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The significance of the nonlinear terms in the governing equations to describe the transiently large deformation of a thin-walled cylindrical shell under impact pressures is discussed in this paper. Firstly, the 1st P-K stress tensor is adopted to depict the motion equations of the shell with respect to the original configuration. More nonlinear terms are retained when the 1st P-K stress is transformed into the symmetrical 2nd P-K stress. Moreover, the Green's strain tensor is employed in the geometrical equation to describe the nonlinearly large deformation of shell, and the curvature change is expressed to involve large deformation as well. Without considering all these nonlinear terms, the governing equation can degenerate to that in references. The circumferential displacement is kept in the motion equations, and the wall thickness change is taken into account. Dividing these nonlinear terms into two parts according to their affiliations, four groups of governing equations involving different nonlinear terms are obtained. Then, the deformation behavior of a shell subjected to a specified loading is solved using different governing equations and compared with FEM results to reveal the significance of these nonlinear terms. It is found that the nonlinear terms from geometrical equations should be kept while the nonlinear terms in equilibrium equations can be ignored. [ABSTRACT FROM AUTHOR]

This paper consider the Cauchy problem for the Schrödinger equation coupled with the stochastic Benjamin-Ono equation. A priori estimates for the stochastic integral and the nonlinear terms corresponding to the coupling system are achieved by using Fourier transform restriction method introduced by Bourgain. It is shown that the Cauchy problem is locally well-posed as the initial data in appropriate Sobolev spaces. [ABSTRACT FROM AUTHOR]

In this study, the first order nonlinear Volterra type integro-differential equations are used in order to identify approximate solutions concerning Euler polynomials of a matrix method based on collocation points. This method converts the mentioned nonlinear integro-differential equation into the matrix equation with the utilization of Euler polynomials along with collocation points. The matrix equation is a system of nonlinear algebraic equations with the unknown Euler coefficients. Additionally, this approach provides analytic solutions, if the exact solutions are polynomials. Furthermore, some illustrative examples are presented with the aid of an error estimation by using the Mean-Value Theorem and residual functions. The obtained results show that the developed method is efficient and simple enough to be applied. And also, convergence of the solutions of the problems were examined. In order to obtain the matrix equations and solutions for the selected problems, code was developed in MATLAB. [ABSTRACT FROM AUTHOR]

Based on Finite Volume Coastal Ocean Model (FVCOM), this study constructed a numerical model covering the Bohai Sea, Yellow Sea, and East China Sea. National Centers for Environmental Prediction's Climate Forecast System Reanalysis (NCEP-CFSR) data were used to drive the model to simulate a large storm surge generated by Typhoon Chan-hom. The model was validated by multiple in situ observations of water levels taken at tidal gauge stations. The effects of the nonlinear terms and topography on the modeling of storm surges were then studied. First, the tide–surge interaction during the storm surge process was analyzed. The results show that the tide–surge interaction can suppress the storm surge at the climax of the astronomical tide and benefit the growth of the storm surge at the ebb of the astronomical tide. The tidal constituents M2, S2 and K1 were added to analyze the influences of the amplitudes and periods of tides on the nonlinear reaction. The results indicate that the nonlinear effect will be enhanced by an increased tidal height; additionally, the nonlinear interaction of semidiurnal tides is more significant than that of diurnal tides. The semidiurnal fluctuation that appears near the peak-value time is also attributed to the tide–surge interaction. Moreover, the tide–surge interaction can be influenced by the water depth and position of the area of interest. According to the numerical results, topography has a certain impact on the storm surge: The peak value of the storm surge will decrease with increasing slope. The existence of the Ryukyu Islands reduces the area influenced by the storm surge on the southeast coast of China but expands the high-value storm surge area. [ABSTRACT FROM AUTHOR]

This study addresses the robust predictive control of a class of discrete‐time switched systems under arbitrary switching signals. The subsystems of the considered switched system involve polytopic uncertainties, the state delay, non‐linear terms, and input constraint. The main goal is to provide two switched delayed state feedback controllers for the cases of known and unknown state delays based on a constrained robust model predictive control method. An appropriate Lyapunov–Krasovskii functional is used to design the controller via an optimisation problem developed as linear matrix inequalities (LMIs). Both approaches are delay dependent because the online LMIs depend on the value of state delay in the first case and the upper bound of the state delay in the second one. The other advantages of the proposed method are considering a non‐constrained switching signal, its ability to handle constraints, and shaping a transient response. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results and also to compare the results with previous researches. [ABSTRACT FROM AUTHOR]

