for multiple unmanned aerial vehicles (multi-UAV) system of moving target tracking in a windy environment. The communication among UAVs is modeled by a directed graph. The first control strategy proposes a distributed dynamic error observer and a guidance law to make the system global uniform asymptotic stability when the wind disturbance is a known constant. The second control strategy employs a distributed fixed-time observer and a finite-time stable guidance law to make the system globally finite-time stable with unknown wind disturbances. The stability of both formation control strategies is rigorous demonstrated mathematically. Finally, the excellent performance and reliability of the proposed guidance law for target tracking in a windy environment are verified through several simulation examples. • An uncertain kinematic model is used to describe the transient performance of UAV formation. • Existing infinite-time methods have uncertain convergence time and have less robustness. • A distributed fixed-time observer is designed to estimate the tracking error. • A global finite-time robust guidance law is designed to achieve target tracking for UAV formation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we derive some sufficient conditions for local and global asymptotic stability of both continuous-time and discrete-time nonlinear cascade interconnected systems. We prove our results using converse Lyapunov stability theorems and LaSalle''s invariance principle for continuous-time and discrete-time nonlinear systems. [Copyright &y& Elsevier]

This paper proposes a control algorithm for controlling the position and attitude of a coaxial rotor drone without knowing the model dynamics. To overcome the major drawback of model-dependent approaches, an optimal model-free fuzzy controller (OMFFC) based on the estimation of the unknown dynamic function of the system is proposed. A time-delay estimation (TDE) technique is effectively exploited to approximate the unknown dynamic function of the system. The estimation error is then offset using a robust adaptive fuzzy logic compensator. Based on Lyapunov stability arguments, the global asymptotic stability of the coaxial rotor drone system is proven. Moreover, a flower pollination-based algorithm is also proposed to generate the optimal parameters to address the trade-off between optimal tracking performance and the design conditions related to the closed-loop stability requirements. The numerical simulations illustrate how the proposed methodology leads to the best performance, as well as less computational complexity compared to the standard proportional–integral–derivative and time-delay estimation-based controllers in the presence of external disturbances. [ABSTRACT FROM AUTHOR]

Global asymptotic stability and synchronization are explored in this paper for fractional delayed memristive neural networks with reaction–diffusion terms (FDRDMNNs) in sense of Riemann–Liouville. First, we introduce diffusion into the existing model of fractional delayed memristive neural networks. Next, in terms of Green's theorem and inequality technique, a less conservative criterion for the asymptotic stability of FDRDMNNs is given by endowing Lyapunov direct method. Then, the appropriate pinning feedback controllers and adaptive controllers are designed to achieve the synchronization of the FDRDMNNs, and two sufficient conditions for global asymptotic synchronization are acquired. In addition, the results based on algebraic inequalities enhance some existing ones. The numerical simulations finally verify the validity of the derived results. • We research a type of fractional memristive neural networks models with diffusion. • A new stability algebraic criterion is obtained by the Lyapunov direct method. • Two synchronization conditions are gained by appropriate pinning control schemes. • Our results can be viewed as an extension of the existing ones. [ABSTRACT FROM AUTHOR]

The core idea of traditional adaptive control is to reconstruct parameter estimation errors with known signals and damping injection based on tracking error, while the formulation of desired damping in controller designs is usually a nontrivial task. The main contribution of this paper lies in the development of the classic RISE result and a constructive damping injection procedure for the adaptive tracking control of Euler–Lagrange mechanical systems. By utilizing generalized dynamic scaling function, scalar filtering, the improved RISE method and analyzing the existence of finite escape time of the closed-loop system, a globally asymptotically stable result is obtained with facilitative damping injection, significant order reduction and improved design efficiency when compared with the existing results. Simulations on a fully actuated 2-DOF planar robot manipulator model demonstrate the effectiveness of the proposed methods. • Order reduction. The extended dynamic orders of the proposed adaptive controller is less than composite adaptive RISE controller. • Performance improvement. The proposed controller achieves the global asymptotic stability with the non-CE-alike adaptive estimation performance. • Design simplification. There are many control parameters in the controller that can be adjusted to obtain the desired performance, and the computational difficulties are avoided such as analytical solution of PDE in I&I. [ABSTRACT FROM AUTHOR]

