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

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

Mathematical models play a crucial role in controlling and preventing the spread of diseases. Based on the communication characteristics of diseases, it is necessary to take into account some essential epidemiological factors such as the time delay that takes an individual to progress from being latent to become infectious, the infectious age which refers to the duration since the initial infection and the occurrence of reinfection after a period of improvement known as relapse, etc. Moreover, age-structured models serve as a powerful tool that allows us to incorporate age variables into the modeling process to better understand the effect of these factors on the transmission mechanism of diseases. In this paper, motivated by the above fact, we reformulate an SEIR model with relapse and age structure in both latent and infected classes. Then, we investigate the asymptotic behavior of the model by using the stability theory of differential equations. For this purpose, we introduce the basic reproduction number R 0 of the model and show that this threshold parameter completely governs the stability of each equilibrium of the model. Our approach to show global attractivity is based on the fluctuation lemma and Lyapunov functionals method with some results on the persistence theory. The conclusion is that the system has a disease-free equilibrium which is globally asymptotically stable if R 0 < 1 , while it has only a unique positive endemic equilibrium which is globally asymptotically stable whenever R 0 > 1 . Our results imply that early diagnosis of latent infection with decrease in both transmission and relapse rates may lead to control and restrict the spread of disease. The theoretical results are illustrated with numerical simulations, which indicate that the age variable is an essential factor affecting the spread of the epidemic. [ABSTRACT FROM AUTHOR]

In this paper, a new two-body self-synchronization vibration system characterized by two ideal vibration-exciting motors (asynchronous motors) installed on different vibrating bodies is investigated. Firstly, differential equations of the system are established via the Lagrange equation. Moreover, natural frequencies and stable solutions are obtained. Then, the conditions for the system to implement stable self-synchronization are derived using the equilibrium point theory of the dynamics system and Lyapunov's stability theory. The effects of spring stiffness on the natural frequencies and synchronous motion are numerically analyzed. The steady-state responses of the system are obtained for different structure parameters. The research results show that this system can implement two types of self-synchronization motion under different structure parameters. The first type fluctuates the phase differences in the proximity of zero rad, while the other one fluctuates the phase differences near π rad. Resonance significantly affects the synchronous motion of the system, rapidly changing in phase differences and amplitudes. An increase in the value of k y 2 is not conducive to implementing the stable synchronous motion. Finally, the correctness of the theory and electromechanical coupling simulation results is experimentally validated. The results of this paper can be directly used to determine the structural parameters for a new type of vibrating machine. [ABSTRACT FROM AUTHOR]

The results of the swept wing boundary layer stability investigation are presented for the case, when the wing surface has a region of gas suction through the wall normal to the surface, while the wing is in Mach number 2 flow. In the flow regime considered the predominant boundary layer instability type is the crossflow instability. The gas suction effect on the development of unstable modes in the boundary layer is investigated using the linear stability theory and direct numerical modeling. The numerical modeling of laminar (undisturbed) flow fields with regions of gas suction and disturbed flow fields is carried out by integrating Navier–Stokes equations. An analysis within the framework of the linear stability theory is performed using the -method. The suction region location is varied with conservation of the integral intensity. It is shown that the mode instability growth can be considerably suppressed at the expense of an optimal disposition of the suction region. [ABSTRACT FROM AUTHOR]

Recently, a stability theory has been developed to study the linear stability of modified Patankar–Runge–Kutta (MPRK) schemes. This stability theory provides sufficient conditions for a fixed point of an MPRK scheme to be stable as well as for the convergence of an MPRK scheme towards the steady state of the corresponding initial value problem, whereas the main assumption is that the initial value is sufficiently close to the steady state. Initially, numerical experiments in several publications indicated that these linear stability properties are not only local but even global, as is the case for general linear methods. Recently, however, it was discovered that the linear stability of the MPDeC(8) scheme is indeed only local in nature. Our conjecture is that this is a result of negative Runge–Kutta (RK) parameters of MPDeC(8) and that linear stability is indeed global if the RK parameters are nonnegative. To support this conjecture, we examine the family of MPRK22( α ) methods with negative RK parameters and show that even among these methods there are methods for which the stability properties are only local. However, this local linear stability is not observed for MPRK22(α ) schemes with nonnegative Runge–Kutta parameters. In particular, it is shown that MPRK22(α ) schemes with 0 < α < 0.5 or - 0.5 < α < 0 are only stable if the time step size is sufficiently small. But schemes with α ≤ - 0.5 are stable and converge towards the steady state of the initial value problems for all time step sizes, at least for the test problem under consideration. Furthermore, it is shown that for some of the latter systems, the initial values must actually be close enough to the steady state to guarantee this result. [ABSTRACT FROM AUTHOR]

The predefined-time fuzzy adaptive output feedback control problem is considered for non-strict feedback stochastic nonlinear systems with state constraints. Since the controlled plant contains unknown nonlinear dynamics and unmeasured states, the unknown nonlinear dynamics are handled by using fuzzy approximation technique, and a fuzzy state observer is established to estimate unmeasured states. Then, under the frameworks of a predefined-time stability theory and backstepping control design technique, a new fuzzy adaptive output feedback control method is proposed. It is proved that the controlled system is semi-global practically predefined-time stable in probability by constructing suitable barrier Lyapunov functions. Finally, the spring–mass–damper system is given to confirm the effectiveness of the presented control method. [ABSTRACT FROM AUTHOR]

