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This paper addresses the adaptive output feedback control design problem for a class of nonlinear systems with unknown state time delays by combining the dynamic gain and neural network. A novel reduced-order dynamic gain observer is introduced to estimate the unmeasured system states. Radial basis function neural networks (RBF NNs) are used to approximate unknown functions. An adaptive NN output feedback controller is designed based on the backstepping technique. By arranging the proper Lyapunov–Krasovskii functional, we prove that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, a physical example and a numerical example are given to prove the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, by using bound estimation method, Nussbaum function, K‐filters and higher‐order Lyapunov function, an adaptive output feedback compensation control scheme is proposed for uncertain nonlinear systems with infinite number of actuator failures and unknown control direction. A parametric model with unknown system uncertainties and infinite actuator failures is established, which is different from the existing results. This scheme ensures that closed‐loop signals are globally uniformly bounded. By properly selecting the design parameters, the tracking errors converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate its efficiency of the proposed design scheme. [ABSTRACT FROM AUTHOR]

In this paper, asymptotic stabilization problem for a class of nonlinear systems with unknown time‐varying delays is addressed. With the introduced static gain functions and new Lyapunov–Krasovskii functionals, a novel output feedback control strategy is developed. A memoryless output feedback controller which does not need precise knowledge of time delays is designed. The asymptotic stabilization and the boundedness of the closed‐loop system are proved via Lyapunov analysis. Finally, numerical simulation validates the effectiveness of this method for the nonlinear time‐delay system. [ABSTRACT FROM AUTHOR]

Summary: This article develops a disturbance rejection control strategy using partial‐state feedback model reference adaptive control for discrete‐time uncertain systems with unknown input disturbances. Adaptive control schemes are proposed for constant disturbances, sinusoidal disturbances, and generic bounded disturbances. The partial‐state feedback control is designed based on measurable signals and the parameterization method to counteract the effect of disturbances. The plant‐model output matching condition is established. The developed control law is more flexible for applications and has a more concise structure than output feedback control. Additionally, closed‐loop stability and asymptotic output tracking are derived. The effectiveness and the feasibility of partial‐state feedback disturbance rejection control are verified by simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inverse source problem for the helium production-diffusion equation. That is to determine a space-dependent source term in the helium production-diffusion equation from a noisy final data. Since the problem is ill-posed, we propose an effective iterative scheme to deal with the problem. More specifically, we use an acceleration technique to speed up a simple iterative scheme. We also give two kinds of convergence rates by using an a priori and a posteriori regularization parameter choice rule, respectively. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the output-feedback control problem for a class of nonlinear time-delay systems has been considered. Unmeasured system states and the time-varying delays which appear in all state variables bring great challenges to the controller design. Novel Lyapunov–Krasovkii functionals with control gains are proposed for a delay-independent controller. The system is proved to be asymptotically stable driven by the controller with suitable design parameters. Finally, we apply the new control scheme to a two-stage chemical reactor system and the time-delay tension leg platform system, the effectiveness of the control scheme is illustrated in the simulation results. [ABSTRACT FROM AUTHOR]

It is crucial to obtain better fatigue property for the safe application of materials, while nature provides new structural design ideas for effectively improving fatigue property. In this study, a "soft‐hard" alternating bionic structure was fabricated on the surface of TIG welded AZ31B Mg alloy joints by laser bionic treatment (LBT). Microstructure of welded joints was tailored by LBT, resulting in fine equiaxed grains with random orientations and increased microhardness. The fatigue crack growth threshold of the welded joints with bionic structure is increased by more than 40%, and crack growth rate was lower. LBT could significantly affect crack growth behavior and presented obvious crack deflection, resulting in a rougher fracture surface and more second cracks and branches. LBT significantly improved the fatigue crack growth resistance, inducing a series of strengthening mechanisms. The present work opens a new alternative to improve the fatigue properties of welded joints. Highlights: "Soft‐hard" alternating structure was formed in joints by laser bionic treatment (LBT).The refined grains coupled with coarser grains provide the ideal microstructure.Fatigue crack growth resistance of welded joints was improved significantly by LBT.Strengthening mechanisms induced by LBT were discussed. [ABSTRACT FROM AUTHOR]