This research paper conducts an investigation into the stability issue for a more general class of neutral-type Hopfield neural networks that involves multiple time delays in the states of neurons and multiple neutral delays in the time derivatives of the states of neurons. By constructing a new proper Lyapunov functional, an alternative easily verifiable algebraic criterion for global asymptotic stability of this type of Hopfield neural systems is derived. This new stability condition is entirely independent of time and neutral delays. Two instructive examples are employed to indicate that the result obtained in this paper reveals a new set of sufficient stability criteria when it is compared with the previously reported stability results. Therefore, the proposed stability result enlarges the application domain of Hopfield neural systems of neutral types. [ABSTRACT FROM AUTHOR]

This paper will review some fundamental results in the understanding of several basic problems concerning feedback and uncertainty. First, we will consider adaptive control of linear stochastic systems, in particular, the global stability and optimality of the well-known self-tuning regulators, designed by combining the least-squares estimator with the minimum variance controller. This natural and seemingly simple case had actually been a longstanding central problem in the area of adaptive control, and its solution offers valuable insights necessary for understanding more complex problems. Next, we will discuss the theoretical foundation of the classical proportional-integral-derivative (PID) control, to understand the rationale behind its widespread successful applications in control practice where almost all of the systems to be controlled are nonlinear with uncertainties, by presenting some theorems on the global stability and asymptotic optimality of the closed-loop systems, and by providing a concrete design method for the PID parameters. Finally, we will consider more fundamental problems on the maximum capability and limitations of the feedback mechanism in dealing with uncertain nonlinear systems, where the feedback mechanism is defined as the class of all possible feedback laws. Some extensions and perspectives will also be discussed in the paper. [ABSTRACT FROM AUTHOR]

The major target of this research article is to conduct a new Lyapunov stability analysis of a special model of Cohen–Grossberg neural networks that include multiple delay terms in state variables of systems neurons and multiple delay terms in time derivatives of state variables of systems neurons in the network structure. Employing some proper linear combinations of three different positive definite and positive semi-definite Lyapunov functionals, we obtain some novel sufficient criteria that guarantee global asymptotic stability of this type of multiple delayed Cohen–Grossberg type neural systems. These newly derived stability results are determined to be completely independent of the involved time delay terms and neutral delay terms, and they are totally characterized by the values of the interconnection parameters of Cohen–Grossberg neural system. Besides, the validation of the obtained stability criteria can be justified by applying some simple appropriate algebraic equations that form some particular relations among the constant system elements of the considered neutral neural systems. A useful and instructive numerical example is analysed to exhibit some major advantages and novelties of these newly proposed global stability results in this paper over some previously reported corresponding asymptotic stability conditions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the protocol-based fault detection (FD) issue for state-saturated delayed nonlinear systems with both redundant channels and sensor nonlinearities. Specifically, in pursuit of relieving the communication pressure, the stochastic communication protocol is adopted, which can regulate the transmission of output signal during the communication process. Moreover, for the purpose of decreasing the negative impact of one channel failure on network communication and enhancing data reliability, the redundant channels transmission is introduced. Then, the protocol-based FD filter is constructed such that the resultant FD dynamics system attains the global asymptotic stability in mean-square sense and satisfies the H ∞ performance index. Moreover, an implement-to-easy algorithm is developed to facilitate the solvability of the desirable FD filtering method. In the end, two illustrative examples are utilized to demonstrate the validity of the developed FD filtering algorithm. • The stochastic communication protocol is adopted to regulate the network communication. • The redundant channels transmission mechanism is introduced into the signal communication process. • New sufficient criteria are derived to assure the existence of desirable FD filtering scheme for state-saturated systems. [ABSTRACT FROM AUTHOR]