The extensive involvement of blowing in ablation and transpiration cooling directly influences the hypersonic boundary layer (HBL) transition. This work investigates the coupled effect of stabilization through micro-blowing and the corresponding porous blowing medium on a Mach 6 HBL flow. Linear stability theory (LST) and the eN method are used to interpret the characteristics of stability, and direct numerical simulations are used to resolve the detailed flow field among the porous microstructures to verify the predictions of LST. The sole effect of micro-blowing is first investigated by emphasizing the locations of the blowing strip. The results show that micro-blowing alone can significantly excite the first mode but stabilize the second mode. In general, the HBL becomes unstable if the blowing strip is installed upstream of the synchronization points of the dominant disturbances, and otherwise becomes stable. In the context of the blowing medium, a porous coating can suppress high-frequency disturbances and help stabilize the HBL if the blowing strip is placed upstream of the synchronization points of the dominant disturbances. On the contrary, the coating can prematurely excite lower-frequency disturbances and degrade the overall stabilization when the strip is located in the dominant region of the second mode. [ABSTRACT FROM AUTHOR]

Under the low-noise Mach 3 flight conditions for a supersonic passenger aircraft having unswept wings with a thin parabolic airfoil, laminar-turbulent transition is due to amplification of the first mode. Stability of a local self-similar boundary layer over such a wing is investigated both using the e N method in the framework of linear stability theory and direct numerical simulation (DNS). It is found that the instability amplitude should reach a maximum over the entire spectral range above the profiles of 2.5% and thicker. The locus of maximum appears at the trailing edge and moves to the leading edge as the profile becomes thicker, while the maximum amplitude decreases. The theoretical findings are supported by DNS of the linear wave packets propagating in the boundary layer. Significance of these results to the design of laminar supersonic wings is discussed. [ABSTRACT FROM AUTHOR]

The skin made of micro floating raft arrays is a novel method in drag reduction engineering, the study of nonlinear boundary layer stability of flow over the skin is necessary. The weakly nonlinear stability theory is applied to flow over the skin. The weakly nonlinear stability problem of flow over the skin is solved for the first time. The weakly nonlinear flow stability characteristics of skin are analyzed. The results show that increase in the stiffness and damping ratios intensifies the distorted velocity of the Tollmien–Schlichting waves (TSW) but decrease the distorted velocity of travelling-wave flutter (TWF). Reducing the interval and the middle mass of the micro floating raft element can lead to a similar influence on the distorted velocity. The nonlinearity does not change the objective law of the effect of skin's parameters on stability in the boundary layer. The skin can effectively improve the weakly nonlinear stability of the Tollmien–Schlichting waves: the skin with appropriate parameters lightens the velocity distortedness and reduces the perturbation nonlinear growth rate. The better control ability of skin on nonlinear flow stability also proves the potential in drag reduction. [ABSTRACT FROM AUTHOR]

This paper probes into the problem of predefined-time consensus tracking for a class of second-order multi-agent systems (MASs) subject to external disturbances based on a predefined-time observer. A predefined-time control strategy based on the use of terminal sliding mode control method is proposed, which can achieve consensus tracking in a predefined time. Firstly, the observer is designed so that observed states and leader states reach consensus. Secondly, according to the designed controller, states of each agent and observed states achieve consensus, namely, leader-following consensus is realized. By employing Lyapunov stability theory, some sufficient criteria are obtained to achieve predefined-time consensus tracking for second-order MASs with disturbances. Finally, some numerical examples are presented to prove the validity of our designs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an AEC framework for studying fields with commuting automorphisms. Fields with commuting automorphisms are closely related to difference fields. Some authors define a difference ring (or field) as a ring (or field) together with several commuting endomorphisms, while others only study one endomorphism. Z. Chatzidakis and E. Hrushovski have studied in depth the model theory of ACFA, the model companion of difference fields with one automorphism. Our fields with commuting automorphisms generalize this setting. We have several automorphisms and they are required to commute. Hrushovski has proved that in the case of fields with two or more commuting automorphisms, the existentially closed models do not necessarily form a first order model class. In the present paper, we introduce FCA-classes, an AEC framework for studying the existentially closed models of the theory of fields with commuting automorphisms. We prove that an FCA-class has AP and JEP and thus a monster model, that Galois types coincide with existential types in existentially closed models, that the class is homogeneous, and that there is a version of type amalgamation theorem that allows to combine three types under certain conditions. Finally, we use these results to show that our monster model is a simple homogeneous structure in the sense of S. Buechler and O. Lessman (this is a non-elementary analogue for the classification theoretic notion of a simple first order theory). [ABSTRACT FROM AUTHOR]