In this article, adaptive state feedback stabilization is addressed for a class of delayed uncertain systems with external disturbance, where the time delays and the bound parameters of the delayed states and disturbance are assumed to be unknown. By introducing a new Lyapunov–Krasovskii functional, we present a memoryless control strategy to stabilize nonlinear time-delay systems through newly defined control gain function. The main contribution of this article lies in the construction of control gain function. Multiple gain functions can be revealed in a function set. The asymptotic stability of the closed delayed nonlinear system is ensured. Simulation examples are presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article deals with the adaptive prescribed performance tracking for nonlinear time-varying systems. To handle multiple unknown control directions, a novel lemma is established by using a general class of Nussbaum functions. To handle unknown time-varying parameters, the congelation of variables method is employed. Different novel functions are introduced to achieve prescribed performance tracking and finite-time prescribed performance tracking, respectively. Meanwhile, the problem of explosion of complexity is avoided by utilizing the command filter and the compensation mechanism. For reasons of saving network resources and reducing communication burden, a new event-triggered mechanism is proposed, which can circumvent the Zeno behavior. Then, an event-triggered adaptive prescribed performance tracking control scheme is constructed and is extended to event-triggered finite-time adaptive prescribed performance tracking, both of which guarantee that all closed-loop signals are bounded and the trajectory of the tracking error can be limited to the prescribed region. Finally, the availability of the control scheme is demonstrated by two examples. • A new Nussbaum lemma is tailored for nonlinear time-varying systems with multiple unknown control directions. • New performance transformation functions are designed to achieve asymmetric global prescribed performance tracking. • The command filter and a novel error compensation scheme are constructed to handle the explosion of complexity. • The congelation of variables method is adopted to cope with unknown time-varying parameters. • An STETS adaptive prescribed performance tracking controller is constructed, which can avert the Zeno behavior successfully. [ABSTRACT FROM AUTHOR]

For a class of nonlinear systems with mismatched time delays and disturbances, robust adaptive stabilization control is studied. The control law is split into two terms. One is used to cope with the delayed states, and the other is to handle the disturbance. The improved robust adaptive laws with control gain function and time-varying σ -modification are constructed to estimate the unknown integrated parameters. It is proved that the designed adaptive controller can ensure the asymptotic convergence of the closed-loop system states. Another adaptive algorithm is also proposed to ensure the asymptotic stability of the closed delayed nonlinear system without external disturbance. • We introduce control gain function ρ (⋅) and embed it into the Lyapunov–'Krasovskii functional. • Continuous memoryless control functions are designed. • The theoretical result is applied to chemical reactor. [ABSTRACT FROM AUTHOR]

In this article, tracking control is considered for a class of uncertain multi-input–multi-output (MIMO) nonlinear systems, where the time-varying parameters, the time-varying control coefficient and the time-varying disturbance are assumed to be unknown but to be bounded. Three stable adaptive tracking schemes for a given reference signal are proposed by devising different control algorithms. In the first scheme, bounded-error tracking is achieved in the sense that the tracking error converges exponentially to an adjustable region around the origin, where the $\sigma $ -modification adaptive laws are used to ensure the boundedness of all closed-loop signals. In the second scheme, asymptotic tracking is obtained in the sense that the tracking error converges to zero asymptotically, where the strictly positive and integral functions are employed in the control law to ensure the signal boundedness and zero-error tracking. In the third scheme, exponential tracking is gotten in the sense that the tracking error exponentially converges to zero with a given convergence speed, where exponential functions are incorporated into control law and adaptive laws to ensure system stability and the faster convergence. Three adaptive tracking schemes are, respectively, applied to nonlinear chaotic Chua’s circuit with control inputs. The parametric model is developed for Chua’s circuit with uncertain parameters and external disturbances. The effectiveness of the proposed control algorithms is demonstrated by comparative simulation studies. [ABSTRACT FROM AUTHOR]

This article investigates the problem of finite-time stability and stabilisation (FTSS) in time-varying stochastic systems with multiplicative noise and time-delays. To simplify research process, the method of dimension expansion is employed to transform systems characterised by constant delays into delay-free models, which enables the extraction of the finite-time stability (FTS) of the original systems by leveraging the FTS analysis conducted on the new model. Two distinct approaches are employed to establish criteria for determining FTSS in systems. The first approach leverages the state transition matrix (STM) method to acquire both necessary and sufficient stability conditions for the simplified models. Furthermore, sufficient conditions for the FTS of the original systems can be obtained. For ease of verification, our second approach integrates the Lyapunov equation with linear matrix inequalities (LMIs), offering a framework to obtain control gains. Finally, the proposed results are instantiated through three simulation examples to demonstrate their efficacy. [ABSTRACT FROM AUTHOR]