The enhancement of accuracy remains a significant concern in state estimation for field mobile robots. This paper introduces a novel sensor fusion method to refine the accuracy of state estimation, employing global navigation satellite systems (GNSS) and encoders. This technique integrates a nonlinear observer for estimating the state of nonlinear systems and an unscented Kalman filter (UKF) to ascertain the robot's state variables using signals from GNSS and encoder-based position sensors. In the proposed method, the nonlinear observer updates sigma points through nonlinear transformation and the UKF optimizes state estimation. Parameters are optimized through the particle swarm optimization method with the objective of minimizing the root mean square error of the state. To demonstrate performance, numerical simulations compare the proposed method with well-known nonlinear estimation algorithms, illustrating its effectiveness in field mobile robot state estimation. The method is further validated through implementation on a real-world mobile robot platform. • A new state estimation method for mobile robot using differential GNSS and encoders. • A sufficient condition for the estimator guarantees global asymptotic stability. • Presentation of the non-linear-observer-unscented-Kalman-filter (NLO-UKF). • Implementation of the NLO-UKF and its comparisons to baseline methods. [ABSTRACT FROM AUTHOR]

The underactuated Quadrotor Hybrid Aerial Underwater Vehicle (HAUV) can operate in multiple mediums and seamlessly transition between them. Affected by the buoyancy, underwater control suffers a critical 180° turnover singular problem. To address this challenge, this paper presents a detailed underwater 6-degree of freedom dynamics based on the unit quaternions. A novel geometric attitude extraction method is introduced to improve the classical geometric control. Subsequently, a cascaded controller is developed for trajectory tracking. This controller consists of a position loop and an attitude loop, integrated through the attitude extraction method. It extracts the desired attitude for the inner loop from the desired thrust direction in the outer loop. Rigorous analysis demonstrates that the closed system exhibits global asymptotic stability, effectively mitigating the singular problem. Simulations demonstrate that the controller effectively adapts the quadrotor HAUV, regardless of its buoyancy (positive, negative, or neutral), to accurately track underwater trajectories and fixed points. • The underwater model of a quadrotor Hybrid Aerial Underwater Vehicle is developed and detailed analyzed. Added mass, buoyancy and fluid drag force are all taken into account. • To mitigate the singular problem, especially the critical 180° turnover singular problem, a novel geometric attitude extraction method to improve the quadrotor's classical geometric controller. The closed system is proven to be globally asymptotically stable. • The controller adapts the quadrotor HAUV with positive, negative or neutral buoyancy to track underwater trajectory and fixed point well. [ABSTRACT FROM AUTHOR]

Magnetic levitation (MagLev) system is an unstable, highly non-linear and dynamically fast. These characteristics make it challenging task to design a suitable controller to ensure any object to stay at a certain distance from the electromagnet with negligible error. It can be achieved by generating the required flux with the help of a control input. This suspension of ferromagnetic object in air is achieved by balancing the forces of attraction of gravity and electromagnetic. This makes the system highly vulnerable to external disturbances and parametric uncertainties. The controller must be able to adapt the changing electrical resistance and be robust if the mass of the levitating object for MagLev changes. In this paper, three nonlinear controllers: adaptive terminal sliding mode control (AT-SMC), adaptive backstepping sliding mode (ABS-SMC) and adaptive integral backstepping sliding mode (AIBS-SMC) based controllers have been proposed for tracking the air gap to desired value while maintaining the momentum and flux to desired values. Lyapunov theory has been used for proving the global asymptotic stability of the proposed controllers. For performance analysis, simulations have been carried out using Matlab/Simulink environment, where the proposed controllers have been compared with each other. Among the proposed controllers, AT-SMC gives better performance in terms of transient and overall dynamical response. The effect of parametric variations/uncertainties on all of the proposed controllers has also been examined by varying parametric values, by adding noise and disturbance in the system. Moreover, simulation results for the proposed controllers have also been compared with recently proposed controllers in literature. The physical realization of proposed AT-SMC has been examined with the help of a comparison between simulation results and the controller hardware in loop (C-HIL) experimental results. • An updated mathematical model of Maglev system has been considered. • Three nonlinear robust adaptive controllers have been proposed. • Using Lyapunov Stability Theory, asymptotic stability of the controller has been proved. • The comparison of the proposed controllers has been done using MATLAB/Simulink. [ABSTRACT FROM AUTHOR]