Emotional controllers have been successfully pursued toward various control objectives in the past two decades, but there remain considerable challenges in exploiting their theoretical and cognitive aspects. This paper addresses these two challenges by proposing a modified thalamic connection based on an averaging operator using a radial basis emotional network (RBEN-ATC). From a theoretical perspective, we prove that the resulting RBEN-ATC mapping has the universal function approximation property. It also becomes continuous and differentiable with respect to the network weights. We then incorporate this structure to approximate the unknown dynamics of a nonlinear affine system with nonsymmetric input saturation and develop a stable adaptive radial basis emotional controller (ARBEC). From a cognitive perspective, we stay committed to the fundamental laws of the emotional brain. While this standpoint considerably complicates the design process, the resulting control system becomes interpretable from a biological perspective. For these purposes, a two-prong approach is employed here. Firstly, we incorporate a first-order compensator that handles the errors due to the nonsymmetric actuator saturation with unknown bounds. Secondly, we use a robust adaptive compensator that lessens the effect of uncertainties. Lyapunov stability analysis shows the overall ARBEC closed-loop stability of the nonlinear system. Furthermore, comparisons with other competing neuro- and fuzzy approaches show that ARBEC has better noise rejection and steady-state tracking while having comparable control energy consumption. [ABSTRACT FROM AUTHOR]

The stability of flow with a constant vertical shear is investigated as part of a two-level quasi-geostrophic model. Analytical expressions for the increment of perturbation growth in linear stability theory are obtained. The Galerkin method with three basic Fourier harmonics is used to describe the nonlinear dynamics of perturbations. A nonlinear system of ordinary differential equations is formulated for amplitudes of Fourier harmonics. It is shown that, in the absence of bottom friction, all solutions of the system describe a periodic mode of nonlinear oscillations or vascillations. The situation changes fundamentally in the model with bottom friction. In this case, for a wide range of parameter values, the system solutions exhibit complex chaotic behavior. Thus, chaos or turbulence emerges for large-scale motions. [ABSTRACT FROM AUTHOR]

This paper treats the problem of H ∞ fault detection for discrete-time networked systems under deception attacks, communication delays, and perturbations. To this end, a mode-dependent fault detection filter (FDF) is presented as a residual generator to detect the occurrence of the fault. As phenomena are occurring randomly via network communication, both the delays and attacks can be appropriately described by mutually independent Markov stochastic process and Bernoulli random variable, respectively. By using the Lyapunov stability theory and linear matrix inequality (LMI) technique, a new sufficient condition for the H ∞ performance analysis of the augmented systems is obtained. Furthermore, and based on the obtained condition, the mode-dependent FDF that ensures the stochastic stability and a prescribed H ∞ performance level of the corresponding augmented system is designed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show usefulness of the designed mode-dependent FDF. [ABSTRACT FROM AUTHOR]

This paper is concerned with chaotic stabilization analysis for a class of memristive neural networks (MNNs) with the effects of neutral delay and time-varying delay. We introduce a time-varying delay into reliable controller to enhance the model, while actuators experience failure signals. Sampled-data controller and reliable time-varying controller are implemented using input-delay approach and linear matrix inequality (LMI) approach. The main analysis of this present work is to utilize Lyapunov stability theory, differential inclusion theory and set-valued maps. By constructing a proper Lyapunov functionals, some sets of sufficient conditions are achieved in terms of LMIs. The considered MNNs with actuator fault guarantee the global asymptotic stability for known and unknown actuators cases. The process of congruence transformation has been applied to reliable time-varying controller to get a gain matrix. Finally, numerical examples demonstrate the less conservatism and effectiveness of the proposed results via MATLAB simulations. [ABSTRACT FROM AUTHOR]

Fast finite-time consensus problem of multi-agent systems under diverse topologies is investigated by a hybrid linear and fractional power protocol, where the linear item improves convergence performance when the state is far away from the equilibrium, and the fractional power one accelerates convergence process when the state is close to the equilibrium. Then a faster convergent rate is achieved in comparison with the individual asymptotic or finite-time consensus protocol. The leaderless multi-agent systems are firstly studied under undirected topology, and then it is extended to the leader-following case under the directed networks. Based on finite-time stability theory, the state consensus tracking errors are guaranteed to be zero within an upper bound of settling time. Finally, numerical simulations are presented to demonstrate the effectiveness and performance of the protocols. [ABSTRACT FROM AUTHOR]

Since the fixed-time stability forms of nonlinear systems satisfy strict conditions, there are few general forms for nonlinear systems to achieve fixed-time stability. This work proposes a new class of more general fixed-time stability criteria. It is worth mentioning that, compared with the traditional method of estimating the convergence time, this paper obtains a more conservative stable time estimation formula through the integration method of the generalized integral mean theorem. In addition, given that the fixed-time stabilization of neural networks and chaotic oscillators have attracted extensive attention in recent years, and there are still many fixed-time stabilizations of nonlinear systems that have not been studied. Therefore, a discontinuous controller is designed in this paper. The above stability theory results are applied to the fixed-time stabilization of the Takagi-Sugeno (T-S) fuzzy competitive neural network and chaotic system (coupled Chua's oscillator). Finally, the validity and applicability of the theoretical results are verified by examples. [ABSTRACT FROM AUTHOR]

Activities aimed at studying stabilization of a high-speed boundary layer with the use of porous coatings are reviewed. All types of coatings used in experimental research are considered. It is demonstrated that a porous coating with optimal parameters can stabilize the second mode of disturbances to a large extent and delay the laminar–turbulent transition in a high-speed boundary layer. A review of numerical investigations of porous coatings is presented, and it is shown that special boundary conditions are imposed for porous coating modeling; otherwise, the flow has to be calculated in each pore of the coating. The major part of results obtained on the basis of the linear stability theory and in direct numerical simulations agree well with experimental data. Examples of methods of porous coating optimization and of using promising metamaterials are provided. [ABSTRACT FROM AUTHOR]