This paper presents a strategy of inexact predictor-feedback control for multi-input nonlinear systems with distinct delays. The controllers designed by an inexact predictor robustly compensate for the different delays. Different from exact predictor feedback, we propose a scheme that can achieve exponential stability of the system without accurately compensating for each delay and has the property of less complexity. For this purpose, we adopt a fixed constant as the prediction horizon, which is restricted to being within a sufficiently narrow range. Its function is to offset the partial effect of each delay. With a new Lyapunov-Krasovskii functional based on an infinite-dimensional backstepping transformation, we prove the global exponential stability of the closed-loop system. Finally, a numerical example is presented to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The paper is concerned with the stability of linear time-invariant (LTI) systems with distinct multi-input unknown delays. Our method is based on transport partial differential equations (PDEs) representation of the multi-input delays and infinite-dimensional backstepping transformation. By introducing the new Lyapunov–Krasovskii functional, exponential stabilization of the closed-loop system is achieved, in which fixed constant horizon prediction-based controllers are introduced to robustly compensate for the different delays. There are two control designs proposed: single-constant and multi-constant horizon prediction-based control design. For the latter, we introduce special infinite-dimensional backstepping transformation, backstepping-forwarding transformation, to offset delays from small to large. In particular, constants selection are required to be within a narrow enough range. At last, to illustrate the validity of the proposed results, a numerical example is provided. [ABSTRACT FROM AUTHOR]

The single crystal diamond (SCD) has great potential in the application of optical windows, photoelectric devices, semiconductors and other fields owing to its excellent performance in optics, mechanics, and thermotics. The SCD was homoepitaxially deposited on High Pressure and High Temperature (HPHT) seed substrate through microwave plasma chemical vapor deposition (MPCVD) method using CH4/H2 as the reaction gas. Hydrogen plasma treatment was proposed to pretreat the seed crystal. The top surface of the epitaxial layer of SCD has a creased morphology and no polycrystalline rim growth on the side. The results showed that the transmittance of the epitaxial SCD film was primarily affected by the surface roughness, which was mainly influenced by the growth time. The photoluminescence at 738 nm was attributed to the silicon color center in the grown SCD, suggesting the application in optoelectronic devices. [ABSTRACT FROM AUTHOR]

In this study, the decentralized model reference adaptive control (DMRAC) problem is tackled for a class of time‐varying delay interconnect systems that comprise unknown system matrices and unknown dead‐zone inputs. Two robust adaptive control methods are proposed for state tracking based on the moderate matching time‐varying delay nonlinear assumptions and the matching between the controlled system and reference model matrices, respectively. The control gain function is explicitly expressed, and it is applied to the adaptive law gains simultaneously. Moreover, a Lyapunov–Krasovskii functional with two integral functions is developed. Besides the properties of the type‐B Nussbaum function, the circumstance where the system parameters are fully unknown is considered. As indicated by the results, all signals in the closed‐loop system are bounded while fulfilling asymptotically tracked control objectives. The simulation example of this study verifies the effectiveness and feasibility of the proposed design method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an inverse problem of identifying a space-dependent source in a time-fractional diffusion-wave equation by using the final time data. Since the problem is ill-posed, we propose an iterative method based on the Nesterov acceleration strategy to deal with it. Two kinds of convergence rates for the regularized solution are given under both the a priori and a posteriori regularization parameter choice rules. Compared with the classical regularization methods, our method is easy to implement with a fewer number of iterations and can always yield the order optimal error estimates provided the iteration parameter is chosen large enough. Some numerical examples including one-dimensional and two-dimensional cases are presented to illustrate the validity and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a partial-state feedback model reference adaptive control strategy for uncertain linear time-invariant systems with unmatched disturbances. The new control design is based on parametrization and observer technique. The control structure and output matching of nominal partial-state feedback disturbance rejection are presented. The adaptive partial-state feedback disturbance rejection scheme guarantees closed-loop system stability and asymptotic output tracking. A simulation example indicates the effectiveness of the presented adaptive partial-state feedback control design. [ABSTRACT FROM AUTHOR]