This paper carries out a theoretical investigation into the stability problem for the class of neutral-type Cohen–Grossberg neural networks with discrete time delays in states and discrete neutral delays in time derivative of states. By employing a more general type of suitable Lyapunov functional, a set of new generalized sufficient criteria are derived for the global asymptotic stability of delayed neural networks of neutral-type. The proposed stability criteria are independently of the values of the time delays and neutral delays, and they completely rely on some algebraic mathematical relationships involving the values of the elements of the interconnection matrices and the other network parameters. Therefore, it is easy to verify the validity of the obtained results by simply using some algebraic equations representing the stability conditions. A detailed comparison between our proposed results and recently reported corresponding stability results is made, proving that the results given in this paper generalize previously published stability results. A constructive numerical example is also given to demonstrate the applicability of the results of the paper. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the global stability of pyramidal traveling fronts for the reaction–diffusion equations with degenerate monostable and combustion nonlinearities. The existence and part of the stability of such fronts have been proved by constructing supersolutions and subsolutions in our works (Bu and Wang, 2017; Wang and Bu, 2016). In this paper we prove the global asymptotic stability of pyramidal traveling fronts. Our main technique is constructing new subsolutions coupled with the comparison principle. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the leakage delay-dependent global asymptotic stability problem for a class of complex-valued neural networks (CVNNs) with discrete and distributed time-varying delays. In order to handle this issue easily, an appropriate Lyapunov–Krasovskii functional (LKF) is constructed with some augmented delay-dependent terms. By employing integral inequalities, several delay-dependent sufficient conditions are derived that ensure the global asymptotic stability of the considered system model. Moreover, the results obtained in this paper have expressed in terms of complex-valued linear matrix inequalities (LMIs), whose feasible solutions can be easily verified by effective YALMIP control toolbox in MATLAB LMI. Finally, two benchmark illustrative examples are given to show the effectiveness and advantages of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider a three-species system which consists of phytoplankton, zooplankton and fish. It is well known that zooplankton are harvested by other creatures besides fish, and it has been reported that zooplankton can absorb energy from other micro-organisms besides phytoplankton in recent decades. For this reason, we add the parts of extra energy source and harvesting effect in the model. Taking account of seasonal variation which can bring affects to many aspects of plankton population, we assume that some factors about the phytoplankton and the zooplankton are time-dependent. In particular, since the environment does not change regularly, we does not require these time-varied factors are periodic, which is quite different with most ecological models. The purpose of this paper is to present sufficient conditions which guarantee that the equilibrium of this three-species system is globally asymptotically stable. Moreover, we will show that the equilibrium is equiasymptotically stable under relatively weaker conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the robust global attitude stabilization problem for a rigid-body system using quaternion-based feedback. We propose a novel synergistic hybrid feedback with the following notable features: (1) It demonstrates central synergism by utilizing a minimal number of potential functions; (2) It ensures consistency with respect to the unit quaternion representation of rigid-body attitude; (3) Its state-feedback laws incorporate a shared action term that steers the system towards the desired attitude. We demonstrate that the proposed hybrid feedback method effectively solves the problem at hand and guarantees robust uniform global asymptotic stability. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the complex nonlinear dynamics, such as the existence and effect of various types of bifurcations, in an infectious disease model system. An S I R delay model that accounts for saturated incidence, saturated treatment, and self-protection in the susceptible population is considered. The model system has a disease free equilibrium, and its local stability is determined by the basic reproduction number for any delay value. The existence of multiple endemic equilibria is obtained, and these equilibria may switch stability due to variation of bifurcation parameters. When incubation delay is zero, Bogdanov–Takens bifurcation occurs, which implies the existence of Hopf bifurcation, saddle–node, and homoclinic bifurcations. Thus, the disease will persist within or on the homoclinic loop and otherwise dies out. We also find the existence of backward bifurcation and forward (transcritical) bifurcation. The delay-induced stability switches are observed due to Hopf bifurcations, leading to endemic bubbles. Incubation delay affects the stability of equilibria when the model system has multiple endemic equilibria, so multi-stability is observed. Due to incubation delay, the two frequency Hopf–Hopf bifurcation and Bogdanov–Takens bifurcation are found. Thus, both codimension 1 and codimension 2 bifurcations in the effect of incubation delay are exhibited in this study. Numerically, we notice that with increasing incubation delay, the endemic equilibrium either changes stability (from stable to unstable or unstable to stable) or remains unstable with different frequencies of oscillations. [ABSTRACT FROM AUTHOR]