In this paper, we develop a nonlinear theory of self-oscillatory solidification mode during directional crystallization in the presence of a quasi-equilibrium two-phase region of constitutional supercooling. This study is based on the linear stability theory (Part 1), where we demonstrated that the indicated regime can be formed due to the oscillatory instability at certain values of physical and operating parameters of the system. The development of oscillatory instability is based on a new frontal model of crystallization with a two-phase region, the main feature of which is the replacement of real two-phase region by a discontinuity surface between purely solid and liquid phases. We derive a nonlinear system of equations for determining frequencies and amplitudes of perturbations responsible for the development of oscillatory instability. The solution of this system allows one to analytically determine the fundamental and secondary harmonics of perturbations and calculate the resulting self-oscillations of the crystallization velocity and impurity distribution. The impurity concentration and period of its layered distribution in the solid phase are in good agreement with experimental data. [ABSTRACT FROM AUTHOR]

We present the new (for Mach numbers М = 3 and 3.5) and generalizing (for Mach numbers from 2 to 4) results of experimental investigations on the effect of small angles of attack on laminar-turbulent transition in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The angle-of-attack variation has a strong effect on the transition Reynolds number. The transition Reynolds number decreases with increase in the Mach number. The measurements were carried out by means of a constant-temperature hot-wire anemometer using the proven procedure of determining the transition location. The eN method is used for the first time for numerically estimating the transition Reynolds numbers in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The growth of the amplitudes of the steady and unsteady modes of the boundary layer crossflow are calculated in accordance with the linear stability theory, within the framework of the Lees–Lin system of equations. The numerical results indicate that, in accordance with the experimental results, laminar-turbulent transition in the boundary layer on the model swept wing is governed by the growth of stationary modes of the crossflow instability. [ABSTRACT FROM AUTHOR]

An adaptive fault-tolerant anti-rollover fuzzy system is proposed to improve the anti-rollover performance of counterbalanced forklifts. Considering the actual control input, various unpredictable actuator failure models in the system are established. Based on the three degree-of-freedom (DOF) model of a counterbalanced forklift, an anti-rollover Takagi-Sugeno (T-S) fuzzy system is established. The stability of this anti-rollover system is analyzed to ensure its stability under specific control inputs and external disturbances. When the upper limits of actuator faults and disturbances are unknown, an adaptive fault-tolerant control method is designed to update the controller parameters. The sufficient conditions for the stability of the forklift anti-rollover system in the presence of actuator faults and external disturbances are given using the Lyapunov stability theory. Simulation and real vehicle tests based on MATLAB/Simulink show that the anti-rollover system with adaptive fault-tolerant control can reduce impacts effectively and quickly after the actuator fails, thereby improving the safety and reliability of the forklift. [ABSTRACT FROM AUTHOR]

In this paper, we study the almost sure boundedness and the convergence of the stochastic approximation (SA) algorithm. At present, most available convergence proofs are based on the ODE method, and the almost sure boundedness of the iterations is an assumption and not a conclusion. In Borkar and Meyn (SIAM J Control Optim 38:447–469, 2000), it is shown that if the ODE has only one globally attractive equilibrium, then under additional assumptions, the iterations are bounded almost surely, and the SA algorithm converges to the desired solution. Our objective in the present paper is to provide an alternate proof of the above, based on martingale methods, which are simpler and less technical than those based on the ODE method. As a prelude, we prove a new sufficient condition for the global asymptotic stability of an ODE. Next we prove a "converse" Lyapunov theorem on the existence of a suitable Lyapunov function with a globally bounded Hessian, for a globally exponentially stable system. Both theorems are of independent interest to researchers in stability theory. Then, using these results, we provide sufficient conditions for the almost sure boundedness and the convergence of the SA algorithm. We show through examples that our theory covers some situations that are not covered by currently known results, specifically Borkar and Meyn (2000). [ABSTRACT FROM AUTHOR]

An extensive number of processes require liquid jets such as cleaning, waterjet cutting, hydroentanglement, and atomization in combustion. The coherence and stability of the jet highly depend on the characteristics of the nozzle. Jet breakup lengths have been extensively studied for a multitude of nozzle characteristics and external stimuli, yet jets issuing from deformable, elastic nozzles have not been considered. In this study, we take the enduring topic of jet breakup into a new realm by introducing nozzles that passively deform when exposed to liquid flow by making an approximately 500 μ m orifice in thin sheets. We perform the experiments with nozzles of varying hardness and thickness, starting with a rigid BeCu nozzle, and continuing with shore hardness 70A, 65A, 35A and 20A. We observe nozzle dilation scales well with Reynolds number and that softer nozzles experiences greater dilation, as expected. We introduce a modification to linear stability theory to describe the break-up length of deformable nozzles to account for the dilation, a scaling which works best for our stiffer nozzles. The three softest materials provide the most stable jets through the range of flow rates in which they can operate before failure. For all nozzles, breakup is highly variable with time and jet velocity. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced a novel five-dimensional (5D) hyperchaotic system by extending the well-known Lorenz system. The dynamical properties of the system are analysed by calculating the Lyapunov exponents, graphing the phase portraits, bifurcation diagrams, the time series and by finding the Kaplan–Yorke dimension. The equilibrium points of the system have been calculated and the stability analysis of these equilibrium points is discussed. Hybrid function projective synchronisation has been carried out between the identical systems using the scheme of adaptive control. Suitable controllers have been designed to attain the desired synchronisation between the systems using Lyapunov stability theory. The theoretical results have been validated by performing numerical simulations using the MATLAB. [ABSTRACT FROM AUTHOR]

