Nonlinear Robust Stabilization of Ship Roll by Convex Optimization

Dear Editor,This letter presents a nonlinear robust controller design method for ship roll stabilization by combining the dual of Lyapunov's stability theorem with the sum of squares(SOS) technique. Varying initial metacentric height and ship speed are regarded as uncertainties, sea waves are considered as external disturbances, and then the robust nonlinear controller is designed. Taking a container ship as an example, simulations are performed to verify the effectiveness of the proposed design scheme.

Limit equilibrium method(LEM) of slope stability and calculation of comprehensive factor of safety with double strength-reduction technique

When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultaneously reduced. Hence, the LE stress method is established to analyze the slope stability by employing the double strengthreduction(DSR) technique in this work. For calculation model of slope stability under the DSR technique, the general nonlinear Mohr–Coulomb(M–C) criterion is used to describe the shear failure of slope. Meanwhile, the average and polar diameter methods via the DSR technique are both adopted to calculate the comprehensive factor of safety(FOS) of slope. To extend the application of the polar diameter method, the original method is improved in the proposed method. After comparison and analysis on some slope examples, the proposed method's feasibility is verified. Thereafter, the stability charts of slope suitable for engineering application are drawn. Moreover, the studies show that:(1) the average method yields similar results as that of the polardiameter method;(2) compared with the traditional uniform strength-reduction(USR) technique, the slope stability obtained using the DSR techniquetends to be more unsafe; and(3) for a slope in the critical LE state, the strength parameter φ, i.e., internal friction angle, has greater contribution on the slope stability than the strength parameters c, i.e., cohesion.

Overview of Moving Particle Semi-implicit Techniques for Hydrodynamic Problems in Ocean Engineering

With the significant development of computer hardware,many advanced numerical techniques have been proposed to investigate complex hydrodynamic problems.This article aims to provide a detailed review of moving particle semi-implicit(MPS)techniques and their application in ocean and coastal engineering.The achievements of the MPS method in stability and accuracy,boundary conditions,and acceleration techniques are discussed.The applications of the MPS method,which are classified into two main categories,namely,multiphase flows and fluid-structure interactions,are introduced.Finally,the prospects and conclusions are highlighted.The MPS method has the potential to solve practical problems.

Robust H_∞ Stabilization of Uncertain Linear Time-Delay System with Delayed/Undelayed State Feedback Controllers

This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm-bounded parameter perturbations in the system state and control/disturbance. On the existence of delayed/undelayed full state feedback controllers, we present a sufficient condition and give a design method in the form of Riccati equation. The controller can not only stabilize the time-delay system, but also make the H∞ norm of the closed-loop system be less than a given bound. This result practically generalizes the related results in current literature.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay

The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.

Advancements and Challenges in Organic–Inorganic Composite Solid Electrolytes for All‑Solid‑State Lithium Batteries

To address the limitations of contemporary lithium-ion batteries,particularly their low energy density and safety concerns,all-solid-state lithium batteries equipped with solid-state electrolytes have been identified as an up-and-coming alternative.Among the various SEs,organic–inorganic composite solid electrolytes(OICSEs)that combine the advantages of both polymer and inorganic materials demonstrate promising potential for large-scale applications.However,OICSEs still face many challenges in practical applications,such as low ionic conductivity and poor interfacial stability,which severely limit their applications.This review provides a comprehensive overview of recent research advancements in OICSEs.Specifically,the influence of inorganic fillers on the main functional parameters of OICSEs,including ionic conductivity,Li+transfer number,mechanical strength,electrochemical stability,electronic conductivity,and thermal stability are systematically discussed.The lithium-ion conduction mechanism of OICSE is thoroughly analyzed and concluded from the microscopic perspective.Besides,the classic inorganic filler types,including both inert and active fillers,are categorized with special emphasis on the relationship between inorganic filler structure design and the electrochemical performance of OICSEs.Finally,the advanced characterization techniques relevant to OICSEs are summarized,and the challenges and perspectives on the future development of OICSEs are also highlighted for constructing superior ASSLBs.

Combined influence of nonlinearity and dilation on slope stability evaluated by upper-bound limit analysis

The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.

Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis(SRFEA) with finite element limit analysis(FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety(FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis(1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SOLUTIONS TO THE QUASILINEAR THERMO-DIFFUSION EQUATIONS WITH SECOND SOUND

This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.

STABILITY OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

In this paper,the stability of a class of impulsive functional differential equations with infinite delays is investigated.A uniform stability theorem and a uniform asymptotic stability theorem are established.