We report a numerical study of the dynamics of laminar axisymmetric jets emerging from an injector of circular cross-section into a quiescent ambient of a heavier fluid. We focus on the critical conditions for the onset of self-sustained oscillations that characterize these jets, which are known to result from a supercritical Hopf bifurcation to a globally unstable flow. Our study aims to shed light on the discrepancies between experimental observations and predictions of linear stability theory. To this end, the unsteady Navier–Stokes equations have been solved using the finite element solver FreeFEM++, starting from a steady solution as the initial condition. The critical conditions for the onset of global instability reported in this paper lie between the experimentally observed values of Hallberg and Strykowski (2006), and those predicted by the global linear stability analysis of Coenen et al. (2017). • Simulations successfully replicate Hopf bifurcation towards a self-sustained state. • Critical conditions lie between experiments and global linear stability theory. • Frequencies slightly exceed those reported in experiments and theoretical analyses. [ABSTRACT FROM AUTHOR]

This paper studies the stabilization problem of networked control systems (NCSs) with random packet dropouts caused by stochastic channels. To describe the effects of stochastic channels on the information transmission, the transmission times are assumed to be deterministic, whereas the packet transmission is assumed to be random. We first propose a stochastic scheduling protocol to model random packet dropouts, and address the properties of the proposed stochastic scheduling protocol. The proposed scheduling protocol provides a unified modelling framework for a general class of random packet dropouts due to different stochastic channels. Next, the proposed scheduling protocol is embedded into the closed-loop system, which leads to a stochastic hybrid model for NCSs with random packet dropouts. Based on this stochastic hybrid model, we follow the emulation approach to establish sufficient conditions to guarantee uniform global asymptotical stability in probability. In particular, an upper bound on the maximally allowable transmission interval is derived explicitly for all stochastic protocols satisfying Lyapunov conditions that guarantee uniform global asymptotic stability in probability. Finally, two numerical examples are presented to demonstrate the derived results. [ABSTRACT FROM AUTHOR]

In this paper, we study the global dynamics and asymptotic spreading speed for a biological invasion model with free boundaries and time delay. Given a suitable initial value compatibility condition, the well-posedness of solution is established and some sufficient conditions for spreading and vanishing are derived. Furthermore, by studying an associated semi-wave solution problem, the asymptotic spreading speed for the invasive species is given. It is shown that time delay can slow down the spreading speed. Finally, the dynamics and asymptotic spreading speed are analyzed by numerical simulations. [ABSTRACT FROM AUTHOR]

