Novel Criteria on Finite-Time Stability of Impulsive Stochastic Nonlinear Systems

Dear Editor,This letter considers the finite-time stability(FTS)problem of generalized impulsive stochastic nonlinear systems(ISNS).By employing the stochastic Lyapunov and impulsive control approach,some novel criteria on FTS are presented,where both situations of stabilizing and destabilizing impulses are considered.Furthermore,new impulse-dependent estimation strategies of stochastic settling time(SST)are proposed.

Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.

Controlling chaos in power system based on finite-time stability theory

Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.

Finite-time stability with respect to a closed invariant set for a class of discontinuous systems

This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.

Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects

Many practical systems in physics, biology, engineer- ing and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynami- cal processes. The problems of finite-time stab!lity analysis are investigated for a class of Markovian switching stochastic sys- tems, in which exist impulses at the switching instants. Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system. Furthermore, a state feedback controller, which stabilizes the closed loop sys- tems in the finite-time sense, is then addressed. Moreover, the controller appears not only in the shift part but also in the diffu- sion part of the underlying stochastic subsystem. The results are reduced to feasibility problems involving linear matrix inequalities （LMIs）. A numerical example is presented to illustrate the proposed methodology.

Finite-Time Stability for Nonlinear Fractional Differential Equations with Time Delay

The finite-time stability and the finite-time contractive stability of solutions for nonlinear fractional differential equations with bounded delay are investigated. The derivative of Lyapunov function along solutions of the considered system is defined in terms of the Caputo fractional Dini derivative. Based on the Lyapunov-Razumikhin method, several sufficient criteria are established to guarantee the finite-time stability and the finite-time contractive stability of solutions for the related systems. An example is provided to illustrate the effectiveness of the obtained results.

Finite-time Stability of Heating Furnace Temperature Control System

A finite-time stabilization controller for the heating furnace temperature control system is proposed.Based on the extended Lyapunov finite-time stability theory and power integral method,a finite-time stable condition of the heating furnace temperature control system is given.The temperature of the heating furnace is directed by the finite-time stabilization controller to make it stable in finite time.And the quality and quantity of slabs is improved.The simulation example is presented to illustrate the applicability of the developed results.

Finite-Time Stability of Nonautonomous Delayed Systems

The finite-time stability to linear discontinuous time-varying delayed system was investigated. By applying the method of upper and lower solutions, some sufficient conditions of this kind of stability were obtained. Furthermore, it also developed a monotone iterative technique for obtaining solutions which are obtained as limits of monotone sequences

Finite-Time Stability and Instability of Nonlinear Impulsive Systems

In this paper,the finite-time stability and instability are studied for nonlinear impulsive systems.There are mainly four concerns.1)For the system with stabilizing impulses,a Lyapunov theorem on global finite-time stability is presented.2)When the system without impulsive effects is globally finite-time stable(GFTS)and the settling time is continuous at the origin,it is proved that it is still GFTS over any class of impulse sequences,if the mixed impulsive jumps satisfy some mild conditions.3)For systems with destabilizing impulses,it is shown that to be finite-time stable,the destabilizing impulses should not occur too frequently,otherwise,the origin of the impulsive system is finite-time instable,which are formulated by average dwell time(ADT)conditions respectively.4)A theorem on finite-time instability is provided for system with stabilizing impulses.For each GFTS theorem of impulsive systems considered in this paper,the upper boundedness of settling time is given,which depends on the initial value and impulsive effects.Some numerical examples are given to illustrate the theoretical analysis.

Finite-Time Stabilization for Constrained Discrete-time Systems by Using Model Predictive Control

In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guarantees the finite-time convergence property by assigning the control horizon equal to the dimension of the overall system, and only penalizing the terminal cost in the optimization, where the stage costs are not penalized explicitly. A terminal inequality constraint is added to guarantee the feasibility and stability of the closed-loop system.Initial feasibility can be improved via augmentation. The finite-time convergence of the proposed MPC is proved theoretically,and is supported by simulation examples.

Finite-Time Stability of Fractional-Order Neural Networks with Delay

Finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwa11 inequality and estimates of Mittag-Leffier functions, sufficient conditions are pre- sented to ensure the finite-time stability of such neural models with the Caputo fractionM derivatives. Furthermore, results about asymptotical stability of fractional-order neural models are also obtained.

Input-output finite-time stability of time-varying linear singular systems

This paper studies the input-output finite-time stabilization problem for time-varying linear singular sys- tems. The output and the input refer to the controlled output and the disturbance input, respectively. Two classes of dis- turbance inputs are considered, which belong to L-two and L-infinity. Sufficient conditions are firstly provided which guarantee the input-output finite-time stability. Based on this, state feedback controllers are designed such that the resultant closed-loop systems are input-output finite-time stable. The conditions are presented in terms of differential linear matrix inequalities. Finally, an example is presented to show the validity of the proposed results.

Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.

Finite-Time Stability for Fractional-Order Bidirectional Associative Memory Neural Networks with Time Delays

This paper is concerned with fractional-order bidirectional associative memory(BAM) neural networks with time delays. Applying Laplace transform, the generalized Gronwall inequality and estimates of Mittag–Leffler functions, some sufficient conditions which ensure the finite-time stability of fractional-order bidirectional associative memory neural networks with time delays are obtained. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results.