In this paper, we aim to develop adaptive asymptotic stability for heterodirectional 2 × 2 hyperbolic PDEs with parametric-strict-feedback nonlinear actuator dynamics. First, we transform the heterodirectional 2 × 2 hyperbolic PDEs with spatially varying coefficients into a stable target subsystem by utilizing the infinite-dimensional backstepping transformation. Second, an adaptive state feedback controller is constructed by combining finite-dimensional state transformation and adaptive compensation technology to assure the boundedness of all the signals in the closed-loop system. Meanwhile, we show that the PDE states converge to zero pointwise in space, the nonlinear ODE states and the control input also converge to zero. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article addresses the problem of adaptive tracking control for stochastic nonlinear systems with asymmetric full state constraints. Different from the traditional log‐type or tan‐type barrier Lyapunov functions (BLFs), a new asymmetric BLF is proposed in this article. Then, a state feedback controller is constructed with backstepping method so that all signals of the closed‐system are bounded and the asymmetric state constraint is well kept all the time. Without changing the structure of the controller, the design and the analysis for constrained and unconstrained systems are unified. Finally, the effectiveness of proposed control strategy has been demonstrated by simulations of numerical example and the single‐link robot arm model. [ABSTRACT FROM AUTHOR]

• Grains of weld joint has refined by laser bionic treatment (LBT). • Fatigue behavior was correlated with 'soft-hard' alternating structure formed by LBT. • Roles of LBT in fatigue resistance improvement were discussed. In this study, laser bionic treatment (LBT) was utilized to improve the fatigue crack growth behavior (FCGB) of AZ31B magnesium alloy welded joints. After LBT, fine equiaxed grains with random orientations were achieved on welded joints. Meanwhile, gradient structure and surface strengthening layer with 'soft-hard' alternating structure were achieved on welded joints, and fatigue crack growth threshold was significantly increased, and fatigue crack growth rate was significantly decreased. LBT results in changes of FCGB and fracture mode, and can affect all stages of crack growth. In addition, the mechanism of strengthening fatigue was analyzed based on microstructure, fracture and structural characteristics. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive tracking control is addressed for a class of nonlinear systems with unknown constant parameters and unknown actuator nonlinearity. The actuator nonlinearity is modelled as the backlash-like hysteresis, which is described by a differential model. The prior knowledge on the control gain sign is not required, and only the assumption on the reference signal is made. By combining the adaptive backstepping technique with the Nussbaum gain approach, an adaptive compensation controller design approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking error can converge to zero asymptotically despite the presence of the actuator hysteresis. Two simulation examples are included to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper is centered on delay-dependent state feedback stabilization for a networked control model with two additive input delays. Firstly delay-dependent stability is investigated. By splitting the whole delay interval into subintervals according to the delays, a Lyapunov functional is constructed. To reduce conservatism we handle the Lyapunov functional in two ways. More specifically, we take the Lyapunov functional as a whole to examine its positive definite, rather than restrict each term of it to positive definite as usual. In addition, when estimating the derivative of the Lyapunov functional, we manage to get a fairly tighter upper bound by introducing different slack variables for the different subintervals. The resulting stability results turn out dependent on the two delays separately, and less conservative than some existing ones. Then, based on the stability results state feedback stabilization is studied. Delay-dependent conditions are formulated for the controller such that the closed-loop system is asymptotically stable. Finally examples are given to show the less conservatism of the stability results and the effectiveness of the proposed stabilization method. [ABSTRACT FROM AUTHOR]

In this paper, the operator spectrum theory is applied to study the general stabilisation issues for mean‐field stochastic Markov jump systems (MF‐SMJSs), where multiple delays, multiplicative noises and homogeneous Markov chain exist simultaneously. The innovative contributions are described as follows. On the one hand, a feasible model augmented strategy is adopted to transform the dynamics into an auxiliary delay‐free form. By introducing a delay‐dependent linear Lyapunov operator (DDLLO), the Lyapunov/spectrum stabilising conditions are constructed, which are both necessary and sufficient. On the other hand, in terms of spectral analysis technique, the notions of interval stabilisation and essential destabilisation are generalised to MF‐SMJSs for the first time. The necessary and sufficient stabilisation conditions are derived, respectively, which can be verified availably by LMI feasibility tests. To confirm the effectiveness of the theoretic results, two illustrative examples are included. [ABSTRACT FROM AUTHOR]