In Diabetes Mellitus, the pancreas remains incapable of insulin administration that leads to hyperglycaemia, an escalated glycaemic concentration, which may stimulate many complications. To circumvent this situation, a closed‐loop control strategy is much needed for the exogenous insulin infusion in diabetic patients. This closed‐loop structure is often termed as an artificial pancreas that is generally established by the employment of different feedback control strategies. In this work, the authors have proposed an arbitrary‐order sliding mode control approach for development of the said mechanism. The term, arbitrary, is exercised in the sense of its applicability to any n ‐order controllable canonical system. The proposed control algorithm affirms the finite‐time effective stabilisation of the glucose–insulin regulatory system, at the desired level, with the alleviation of sharp fluctuations. The novelty of this work lies in the sliding manifold that incorporates indirect non‐linear terms. In addition, the necessary discontinuous terms are filtered‐out once before its employment to the plant, i.e. diabetic patient. The robustness, in the presence of external disturbances, i.e. meal intake is confirmed via rigorous mathematical stability analysis. In addition, the effectiveness of the proposed control strategy is ascertained by comparing the results with the standard literature. [ABSTRACT FROM AUTHOR]

This study considers the event‐triggered tracking control problem for a family of non‐linear systems via output feedback. The uncertainty in the parameters is a significant feature, and the growth condition of the non‐linear terms is related to an output polynomial function. An observer based on the given tracking signal is constructed, and a dynamic equation is established by the high‐gain scaling method. In order to reasonably process the measurement error, an intermediate controller in the form of the hyperbolic tangent function is designed. Based on the relative threshold strategy, an event‐triggered controller is naturally given such that all the closed‐loop signals are globally bounded and the Zeno‐behaviour is favourably avoided. Furthermore, by analysing the constructed dynamic equation, the tracking error converges to a prescribed small residual set. The theoretical results are verified by two numerical examples. [ABSTRACT FROM AUTHOR]

This study focuses on the delay‐dependent robust exponential stabilisation and H∞ control for uncertain stochastic time‐delay systems with non‐linear terms. Uncertain parameters are assumed to be time‐varying norm bounded, while time‐varying delay terms include both discrete and distributed delays. Firstly, by choosing an appropriate Lyapunov–Krasovskii functional, a sufficient condition for the robust exponential stabilisation is obtained. Secondly, the H∞ control is also discussed. All criteria are presented in the form of linear matrix inequalities with less conservatism. Finally, an example verifies the validity of the proposed method. [ABSTRACT FROM AUTHOR]

This study investigates a distributed leader‐following consensus problem for a class of high‐order uncertain non‐linear multiagent systems. For the uncertain non‐linear terms in the systems, the authors propose a less conservative Lipschitz condition, which the Lipschitz growth parameters are unknown. By using the adaptive method, the unknown Lipschitz growth parameters are estimated asymptotically. Furthermore, to lower the frequency of controller updates, a new dynamic event‐triggered control strategy with the novel dynamic variable is constructed based on the event‐triggered method. The distributed consensus protocol is proposed based only on the relative state information of neighbouring agents and the protocol can ensure that the Zeno‐behaviour no longer occurred. Based on the Lyapunov stability theory, it is strictly proved that the state variables of the followers can track asymptotically those of the leader. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This study is concerned with the output feedback stabilisation problem for a class of large‐scale non‐linear time‐delay systems with unknown measurement sensitivities. The non‐linear terms are assumed to be bounded by states or delayed states multiplied by outputs polynomial functions. The state observers are given by the dynamic gain control design technique. By constructing an appropriate Lyapunov–Krasovskii functional, the global asymptotic stability of the closed‐loop control system is analysed. A numerical example is given to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Abstract The interaction of tides and storm surges can significantly modify the final levels reached by storm surges that threaten coastal areas. In this paper, numerical experimental results are presented that examine tidal influence on storm surges. This is done using a two-dimensional ADCIRC (Advanced Circulation Model) applied to the effects of Typhoon Rammasun (July 2014) on Tieshan Bay, China. The results show that, without considering tidal forcing, there is an underestimation of positive surge levels, while negative surge levels are overestimated. It is also shown that the prevailing wind direction and shape of Tieshan Bay affect the distribution of storm surges. The nonlinear residual levels caused by tide-surge interaction can reach 0.94 m at the top of the bay when peak negative storm surge levels occur, with nonlinear levels increasing from the outside to the head of the bay. Through the derivation of mathematical terms, a direct relationship between the nonlinear residual levels and the dynamic influencing factors is established. Further, it is demonstrated that the combination of wind stress and bottom friction terms and advection terms play leading roles in the derivations, whereas terms related to local acceleration and Coriolis force contribute little to the nonlinear levels. The combination of wind stress and bottom friction terms and advection terms show complex spatial and temporal variation. Highlights • An unstructured-grid and high resolution tide-surge coupled model was applied in this study. • The storm prediction error and nonlinear residual levels characteristics due to tide-surge interaction are investigated. • Direct relationship between the nonlinear residual levels and influencing factors is established. [ABSTRACT FROM AUTHOR]