Hepatitis C virus (HCV) can establish infection via two distinct modes: virus-to-cell infection and cell-to-cell transmission. These infections prompt the activation of two types of adaptive immune responses: the cytotoxic T lymphocyte response and the antibody response. In this paper, we study HCV dynamics by developing a multiscale model that incorporates both modes of infection as well as the two types of immune responses. We derive both the basic reproduction number of virus and four immune reproduction numbers for the model. We identify five equilibria, the existence of which depends on the values of basic reproduction number of virus and the immune reproduction numbers. We also establish the global asymptotic stability of the equilibria by employing Lyapunov functions, which further underscores the profound impact of the aforementioned reproduction numbers on the model's overall stability. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the fractional compartmental model in the sense of Caputo derivative for the dynamics of the novel human papillomavirus, which causes cervical cancer. We study and investigate the dynamical analysis of a nonlinear fractional-order cervical cancer epidemic model with the nonstandard finite difference method. The newly proposed nonlinear fractional model is an extension of an integer-order cervical cancer mathematical model. We demonstrate the solution's existence, uniqueness, non-negativity, and boundedness by utilizing fundamental concepts of the fixed-point theory. The basic reproduction number, which analyzes whether or not the infection spreads to the population, is computed using the next-generation matrix method. We investigate the local and global asymptotic stability of the derived cervical-free and cervical-present equilibrium points and discuss the sensitivity of the basic reproduction number, which depends on the parameters of the proposed model. Furthermore, a mathematical simulation of the suggested continuous model is performed to evaluate the reported theoretical results using the nonstandard finite difference method. The acquired results are displayed, which show that a fractional parameter plays a pivotal role in controlling the cervical cancer. [ABSTRACT FROM AUTHOR]

This paper puts forward a multi-loop nonlinear control (MLNC) strategy to overcome the limited performance of LTI controllers due to the so-called “waterbed” effect. According to “Bode's sensitivity integral”, increasing the bandwidth or additional integral gain of LTI controller to improve the low-frequency disturbance attenuation irrefutably increases the sensitivity to high-frequency disturbances or measurement noise. Hence, it is impossible to attain the best of both worlds in the case of linear controllers. Therefore, with an aim to improve the transient and steady state performance of linear controllers, in this paper, a nonlinear control framework using circle criterion method and saturation nonlinearity, which adjusts the integral gain based on the error threshold, is discussed. The global asymptotic stability (GAS) of the MLNC strategy is theoretically proved using LaSalle's invariance principle and experimentally validated using measured frequency response function (FRF). Moreover, the performance of the MLNC strategy is compared with that of the multi-loop linear control (MLLC) strategy on a benchmark magnetic levitation system for tracking application. The cumulative power spectral density (CPSD) of tracking error, which is used as the performance index to assess the overall closed loop performance, accentuates that MLNC can yield better steady state and transient performance compared to MLLC scheme. [ABSTRACT FROM AUTHOR]

In this paper, the nonminimum phase problem of a flexible hypersonic vehicle is investigated. The main challenge of nonminimum phase is the prevention of dynamic inversion methods to nonlinear control design. To solve this problem, we make research on the relationship between nonminimum phase and backstepping control, finding that a stable nonlinear controller can be obtained by changing the control loop on the basis of backstepping control. By extending the control loop to cover the internal dynamics in it, the internal states are directly controlled by the inputs and simultaneously serve as virtual control for the external states, making it possible to guarantee output tracking as well as internal stability. Then, based on the extended control loop, a simplified control-oriented model is developed to enable the applicability of adaptive backstepping method. It simplifies the design process and releases some limitations caused by direct use of the no simplified control-oriented model. Next, under proper assumptions, asymptotic stability is proved for constant commands, while bounded stability is proved for varying commands. The proposed method is compared with approximate backstepping control and dynamic surface control and is shown to have superior tracking accuracy as well as robustness from the simulation results. This paper may also provide a beneficial guidance for control design of other complex systems. [ABSTRACT FROM AUTHOR]