Mechanical Modeling and Analysis of Stability Deterioration of Production Well During Marine Hydrate Depressurization Production

Different from oil and gas production,hydrate reservoirs are shallow and unconsolidated,whose mechanical properties deteriorate with hydrate decomposition.Therefore,the formations will undergo significant subsidence during depressurization,which will destroy the original force state of the production well.However,existing research on the stability of oil and gas production wells assumes the formation to be stable,and lacks consideration of the force exerted on the hydrate production well by formation subsidence caused by hydrate decomposition during production.To fill this gap,this paper proposes an analytical method for the dynamic evolution of the stability of hydrate production well considering the effects of hydrate decomposition.Based on the mechanical model of the production well,the basis for stability analysis has been proposed.A multi-field coupling model of the force state of the production well considering the effect of hydrate decomposition and formation subsidence is established,and a solver is developed.The analytical approach is verified by its good agreement with the results from the numerical method.A case study found that the decomposition of hydrate will increase the pulling-down force and reduce the supporting force,which is the main reason for the stability deterioration.The higher the initial hydrate saturation,the larger the reservoir thickness,and the lower the production pressure,the worse the stability or even instability.This work can provide a theoretical reference for the stability maintaining of the production well.

Impact of spatially varying rock disturbance on rock slope stability

Degradation of rock mass produced by rock blasting,stress relief,and other causes is an important factor in the assessment of rock strength.Quantified as a disturbance factor,such degradation varies depending on blasting control,stress state and stress relief,and rock mass quality.This study focuses on the impact of disturbance on the safety of slopes.The disturbance in the rock mass is characterized by the geometry of the disturbed zone,its size,the magnitude,and the decaying rate with the distance away from the slope surface.A method accounting for decay of rock disturbance is presented.A study of the impact of rock disturbance characteristics on the quantitative stability measures of slopes was carried out.These characteristics included disturbed zone geometry,its thickness,the maximum magnitude of the disturbance factor,and the rate of disturbance decaying.The thickness of the disturbed zone and the maximum factor of disturbance were found to have the greatest impact.For example,the factor of safety for a 45slope in low-quality rock mass can decrease from 1.96 to 1.09 as the thickness of the disturbed zone increases from 1/4 of slope height H to the double of H and the maximum disturbance factor increases from 0.5 to 1.Uniform thickness of a disturbed zone was found to yield more conservative outcomes than the triangular zones did.The critical failure surfaces were found to be shallow for high rates of disturbance decay,and they were the deepest for spatially uniform disturbance factors.

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

Probabilistic analysis of tunnel face seismic stability in layered rock masses using Polynomial Chaos Kriging metamodel

Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.

Evaluation of slope stability through rock mass classification and kinematic analysis of some major slopes along NH-1A from Ramban to Banihal, North Western Himalayas

The network of Himalayan roadways and highways connects some remote regions of valleys or hill slopes,which is vital for India’s socio-economic growth.Due to natural and artificial factors,frequency of slope instabilities along the networks has been increasing over last few decades.Assessment of stability of natural and artificial slopes due to construction of these connecting road networks is significant in safely executing these roads throughout the year.Several rock mass classification methods are generally used to assess the strength and deformability of rock mass.This study assesses slope stability along the NH-1A of Ramban district of North Western Himalayas.Various structurally and non-structurally controlled rock mass classification systems have been applied to assess the stability conditions of 14 slopes.For evaluating the stability of these slopes,kinematic analysis was performed along with geological strength index(GSI),rock mass rating(RMR),continuous slope mass rating(CoSMR),slope mass rating(SMR),and Q-slope in the present study.The SMR gives three slopes as completely unstable while CoSMR suggests four slopes as completely unstable.The stability of all slopes was also analyzed using a design chart under dynamic and static conditions by slope stability rating(SSR)for the factor of safety(FoS)of 1.2 and 1 respectively.Q-slope with probability of failure(PoF)1%gives two slopes as stable slopes.Stable slope angle has been determined based on the Q-slope safe angle equation and SSR design chart based on the FoS.The value ranges given by different empirical classifications were RMR(37-74),GSI(27.3-58.5),SMR(11-59),and CoSMR(3.39-74.56).Good relationship was found among RMR&SSR and RMR&GSI with correlation coefficient(R 2)value of 0.815 and 0.6866,respectively.Lastly,a comparative stability of all these slopes based on the above classification has been performed to identify the most critical slope along this road.

Reliability analysis of slope stability by neural network,principal component analysis,and transfer learning techniques

The prediction of slope stability is considered as one of the critical concerns in geotechnical engineering.Conventional stochastic analysis with spatially variable slopes is time-consuming and highly computation-demanding.To assess the slope stability problems with a more desirable computational effort,many machine learning(ML)algorithms have been proposed.However,most ML-based techniques require that the training data must be in the same feature space and have the same distribution,and the model may need to be rebuilt when the spatial distribution changes.This paper presents a new ML-based algorithm,which combines the principal component analysis(PCA)-based neural network(NN)and transfer learning(TL)techniques(i.e.PCAeNNeTL)to conduct the stability analysis of slopes with different spatial distributions.The Monte Carlo coupled with finite element simulation is first conducted for data acquisition considering the spatial variability of cohesive strength or friction angle of soils from eight slopes with the same geometry.The PCA method is incorporated into the neural network algorithm(i.e.PCA-NN)to increase the computational efficiency by reducing the input variables.It is found that the PCA-NN algorithm performs well in improving the prediction of slope stability for a given slope in terms of the computational accuracy and computational effort when compared with the other two algorithms(i.e.NN and decision trees,DT).Furthermore,the PCAeNNeTL algorithm shows great potential in assessing the stability of slope even with fewer training data.