This paper proposes a fractional-order adaptive backstepping control (FOABC) with disturbance and uncertainty terms compensation for improving the MPPT (maximum power point tracking) performance and output power quality of a doubly fed induction generator (DFIG)-based wind turbine. In the proposed high-efficacy controller, disturbance and uncertainty terms are estimated in real time using an adaptive estimator designed using a recursion design process based on the nonlinear backstepping control. Meanwhile, a robust compensator is schemed and incorporated into the backstepping control algorithm so that it suppresses the effects of external disturbances and system uncertainties and, as a result, ensures the maximum wind energy extraction as much as possible, which is usually well known as MPPT. Furthermore, the fractional-order control approach was deployed in the proposed adaptive backstepping controller to provide a smooth control signal for enhancing the quality of the power injected into the grid. The stability analysis of the overall closed-loop system was performed using Lyapunov's stability theory. The high effectiveness of the proposed control method was assessed through simulation studies carried out in MATLAB/Simulink of a DFIG-wind turbine operating in various conditions. [ABSTRACT FROM AUTHOR]

A problem of the fracture of a semi-infinite body with a penny-shaped crack located near the surface of the body under compressive loading along the crack was considered. It is assumed that the fracture process under such loading scheme is initiated by a local buckling of a part of the material adjacent to the crack. The case of a short distance between the surface of the body and the crack plane was analyzed. To study this problem, the approach in the framework of 3D linearized theory of stability of deformable bodies was applied. The technique based on Bubnov–Galerkin method to investigate resolving Fredholm integral equations of the second kind was also used. The critical (limiting) loading parameters corresponding to the local buckling of the material in the cracks vicinity under compression were calculated for some types of highly elastic materials and composites. The dependence of these critical parameters on the distance between the surface of the body and the crack plane was studied. The results obtained give the possibility to evaluate the applicability limits of the approximate approach, so called "beam approximation", in the analysis of this problem. [ABSTRACT FROM AUTHOR]

In this work, the problem of adaptive neural control for nonlinear systems with input nonlinearities and sensor fault in non-strict feedback form is addressed. Input saturation and dead-zone exist in the nonlinear system simultaneously. The impact of external disturbances and sensor fault in nonlinear systems is considered. To approximate the unknown functions in the system, radial basis function neural networks are used. An adaptive neural controller is developed by using the approximation ability of the neural networks and the backstepping method. Based on Lyapunov stability theory, the proposed control method ensures that all signals in the closed-loop system are semi-globally uniformly ultimately bounded and that the output of the system follows the reference signal within a bounded error. Finally, to demonstrate the effectiveness of the proposed control method, one numerical example and a real-life example about an electromechanical system are provided. [ABSTRACT FROM AUTHOR]

This paper investigates finite-time mean square average consensus of second-order multi-agent systems, where connected typologies are directed and subject to Markovian switching, agents dynamics are nonlinear and interrupt by impulses. In order to eliminate the chattering phenomenon in finite-time control, we propose a protocol without sign function, that contains neighborhood and self state feedbacks. Also, by employing graph theory, some graph-related matrices are formed to analyze directed switching topologies. Then, expectations of multi-agent systems energy evolution are bounded in both continuous and discontinuous time by using stochastic and discontinuous stability theories. In this basis, sufficient finite-time mean square consensus criteria are established and their settling times are obtained. Simulation examples prove the theoretical results are correct and the finite-time protocol is valid. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy control approach for incommensurate fractional-order multi-input multi-output (MIMO) systems with unknown nonlinearities and input saturation is presented. First, the nonlinear terms of MIMO systems are identified by introducing the fuzzy logic systems, and an adaptive compensating control term is provided to estimate the approximation errors. Then, the drawback of "explosion of complexity" in the typical backstepping is effectively figured out via an improved command filter, and the influence of filtered error is avoided by constructing the error compensation laws. Meanwhile, the input saturation issue is addressed by utilizing the fractional-order auxiliary equations. Derived from the fractional-order Lyapunov stability theory, it is proved that all signals of the closed-loop system are guaranteed to be bounded. Finally, the availability of the investigated control scheme is verified by simulation examples. [ABSTRACT FROM AUTHOR]

The linearization of semiclassical theories of gravity is investigated in a toy model, consisting of a quantum scalar field in interaction with a second classical scalar field which plays the role of a classical background. This toy model mimics also the evolution induced by semiclassical Einstein equations, such as the one which describes the early universe in the cosmological case. The equations governing the dynamics of linear perturbations around simple exact solutions of this toy model are analyzed by constructing the corresponding retarded fundamental solutions, and by discussing the corresponding initial value problem. It is shown that, if the quantum field which drives the back-reaction to the classical background is massive, then there are choices of the renormalization parameters for which the linear perturbations with compact spatial support decay polynomially in time for large times, thus indicating stability of the underlying semiclassical solution. [ABSTRACT FROM AUTHOR]