Study on Robust Uniform Asymptotical Stability for Uncertain Linear Impulsive Delay Systems

In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.

Numerical Simulation of PMM Tests for A Ship in Close Proximity to Sidewall and Maneuvering Stability Analysis

As the maneuverability of a ship navigating close to a bank is influenced by the sidewall, the assessment of ship maneuvering stability is important. The hydrodynamic derivatives measured by the planar motion mechanism （PMM） test provide a way to predict the change of ship maneuverability. This paper presents a numerical simulation of PMM model tests with variant distances to a vertical bank by using unsteady RANS equations. A hybrid dynamic mesh technique is developed to realize the mesh configuration and remeshing of dynamic PMM tests when the ship is close to the bank. The proposed method is validated by comparing numerical results with results of PMM tests in a circulating water channel. The first-order hydrodynamic derivatives of the ship are analyzed from the time history of lateral force and yaw moment according to the multiple-run simulating procedure and the variations of hydrodynamic derivatives with the ship-sidewall distance are given. The straight line stability and directional stability are also discussed and stable or unstable zone of proportional-derivative （PD） controller parameters for directional stability is shown, which can be a reference for course keeping operation when sailing near a bank.

Research on stability of a slope due to underground mining

This paper will present a detailed analysis of the deformation mechanism and stability assessment of the slope through field investigations, numerical modeling and measurements. Field investigation indicated that three thin coal seams encountered large mined-out area at one side and free surface of hill slope at the other side, which lead to the caving of roof strata movement, ground movement and crown crack along the preferred orientations of joints. The three-dimensional numeri- cal modeling study on the case demonstrated that the plasticity failure occurred gradually along with the extension of mined-out area in depth. When the depth of mining reached the verge defined by the seismic prospecting method, a large mount of tension failure occurred on the crown of the slope. The factor of safety was 1.36 calculated by the shear strength reduction technique, which indicated the slope was in stable state. The measurement showed that the residual deformation occurred before 1998 and became stable subsequently, which indicated that the residual deformation almost finished and the slope is in stable state.

Undrained Stability Analysis of Three-Dimensional Rectangular Trapdoor in Clay

A new collapse model of the trapdoors,three-dimensional rectangular trapdoor(3DRT),is presented for ground surface collapse.Undrained stability of 3DRT is examined with the upper bound method of plasticity limit analysis theory.The soil where the trapdoors are located is assumed to be a perfectly plastic model with a Tresca yield criterion.Block analysis technique is employed to investigate the collapse of 3DRT.The model is divided into five different block types and added up to ten rigid blocks.According to the law of conservation of energy,the critical stability ratios of 3DRT are obtained through a search proceeding.The results of upper bound solution for 3DRT are given,and three trapdoor models with depth various are discussed during the application in the stability analysis of square trapdoors.The critical stability ratios can be used in the design of underground excavation and support force.

A New Approach to Robust Stability Analysis of Sampled-data Control Systems

The lifting technique is now the most popular tool for dealing with sampled-data controlsystems. However, for the robust stability problem the system norm is not preserved by the liftingas expected. And the result is generally conservative under the small gain condition. The reason forthe norm di?erence by the lifting is that the state transition operator in the lifted system is zero inthis case. A new approach to the robust stability analysis is proposed. It is to use an equivalentdiscrete-time uncertainty to replace the continuous-time uncertainty. Then the general discretizedmethod can be used for the robust stability problem, and it is not conservative. Examples are givenin the paper.

Theoretical Proof of Unconditional Stability of the 3-D ADI-FDTD Method

In order to eliminate Courant-Friedrich-Levy(CFL) condition restraint and improvecomputational efficiency,a new finite-difference time-domain(FDTD)method based on the alternating-direction implicit(ADI) technique is introduced recently.In this paper,a theoretical proof of the stabilityof the three-dimensional(3-D)ADI-FDTD method is presented.It is shown that the 3-D ADI-FDTDmethod is unconditionally stable and free from the CFL condition restraint.

A NEW TECHNIQUE IN BOUNDEDNESS OF INFINITE DELAY DIFFERENTIAL EQUATIONS

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TENSILE INSTABILITY OF NONLINEAR SPHERICAL MEMBRANE WITH LARGE DEFORMATION

The problem on instability on nonlinear spherical membrane with large axisymmetric tensile deformations is investigated by using the bifurcation theory. It is proved that all singular points of the nonlinear boundary value problem must be simple limit points. The effect of loading and material parameters on the equilibrium state and its stability is discussed.