GLOBAL EXISTENCE,EXPONENTIAL DECAY AND BLOW-UP IN FINITE TIME FOR A CLASS OF FINITELY DEGENERATE SEMILINEAR PARABOLIC EQUATIONS

In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=（X1,X2,…,Xm） is a system of real smooth vector fields which satisfy the H?rmander’s condition,and △X=∑j=1m Xj2 is a finitely degenerate elliptic operator.Using potential well method,we first prove the invariance of some sets and vacuum isolating of solutions.Finally,by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy,and also we discuss the asymptotic behavior of the global solutions.

Finite-Time Thermodynamic Simulation of Circulating Direct Condensation Heat Recovery on Chillers

A time series model is used in this paper to describe the progress of circulating direct condensation heat recovery of the compound condensing process (CCP) which is made of two water cooling condensing processes in series for a centrifugal chiller in the paper. A finite-time thermodynamics method is used to set up the time series simulation model. As a result, an upper bound of recoverable condensation heat for the compound condensing process is obtained which is in good agreement with experimental result. And the result is valuable and useful to optimization design of condensing heat recovery.

Neural-Network-Based Adaptive Finite-Time Control for a Two-Degree-of-Freedom Helicopter System With an Event-Triggering Mechanism

Helicopter systems present numerous benefits over fixed-wing aircraft in several fields of application.Developing control schemes for improving the tracking accuracy of such systems is crucial.This paper proposes a neural-network(NN)-based adaptive finite-time control for a two-degree-of-freedom helicopter system.In particular,a radial basis function NN is adopted to solve uncertainty in the helicopter system.Furthermore,an event-triggering mechanism(ETM)with a switching threshold is proposed to alleviate the communication burden on the system.By proposing an adaptive parameter,a bounded estimation,and a smooth function approach,the effect of network measurement errors is effectively compensated for while simultaneously avoiding the Zeno phenomenon.Additionally,the developed adaptive finite-time control technique based on an NN guarantees finitetime convergence of the tracking error,thus enhancing the control accuracy of the system.In addition,the Lyapunov direct method demonstrates that the closed-loop system is semiglobally finite-time stable.Finally,simulation and experimental results show the effectiveness of the control strategy.

PD-like finite time controller with simple structure for satellite attitude control

A finite time controller with PD-like structure for satellite attitude control is proposed in this paper.The controller is constructed with simple structure based on standard PD controller.The fractional order term is designed hence system could both have strong robustness and finite time convergence rate,and the advantage of finite time control and PD control is combined in this paper.System convergence rate is discussed by Lyapunov method,and the constraint on control parameters is given by implementing the coupled term of angular velocity and attitude quaternion.Moreover,the accuracy at steady stage depending on control parameters is given hence system could converge to this field within finite time.System stability and performance is demonstrated by numerical simulation results.

Proper orthogonal decomposition based seismic source wavefield reconstruction for finite element reverse time migration

The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.

Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic

A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the computation costs,the fast Fourier transform technic is applied to a pair of equivalent coupled differential equations.The effectiveness of the proposed algorithm is verified by the first numerical example.The mass conservation property and stability statement are confirmed by two other numerical examples.

Finite Time Domain Dynamics of Dirac Fields

In the present paper we consider the case of a Dirac field in a finite time domain and coupled to an external field. We decompose the field and its Hamiltonian in terms of creation and annihilation operators and path integrate it via Grassmannian variables techniques. In that way we obtain its finite time domain Green function. We use it in the perturbative study of the interaction of Dirac particles with classical electromagnetic waves.

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

Global Existence and Blow-up in Finite Time for a Class of Finitely Degenerate Semilinear Pseudo-parabolic Equations

In this paper, we study the initial-boundary value problem for the semilinear pseudoparabolic equations ut —△xut —△xu =|u|^p-1u, where X =(X1, X2,..., Xm) is a system of real smooth vector fields which satisfy the Hormander's condition, and △x =∑j=1^m Xj^2 is a finitely degenera te elliptic operator. By using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy. The asymptotic behavior of the global solutions and a lower bound for blow-up time of local solution are also given.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

Finite-Time H∞ Control of Switched Nonlinear Systems under State-Dependent Switching

This paper investigates the finite-time H∞ control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H∞ control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.