For the parametric strict-feedback nonlinear systems with unknown virtual control coefficients and unknown control directions, the control schemes presented in the existing literature have the disadvantage of overparametrization. In this paper, a novel systematic design procedure is developed to solve the overparametrization problem. Two nonlinear controllers are designed by combining the backstepping technique and the Nussbaum gain approach. A main advantage of the proposed controllers is that they contain less or no parameter estimates that need to be updated online. In the first scheme, the number of the estimated parameters is equal to the dimension of the controlled system. In the second scheme, no parameter estimates are required. In both of the control schemes, the boundedness of all the closed-loop signal is guaranteed, and the asymptotic convergence of the system states is achieved. An example is provided to demonstrate the effectiveness of the proposed design approaches. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This study deals with adaptive control of non‐linear systems in the strict‐feedback form with parametric uncertainties and additive disturbance. The disturbance in the systems is assumed to be bounded. No knowledge of the uncertain parameters, an upper bound of the uncertain parameter vector, a bound of unknown disturbance and the differentiability of the external disturbance is required. Under the weakened assumptions, two continuous robust adaptive control schemes are proposed. In the first control scheme, a modified adaptive backstepping design procedure is proposed to remove overparameterisation. A novel damping term with the estimate of unknown disturbance bound and a positive time‐varying integral function are introduced in the control law to counteract the destabilising effects of the external disturbance. In the second scheme, an alternative continuous adaptive controller is designed. Instead of the estimate of the disturbance bound, an adaptive parameter is incorporated into the control design. In both of the two control schemes, the design parameters are freely chosen to improve the control performance. It is proved that the proposed two adaptive control schemes can guarantee that the closed‐loop signals are bounded and the output tracking error converges to zero asymptotically in spite of the disturbance. Finally, a numerical example is included to show the effectiveness of the presented control methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the control design problem for a class of nonlinear systems with the state time-varying time delays and nonsymmetric dead zone. The problem addressed is to design adaptive controllers that guarantee the exact tracking of a given reference signal. Two continuous robust adaptive control schemes are proposed. A positive nonlinear control gain function, which is not required to satisfy an inequality but is expressed explicitly, is carefully constructed and is used in the control law and adaptive law. An illustrative example is provided to demonstrate the validity of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the observer design problem for a class of multi-input–multi-output nonlinear systems with the unmodeled dynamics, unknown parameters and external disturbance. A dynamic signal, which can dominate the unmodeled dynamics, is firstly constructed. Then, two types of observer schemes, that is, adaptive observer and robust observer, are respectively proposed. The observation error in the two schemes can be made arbitrarily small by choosing the appropriate design parameters. An illustrative example is provided to demonstrate the validity of the proposed design methods. [ABSTRACT FROM AUTHOR]

Two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented. We consider two possible input nonlinearities, that is, backlash-like hysteresis and symmetric dead-zone, which can be simultaneously dealt with by using the proposed compensation controllers. The knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required. Only the boundedness of the reference signal is assumed. The Nussbaum gain approach is employed to remove the assumption on the control gain sign. The first scheme is based on the backstepping technique. The final step of the recursive design is crucial for the closed-loop stability. In the second scheme, a direct adaptive control law is designed. The controller has a simple structure and only one adaptation parameter is updated. In both controllers, it is shown that asymptotic tracking is ensured. Two numerical examples are provided to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, an adaptive backstepping tracking control scheme is proposed for a class of nonlinear state time-varying delay systems, which are subject to parametric uncertainties and external disturbances. The bounds of the time delays and their derivatives are assumed to be unknown. Tuning functions method is exploited to construct the control law and adaptive laws. Unknown time-varying delays are compensated by using appropriate Lyapunov-Krasovskii functional. It is shown that the proposed controller can guarantee the boundedness of all the closed-loop signals. The tracking performance can be adjusted by choosing suitable design parameters. At the end, a simulation example is provided to illustrate the effectiveness of the design procedure. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the design of the novel observer that synchronizes with the generalized Lorenz chaotic systems. A simple reduced-order observer scheme is proposed by including extra terms. The boundedness of the state variables in the original system is not necessary for the observer design. The prior knowledge on the derivative signal of the system output is not required. It is also shown that by adopting Lyapunov method and choosing appropriate design parameters, the synchronization (observation) errors can converge to zero exponentially. Finally, numerical examples are provided to illustrate the validity of the theoretical result. [Copyright &y& Elsevier]