Theoretical assessments of the crossflow (CF) stabilization due to flow slip produced by small grooves on a swept supersonic wing are performed using the linear theory for inviscid flow, the local similar approximation of the boundary layer flow, the slip boundary conditions on the grooved surface and the linear stability theory. The e N computations for stationary CF mode predict that spanwise-invariant grooves with their half-period equal to 0.25 of the boundary-layer displacement thickness can delay the CF-induced transition onset by about 10% on a 30 ∘ swept wing having a parabolic airfoil of 5% thickness ratio, at freestream Mach number 2. It is concluded that the groove laminarization concept deserves further studies. [ABSTRACT FROM AUTHOR]

This article investigates the observer-based finite-time adaptive neural network control for the permanent magnet synchronous motor (PMSM) system. The addressed PMSM system includes unknown nonlinear dynamics and constraint immeasurable states. The neural networks are utilized to approximate the unknown nonlinear dynamics and an equivalent control design model is established, by which a neural network state observer is given to estimate the immeasurable states. By constructing barrier Lyapunov functions and under the framework of adaptive backstepping control design technique and finite-time stability theory, a finite-time adaptive neural network control scheme is developed. It is proved that the proposed control scheme ensures the closed-loop system stable and the angular velocity, stator current and other state variables not to exceed their predefined bounds in a finite time. Finally, the computer simulation and a comparison with the existing controller are provided to confirm the effectiveness of the presented controller. [ABSTRACT FROM AUTHOR]

In this paper, a strategy involving the combination of optimal discrete-time sliding-mode control and recurrent neural networks is proposed for a class of uncertain discrete-time linear systems. First, a performance index based on the reaching law and the control signal is defined. Then, the constrained quadratic programming problem is formulated considering the limitations on the control signal as the static constraint. The dynamic and algebraic model of the neural network is derived based on the optimization conditions of the quadratic problem and their relationship with the projection theory. The proposed method prevents the chattering by selecting proper parameters of the twisting reaching law. The convergence of the neural network is analysed using the Lyapunov stability theory. A singular value-based analysis is employed for robustness of the proposed method. The stability conditions of the discrete-time closed-loop system are analysed by studying eigenvalues of the closed-loop matrix using the singular value approach. The performance of the proposed algorithm is assessed in simulated example in terms of chattering elimination, solution feasibility, and encountering uncertainties and is compared with the recently proposed DSMC methods in the literature. [ABSTRACT FROM AUTHOR]

Using Pyatnitskiy's convolution theorem, the circle criterion of absolute stability for Lurie systems with several nonlinearities is obtained without use of the S-lemma. For connected systems with switching between three linear subsystems, a new criterion for the existence of a quadratic Lyapunov function is proposed. On the basis of the convolution theorem, two theorems are proved which lead to a substantial reduction in the dimensionality of connected systems of linear matrix inequalities. Issues of improving the circle criterion for Lurie systems with two nonlinearities are also discussed. [ABSTRACT FROM AUTHOR]

A class of nonlinear systems with unknown input power is discussed about their tracking control problem in this paper. To guarantee that the output of this system can converge asymptotically to the reference signal, a robust adaptive control method is proposed. Based on Lyapunov stability theory, it is proven that the tracking error asymptotically converges to an adjustable neighborhood of the origin. The method improves some inadequacies of existing results and relaxes several assumptions imposed on the system. Finally, the viability and effectiveness of the control method presented in this paper are verified by performing numerical simulations. [ABSTRACT FROM AUTHOR]

The rock slopes along the Sichuan–Tibet railway are characterized by noncontactless, inaccessible, dramatically fluctuating topography and large-scale areas. Numerous high-position, concealed dangerous rock blocks (HPCDRBs) are located on such slopes, potentially threatening the construction and safety operation of the Sichuan–Tibet railway. To this end, a new framework is proposed for geometrical investigation and stability analysis of HPCDRBs. The main steps of the framework are: (1) establishment of a three-dimensional high-resolution rock surface model using a new unmanned aerial vehicle-based photography method; (2) identification of possible HPCDRBs based on the theory of structure-controlled rock mass; (3) geometrical characterization of possible HPCDRBs utilizing polyhedral models; and (4) application of block theory for the stability analysis of possible HPCDRBs. In this framework, the actual positions and geometric information of these blocks are well-reflected, and the obtained parameters can directly serve the stability analysis. The proposed method is applied to an ultrahigh-steep rock slope located on the left bank of the Kang Yu Qu (KYQ) Bridge of the Sichuan–Tibet railway. A total of 40 HPCDRBs with volumes between 2.1 and 148.2 m3 are determined, and the geometric shapes are mainly hexahedron and heptahedron. The mean sliding orientation of these blocks is 124.6°∠51.4°. A seismic stability analysis is finally conducted to further discuss the stability of the HPCDRBs under a real earthquake. In summary, the collapse of the unstable HPCDRBs may cause single block falls which pose a potential threat to the KYQ Bridge. [ABSTRACT FROM AUTHOR]