DELAY-TIME MODEL BASED ON IMPERFECT INSPECTION OF AIRCRAFT STRUCTURE WITHIN FINITE TIME SPAN

According to the failure characteristics of aircraft structure, a delay-time model is an effective method to optimize maintenance for aircraft structure. To imitate the practical situation as much as possible, imperfect inspections, thresholds and repeated intervals are concerned in delay-time models. Since the suggestion by the existing delay-time models that the inspections are implemented in an infinite time span lacks practical value, a de- lay-time model with imperfect inspection within a finite time span is proposed. In the model, the nonhomogenous Poisson process is adopted to obtain the renewal probabilities between two different successive inspections on de- fects or failures. An algorithm is applied based on the Nelder-Mead downhill simplex method to solve the model. Finally, a numerical example proves the validity and effectiveness of the model.

Viscoacoustic prestack reverse time migration based onthe optimal time-space domain high-order finite-difference method

Prestack reverse time migration （RTM） is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference （FD） method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency noise.Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution.

Boundary Value Problems of p-Laplace Equations with Finite Time Delay

By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed with p Laplacian. The topological degree and fixed point theorem on cone are used to prove the existence of solution and positive solution. The conditions are all easy to check.

Full-Wave Analysis of Slotline Using Time-Domain Finite-Difference Method

The transmission and dispersive characteristics of slotline are calculated in this paper. The tail of Gaussion pulse is improved because a modified dispersive boundary condition (DBC) is adopted. It leads to a reduction in computer memory requirements and computational time. The computational domain is greatly reduced to enable performance in personal computer. At the same time because edges of a boundary and summits are treated well, the computational results is more accurate and more collector.

Finite-time Adaptive Fault-tolerant Control for Nonlinear Systems With Multiple Faults

This paper focuses on the problem of adaptive finitetime fault-tolerant control for a class of non-lower-triangular nonlinear systems.The faults encountered in the control system include the actuator faults and the abrupt system fault.By applying backstepping design and neural networks approximation,an adaptive finite-time fault-tolerant control scheme is developed.It is shown that the proposed controller ensures that all signals in the closed-loop system are semi-globally practically finite-time stable and the track-ing error converges to a small neighborhood around the origin within finite time.The simulation is carried out to explain the validity of the developed strategy.

Impact angle control over composite guidance law based on feedback linearization and finite time control

The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation of guidance systems into the feedbackable linearization model, in which the guidance law is obtained without considering the impact angle via FLC. For the purpose of the line of sight(LOS) angle and its rate converging to the desired values, the second-order LOS angle is considered as a double-integral system. Then, this paper utilizes FTC to design a controller which can guarantee the states of the double-integral system converging to the desired values. Numerical simulation illustrates the performance of the IACG, in contrast to the existing guidance law.

Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance

In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying and bounded. Sufficient conditions are obtained for the existence of a linear parameter-dependent state feedback gain, which can ensure that the closed-loop system is finite-time bounded （FTB）. The conditions can be reduced to feasibility problems involving LMIs. Numerical examples show the validity of the proposed methodology.

BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS

Let G =（V, E） be a locally finite connected weighted graph, and ？ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ？u ＋ f（u） on G. The blow-up phenomenons for ut = ？u ＋ f（u） are discussed in terms of two cases：（i） an initial condition is given;（ii） a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.

Time-Varying Asymmetrical BLFs Based Adaptive Finite-Time Neural Control of Nonlinear Systems With Full State Constraints

This paper concentrates on asymmetric barrier Lyapunov functions(ABLFs)based on finite-time adaptive neural network(NN)control methods for a class of nonlinear strict feedback systems with time-varying full state constraints.During the process of backstepping recursion,the approximation properties of NNs are exploited to address the problem of unknown internal dynamics.The ABLFs are constructed to make sure that the time-varying asymmetrical full state constraints are always satisfied.According to the Lyapunov stability and finitetime stability theory,it is proven that all the signals in the closedloop systems are uniformly ultimately bounded(UUB)and the system output is driven to track the desired signal as quickly as possible near the origin.In the meantime,in the scope of finitetime,all states are guaranteed to stay in the pre-given range.Finally,a simulation example is proposed to verify the feasibility of the developed finite time control algorithm.