In the long‐term transmission system hardening, critical components in transmission infrastructure should be identified and hardened to reduce the load loss risk in the presence of scheduled and unscheduled outages. Generally, the probabilistic information of assets in power systems can be evaluated via historical statistics. On the basis of the prior probabilistic information, this study proposed a tri‐level optimisation model to deal with the problem of long‐term transmission system hardening, in which the risk assessment is taken into account in the objective function. Furthermore, the problem is formulated as a two‐stage robust optimisation model. To address the non‐linear problem in the inner model, logarithmic transformation and piecewise linearisation are utilised to exactly linearise the non‐linear terms in the model. Finally, the standard column‐and‐constraints generation algorithm is employed to solve the proposed model with a master–sub‐problem framework. The test results on a standard IEEE RTS‐96 system show the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

This study focuses on the stability analysis and design of output feedback controllers for a non‐linear discrete‐time switched system with uncertain subsystems. The considered system involves time‐varying delay, non‐linear terms, and affine parametric uncertainties. The main goals of this study are first to derive sufficient conditions to guarantee the stability of the unforced switched system and then, to construct two stabilising output feedback controllers (static and dynamic) to stabilise the closed‐loop system with considering arbitrary switching signals. In this regard, based on switched Lyapunov functions, an appropriate Lyapunov–Krasovskii functional is constructed to establish the sufficient conditions; these conditions depend only on the upper bounds of the time‐delay and uncertain parameters. Furthermore, in the proposed method, the admissible bound of time‐delay and the maximum non‐linearity of subsystems could be calculated. Finally, numerical examples are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Incorporation of the short‐circuit level constraints in the transmission expansion planning (TEP) has a direct impact on the final solution. Conventionally, in TEP models, a substation is tackled as a single node where are all transmission lines, power transformers, and generating units are connected to each other. However, bus splitting is a common option in most substations that divides the connected elements into two groups. Doing so, bus splitting can alter the flow path impedances and accordingly manage the short‐circuit levels. Here, the short‐circuit level constraints are modelled in terms of conventional TEP and bus splitting decision variables. The modelling process is very complex and some non‐linear terms appear in the models. To have a tractable model in real‐world problems, the non‐linearities are converted to linear equivalents making the final TEP model conforming the mixed‐integer linear programming format. The performance of the proposed model is examined on the 24‐bus reliability test system. The results show that incorporation of the bus splitting option in the TEP problem decreases the total cost of the optimal expansion plan. [ABSTRACT FROM AUTHOR]

• Dynamic model of a dual-flexible servo system considering two-dimensional deformation is established. • Influence of the nonlinear terms and friction torque in dynamic equations is analyzed. • Control law of the neural network sliding mode controller is designed to identify the uncertain part. • Experimental platform of the dual-flexible servo system is built to carry out control experiment. A variable-length dual-flexible servo system is a complex nonlinear system that consists of a servo motor, a flexible joint, and a variable-length flexible load. In order to describe the mechanical behavior of the servo system more accurately, the two-dimensional (2D) deformation of flexible load needs to be considered. The coupled nonlinear terms, friction torque, and time variation of parameters in the dynamic equations constitute the uncertain part of the servo system. These mentioned factors will cause fluctuations in the flexible load's rotation angle. In this paper, a sliding mode control strategy based on neural network compensation is proposed to control the servo system. Firstly, the dynamic equations of the dual-flexible servo system considering the 2D deformation are established according to Lagrange's theorem. Then the control law of the sliding mode controller based on neural network is designed. The adaptive law of weight coefficients in the neural network is designed by the Lyapunov stability theorem. Finally, the numerical simulation analysis and control experiments are carried out. The experiment results prove that the control strategy can reduce the tracking error by 43.6%. [ABSTRACT FROM AUTHOR]

A high‐order curvature‐compensated current mode bandgap reference (BGR) over a very wide temperature range is presented. High‐order curvature correction for this reference is accomplished by the proposed multipoint corrected technique, which realises exponential curvature‐compensation terms in lower and higher temperature ranges separately through simple structures. The compact multipoint curvature‐compensation circuit cancels out the nonlinear terms of the BGR using sub‐threshold operated metal–oxide semiconductor field effect transistors, which subtract those currents that are proportional to the nonlinearity out of the reference voltage. As a result, a flattened and better effect of curvature compensation in a wide temperature range is realised. The circuit performance was verified experimentally. The measurements indicate that the proposed BGR can achieve a temperature coefficient as low as 1.01 ppm/°C over the temperature range of 160°C (−40 to 120°C). [ABSTRACT FROM AUTHOR]

In order to both experimentally and numerically investigate nonlinear femtosecond ultrabroadband-pulse propagation in a silica fiber, we have extended the finite-difference time-domain (FDTD) calculation of Maxwell's equations with nonlinear terms to that including all exact Sellmeier-fitting values. We have compared results of this extended FDTD method with experimental results, as well as with the solution of the generalized nonlinear Schrodinger equation by the split-step Fourier method with a slowly varying-envelope approximation. To the best of our knowledge, this is the first comparison between FDTD calculation and experimental results for nonlinear propagation of a very short (12 fs) laser pulse in a silica fiber [ABSTRACT FROM PUBLISHER]