This study concerned with the synchronization problem over a finite-time domain for a class of fractional-order stochastic neural networks via non-fragile controller with discontinuous activation functions. Specifically, the suggested state feedback controller sequentially cope with non-fragile scheme for gain scheduling process. Notably, the main objective of this work is to obtained the finite-time synchronization criterion for the resulting synchronized error system over finite bound with the developed non-fragile controller. For that, some consignment of sufficient conditions is derived systematically by implementing Lyapunov's indirect method and finite-time stability theory which ensures the finite-time stochastic synchronization of the stipulated neural networks. Later on, the controller gain fluctuations that obeying certain white noise sequels derived from Bernoulli distribution are formulated in terms of linear matrix inequalities. Eventually, the illustrated study are substantiated through two numerical examples and the simulation results manifest the advantage and accuracy of the proposed synchronization criteria. [ABSTRACT FROM AUTHOR]

The investigation of differential-algebraic boundary-value problems was originated in the works by Weierstrass, Luzin, and Gantmakher. The works by Campbell, Boyarintsev, Chistyakov, Samoilenko, Perestyuk, Yakovets, Boichuk, Ilchmann, and Reis were devoted to the systematic study of differential-algebraic boundary-value problems. At the same time, the investigation of differential-algebraic boundary-value problems is closely connected with the analysis of linear boundary-value problems for ordinary differential equations originated in the works by Poincaré, Lyapunov, Krylov, Bogolyubov, Malkin, Myshkis, Grebenikov, Ryabov, Mitropolskii, Kiguradze, Samoilenko, Perestyuk, and Boichuk. The investigation of linear differential-algebraic boundary-value problems is connected with numerous applications of the corresponding mathematical models to the theory of nonlinear oscillations, mechanics, biology, radio-engineering, and the theory of stability of motion. Thus, the problem of generalization of the results obtained by Campbell, Samoilenko, and Boichuk to the case of nonlinear integrodifferential boundary-value problems unsolved with respect to the derivative is quite actual. In particular, this is true for the problem of finding necessary and sufficient conditions for the existence of solutions of nonlinear integrodifferential boundary-value problems unsolved with respect to the derivative. In the present paper, we establish conditions for the existence of solutions of the nonlinear integrodifferential boundary-value problem unsolved with respect to the derivative and present a constructive scheme for their finding. [ABSTRACT FROM AUTHOR]

To achieve accurate contour tracking of robotic manipulators with system uncertainties, external disturbance and actuator faults, a cross-coupling contour adaptive nonsingular terminal sliding mode control (CCCANTSMC) is proposed. A nonsingular terminal sliding mode manifold is developed which eliminates the singularity completely. In order to avoid the demand of the prior knowledge of system uncertainties, external disturbance and actuator faults in practical applications, an adaptive tuning approach is proposed. The stability of the proposed control strategy is demonstrated by the finite-time stability theory. Then, the developed controller combines adaptive nonlinear terminal sliding mode control (ANTSMC) of joint trajectory tracking and proportion–differentiation control of end-effector contour tracking by introducing the coupling factor between multiple axes based on Jacobian. Moreover, a unified framework of cross-coupling contour compensation and reference position pre-compensation is built. Finally, numerical simulation and experimental results validate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

The concept of P-stability is a particular case of generalized stability of complete theories. We study injective S-acts with a P-stable theory. It is proved that the class of injective S-acts is (P, 1)-stable only if S is a one-element monoid. Also we describe commutative and linearly ordered monoids S the class of injective S-acts over which is (P, s)-, (P, a)-, and (P, e)-stable. [ABSTRACT FROM AUTHOR]

This study deals to investigate a diverse collection of optical solitons and others solutions to fiber Bragg gratings with dispersive reflectivity having Kerr law of nonlinear refractive index. Bragg gratings are no doubt a technological spectacle that sustained balance between dispersion and nonlinear effects that leads to a stable transmission of solitons across transnational distances. Two recently established norms extended sine–cosine/sinh–cosh and generalized exponential rational function method are capitalizing to formulate bright, dark, singular, combo, complex and exponential solutions. The stability analysis of the studied model is also examined by utilizing linear stability theory. By selecting suitable parametric values, the dynamics of the evaluated results are exemplified by sketching their 2D, 3D and contour profiles. The novelty of the gained outcomes is manifested by a detailed comparison with the results that already exist. The applied computational approaches are concise, outspoken and reliable which lessen the tedious computational work and give it a wide range of applicability. [ABSTRACT FROM AUTHOR]

In this work, we investigate two types of boundary value problems for a system of coupled Atangana–Baleanu-type fractional differential equations with nonlocal boundary conditions. The fractional derivatives are applied to serve as a nonlocal and nonsingular kernel. The existence and uniqueness of solutions for proposed problems using Krasnoselskii's and Banach's fixed-point approaches are established. Moreover, nonlinear analysis is used to build the Ulam–Hyers stability theory. Subsequently, we discuss two compelling examples to demonstrate the utility of our study. [ABSTRACT FROM AUTHOR]