Abstract: In this paper, an adaptive control scheme is proposed for the synchronization of two single-degree-of-freedom oscillators with unknown parameters. We only assume that the master system has the bounded solutions, which is generally satisfied for chaotic systems. Unlike the existing literature, the boundedness of the states of the slave system with control input is not necessarily known in advance. The boundedness of the controlled states is rigorously proved. The unknown parameters not only in the slave system but also in the master system are estimated by designing adaptive laws. By choosing appropriate Lyapunov function and employing Barbalat’s lemma, it is theoretically shown that the synchronization errors can converge to zero asymptotically. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed adaptive control design. [Copyright &y& Elsevier]

Abstract: This paper addresses the problem of adaptive stabilization of uncertain unified chaotic systems with nonlinear input in the sector form. A novel representation of nonlinear input function, that is, a linear input with bounded time-varying coefficient, is firstly established. Then, an adaptive control scheme is proposed based on the new nonlinear input model. By using Barbalat’s lemma, the asymptotic stability of the closed-loop system is proved in spite of system uncertainties, external disturbance and input nonlinearity. One of the advantages of the proposed design method is that the prior knowledge on the plant parameter, the bound parameters of the uncertainties and the slope parameters inside the sector nonlinearity is not required. Finally, numerical simulations are performed to verify the analytical results. [Copyright &y& Elsevier]

Abstract: This paper addresses the problem of globally stable adaptive backstepping output-feedback tracking control for a class of nonlinear systems with unknown high-frequency gain sign. The fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal. Thus, the global stability of closed-loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions. The other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal, which is very important for the choice of the centers and widths of membership functions. Moreover, the Nussbaum-type function is employed to deal with the unknown high-frequency gain sign. Two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper. [Copyright &y& Elsevier]

The main focus of this paper is to explore the finite-time stabilization of mean-field time-varying stochastic systems that are affected by uncertain parameters, multiple disturbances, and delays. In contrast to prior studies, we present a set of sufficient conditions for achieving finite-time stability in the closed-loop model. Notably, these conditions are established based on the analysis of the state transition matrix (STM). Additionally, we address a sufficient condition based on the Lyapunov function, where the STM significantly simplifies the selection process of the Lyapunov function. Finally, we introduce a linear matrix inequality (LMI)-based approach that facilitates the computation of non-fragile controllers. The effectiveness of the developed theoretical results is verified through a stock investment model. [ABSTRACT FROM AUTHOR]

This work addresses the nonfragile $H_{\infty }$ controller design problem for a class of discrete-time uncertain nonlinear systems. The norm-bounded uncertainty is contained in the nonlinear plant, which is described by the well-known Takagi–Sugeno (T–S) fuzzy model. The controller gain perturbation is also considered. When the input signal is transmitted from the controller to the system through the digital communication channels, it will be quantized by a static quantizer. The main attention is to design the nonfragile $H_{\infty }$ state-feedback controller for the closed-loop quantized uncertain T–S fuzzy system. By introducing some auxiliary scalars and the fuzzy basis-dependent Lyapunov function approach, sufficient conditions are established in the form of linear matrix inequalities (LMIs). The construction for the nonfragile $H_{\infty }$ controller can be completed by solving these LMIs. In the end, the applicability and effectiveness of the proposed method have been illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

• Both vacuum heat treatment and hydrogen plasma treatment improved the electrical properties of boron doped diamond. • Oxygen provides new vacancies for the addition of more boron atoms at grain boundary into crystal lattice. • Vacuum heat treatment is a facile and cheap way to improve the electrical conductivity of the boron doped diamond. The electrical conductivity of Boron-doped diamond (BDD) films prepared by the mixture of methanol/acetone/B 2 O 3 was significantly improved after hydrogen plasma and vacuum heat treatment. SEM and Raman spectroscopy were used to characterize the change of morphology and quality of BDD film after heat treatment, and the electrical properties of BDD film were determined by Hall effect. The chemical bonding states of boron atoms were analyzed by X-ray photoelectron spectroscopy. A mechanism at the origin of the improved conductivity after the heat treatments was proposed. It is oxygen that provides new vacancies for the addition of more boron atoms at grain boundary into crystal lattice, thus enhancing the electrical properties. There are different roles of oxygen in different heat treatments. [ABSTRACT FROM AUTHOR]

