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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]

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]

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]

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective. • An adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism instead of constructing the inverse of dead-zone nonlinearity. • Stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. [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]

Abstract This paper is concerned with the observer-based control problem for Markovian jump delay systems with parameter uncertainties using quantized measurements. The parameter uncertainties are assumed to be norm bounded. The aim is to design a suitable observer-based controller which guarantees the stochastic stability of the resulting closed-loop system with a prescribed mixed passivity and H ∞ performance index. A novel stability criterion is obtained by constructing a mode-dependent Lyapunov–Krasovskii functional based on the delay-partitioning technique. Then, with the novel stability criterion, sufficient conditions for the solvability of the presented observer-based controller design problem are derived. All the results obtained in this paper can be tackled by a feasibility problem in terms of linear matrix inequalities. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the fuzzy filtering problem for a class of nonlinear time-delay systems described by T-S fuzzy models. Different from the existing schemes in the literature, this paper aims to solve the fuzzy filtering problem by considering the H ∞ , L 2 − L ∞ and dissipative performance constraints in a unified way. To achieve this purpose, the recently proposed notion of extended dissipativity is applied, which provides an inequality covering the well-known H ∞ , L 2 − L ∞ and dissipative performances. Another purpose of this paper is to design filters involving communication delays. Such filters have a more general form than the delay-free filters that have been largely considered in the traditional studies. In order to design the fuzzy filters under consideration, a novel fuzzy Lyapunov-Krasovskii functional is employed, and delay-dependent conditions for stability and performance analysis of the filtering error system are obtained. Then, LMI-based conditions for the existence of the desired filters are presented. The filter parameters can be obtained by solving the presented LMIs. Finally, the effectiveness of the proposed method is substantiated with an illustrative example. Highlights • The extended dissipative fuzzy filtering problems for nonlinear time-delay systems is solved. • The designed filter includes both delayed states and inputs. • Delay-dependent conditions are derived based on a novel Lyapunov-Krasovskii functional. [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]

This paper revisits the issue of the stabilization for neutral type descriptor hybrid systems (NTDHSs) with time-varying delays. By a novel Lyapunov–Krasovskii functional (LKF) we constructed, a mode dependent and delay dependent criterion is acquired for the unforced NTDHSs to be stochastically admissible. On the basis of the criterion, a mode dependent state feedback controller (SFC) is designed such that the resulting closed-loop system is regular, impulse free and stochastically stable. By singular-value decomposition method, sufficient conditions are established via strict linear matrix inequality (LMI). And the gain of the SFC can be derived. It is worth noting that our results generalize the corresponding results published in latest literatures to some degree. The superiority and validity of our methods are displayed via two numerical examples. [ABSTRACT FROM AUTHOR]

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]

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]

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]

• 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]

This paper investigates the nonfragile H ∞ filtering problem for a class of discrete-time nonlinear switched systems with quantization. The nonlinearity considered in our work is assumed to satisfy the Lipschitz conditions. The asynchronous switching is taken into consideration in the filter design. To study the asynchronous switching, a lag is introduced between the switching of subsystem and its matched filter. The Lyapunov functions are allowed to increase during the running time of activated subsystem with its mismatched filter. Both the measurement output signal and the performance output signal are quantized by two static quantizers before being transmitted, respectively. This consideration of quantization is more practical than the case that the signal quantization only exists in the measurement output signal. The main attention of this paper is to design a set of mode-dependent nonfragile H ∞ filters such that the filtering error systems are globally uniformly asymptotically stable and satisfy a weighted H ∞ performance index. Based on the average dwell time approach and multiple Lyapunov functions, sufficient conditions are established in the form of linear matrix inequalities (LMIs). The desired nonfragile H ∞ filters can be obtained by solving these LMIs. Finally, an example is provided to illustrate the effectiveness of the obtained results. • The H ∞ filtering problem for nonlinear switched systems with quantization is studied. • The signal quantization exists in both measurement output and performance output. • The filter parameters to be designed contain uncertainties. • The asynchronous switching is considered in this paper. [ABSTRACT FROM AUTHOR]

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]

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]

• 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]