The online solving of a dynamic linear complex matrix equation (DLCME) is commonly encountered in many fields, and it exists for lots of engineering applications. For solving the DLCME, the gradient neural dynamics (GND) and the zeroing neural dynamics (ZND) are usually designed based on a predefined error function in scalar or matrix form to monitor the residual error convergence, respectively. In this paper, in order to improve the adaptability as the residual error decreasing with time and to release the limitation of convex activation function, an improved zeroing neural dynamics (IZND) model is proposed with a residual-based adaptive coefficient and a non-convex activation function. By using the Lyapunov stability theory, the global convergence and noise suppression of the proposed IZND model are theoretically discussed under the noise-free and noise-perturbed circumstances. Then, simulative verifications and a dynamic acoustic source localization application illustrate the efficacy and superiority of the proposed model for solving the DLCME. Comparing with some existing GND and ZND models, the proposed IZND model shows advanced performance in solution accuracy, noise suppression and convergence rate. [ABSTRACT FROM AUTHOR]

In this paper we study the robustness of the exponential dichotomy in nonautonomous linear ordinary differential equations under integrally small perturbations in infinite dimensional Banach spaces. Some applications are obtained to the case of rapidly oscillating perturbations, with arbitrarily small periods, showing that even in this case the stability is robust. These results extend to infinite dimensions some results given in Coppel (Dichotomies in stability theory. Lecture notes in mathematics, Springer, Berlin, 1970). Based in Rodrigues (Invariância para sistemas de equações diferenciais com retardamento e aplicações, Tese de Mestrado, Universidade de São Paulo, São Carlos, 1970) and in Kloeden and Rodrigues (Nonlinear Anal 74:2695–2719, 2011), Rodrigues et al. (Stability problems in non autonomous linear differential equations in infinite dimensions. arXiv:1906.04642, 2019) we use the class of functions that we call Generalized Almost Periodic Functions that extend the usual class of almost periodic functions and are suitable to model these oscillating perturbations. We also present an infinite dimensional example of the previous results. [ABSTRACT FROM AUTHOR]

Based on the concept of radius-dependent surface tension (ST), two physically different theories of the stability of bulk nanobubbles (BNB) – the theory of electrostatic pressure (EP) and the theory of adsorption of surfactants – are combined. The obtained analytical expressions allow to calculate the radius of stationary BNB at different dissolved gas saturation levels. [ABSTRACT FROM AUTHOR]

This study examines the magnetic effect on Darcy Brinkman convection in a Bidispersive horizontal porous layer, considering the importance of convective motions of electrically conducting porous media accompanying a magnetic field in real-life applications such as geophysics, metallurgical field and solidification structures. In order to conduct a thorough study, the boundaries are classified as free-free, rigid-free, and rigid-rigid. The fluid motion is described using the Brinkman-Darcy equation with a single temperature in the macropores and micropores. The eigenvalue problem is solved analytically for the free-free case by employing linear stability theory. A non-linear analysis using the energy method is undertaken to prove that linear instability and global non-linear stability thresholds are the same. The eigenvalue problem for rigid-free and rigid-rigid boundaries is numerically solved with the bvp4c routine in MATLAB R2020 with the Rayleigh number as the eigenvalue. It is found that the Hartmann number M 2 , Darcy number Da, permeability ratio κ r , and momentum transfer coefficient γ stabilize the system. Rigid-rigid boundaries are found to be the most stable ones, followed by rigid-free and free-free, which are the least stable boundaries. [ABSTRACT FROM AUTHOR]

In this work, the identical and reduced-order synchronizations between four different Josephson junction models are studied. First, we realized the synchronization between two Resistive–Capacitive–Inductive-Shunted Junction (RCLSJ) models taking into account its non-harmonic dynamics of the junction current I J using the backstepping technique. Next, we showed that this third-order Josephson model can be synchronized with three other second-order Josephson models using both the feedback control technique and Lyapunov's stability theory for different values of the non-harmonicity constant. [ABSTRACT FROM AUTHOR]

The three-dimensional linearized theory of stability and the piecewise homogeneous medium model are used to analyze the near-surface buckling of a layered composite material in an inhomogeneous subcritical state associated with the edge effect in the vicinity of the surface load. The case of imperfect contact between layers modeled by a periodic system of interlayer cracks in the form of a mathematical cut with stress-free edges is considered. The effect of the crack size on the stress decay length, critical loads, and buckling modes is studied. A mesh-based method based on a modified variational-difference approach is used for numerical solution of the problem. The computational experiment uses the sequential and parallel algorithms of the Cholesky method to solve the system of linear algebraic equations and the subspace iteration method to solve the generalized eigenvalue problem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of nonlinear MIMO systems based on prescribed-time sliding mode control (PTSMC). In an effort to extend the concept of fixed-time theory with capability of handling more practical systems, we have developed a PTSMC based on the free-will arbitrary time (FWAT) principle of stability. We propose the FWAT sliding surfaces to improve the convergence of a nonlinear system, what is known as arbitrary convergence in control theory. According to the proposed sliding surface, the states of a system can reach the sliding surfaces (arbitrary reaching phase) within a given time interval and also can hit the origin within a predefined time (arbitrary sliding phase). Using this method, the overall stabilization time can be adjusted freely to suit the needs of the designer. Furthermore, this control method is capable of being implemented independent of any other system parameters. Lyapunov stability theory shows the stability of the proposed control scheme and the designed sliding surfaces. Finally, the efficiency of the proposed approach is demonstrated by performing on two well-known examples such that it verifies the arbitrary convergence of the designed sliding surfaces for various times in spite of revealing the designed control independency of any initial values. [ABSTRACT FROM AUTHOR]