It is crucial to obtain better fatigue life for the safe application of materials, and nature provides a new idea for effectively improving fatigue property. A 'soft-hard' alternating structure imitated biological morphology was fabricated on the surface of welded joints by laser bionic treatment (LBT) for improving the fatigue property of TIG welded AZ31B Mg alloy joints. After LBT, the grains in the weld zone were refined with the average grain size about 5.55 μm and decreased by 76.1%, resulting in an increase of hardness of 12.0% to about 60.12 HV0.1, and formed a 'soft-hard' structure on the surface of welded joints. By adjusting the distribution angle of laser bionic stripe, the high cycle fatigue strength of welded joints was increased by 129.4% at most. The fracture morphology of welded joints was changed by LBT. The weld zone of bionic welded joints was deformed by twinning and slip, while the laser-treated zone was only deformed by slip. The mechanisms of strengthening fatigue properties were discussed based on the microstructure and structural characteristics from EBSD analyze. • Laser bionic treatment was first used to improve fatigue properties of welded joints. • 'soft-hard' bionic structure was performed on the surface of welded joints. • EBSD was used to analyze the microstructure of laser bionic joint after fatigue test. • Strengthening mechanisms induced by laser bionic treatment were discussed. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive neural-network-based dynamic surface control (DSC) method is proposed for a class of stochastic interconnected nonlinear nonstrict-feedback systems with unmeasurable states and dead zone input. First, an appropriate state observer is constructed to estimate the unmeasured state variables of the stochastic interconnected system. Then radial basis function neural networks combined with adaptive backstepping technique are applied to model the unknown nonlinear system functions of the stochastic interconnected system; and the DSC method is adopted to ensure the computation burden is greatly reduced. Furthermore, the proposed controllers guarantee that the closed-loop stochastic interconnected system is semi-globally bounded stable in probability. In the end, two simulation examples are provided to show the effectiveness and practicability of the proposed control scheme. [ABSTRACT FROM AUTHOR]

• We propose L 2 − 1 σ /Hermite–Galerkin spectral method to solve nonlinear fractional differential equation in R d. • Arbitrary time-step size of our scheme can be used without resulting in the nonsense numerical results. • Our method can arrive at the spectral (resp. second-order) accuracy for spatial (resp. temporal) discretization. • Effects of the fractional orders on the pattern formations of fractional Allen–Cahn and Gray–Scott models are studied. • Comparisons between the fractional models and the corresponding integer-order ones are investigated. The aim of this paper is to develop an efficient finite difference/Hermite–Galerkin spectral method for the time-fractional nonlinear reaction–diffusion equation in unbounded domains with one, two, and three spatial dimensions. For this purpose, we employ the L 2 − 1 σ formula to discretize the temporal Caputo derivative. Additionally, we apply the Hermite–Galerkin spectral method with scaling factor for the approximation in space. The stability of the fully discrete scheme is established to show that our method is unconditionally stable. Numerical experiments including one-, two-, and three-dimensional cases of the problem are carried out to verify the accuracy of our scheme. The scheme is show-cased by solving two problems of practical interest, including the fractional Allen–Cahn and Gray–Scott models, together with an analysis of the properties of the fractional orders. [ABSTRACT FROM AUTHOR]

In this letter, we consider the numerical approximation of a two-dimensional distributed-order time–space fractional reaction–diffusion equation. The time- and space-fractional derivatives are considered in the senses of Caputo and Riesz, respectively. By using the composite mid-point quadrature, the original fractional problem is approximated by a multi-term time–space fractional differential equation. Then the multi-term Caputo fractional derivatives are discretized by the L 2 - 1 σ formula. We apply the Legendre–Galerkin spectral method for the spatial approximation. Two numerical experiments with smooth and non-smooth initial conditions, respectively, are performed to illustrate the robustness of the proposed method. The results show that: our scheme can arrive at the spectral accuracy (resp. algebraic accuracy) in space for the problem with smooth (resp. non-smooth) initial condition. For both of these two cases, our scheme can lead to the second-order accuracies in time. Additionally, the convergence rates in both spatial and temporal distributed-order variables are two. [ABSTRACT FROM AUTHOR]