A LOCAL DISCONTINUOUS GALERKIN METHOD FOR TIME-FRACTIONAL DIFFUSION EQUATIONS

In this paper,a local discontinuous Galerkin(LDG)scheme for the time-fractional diffusion equation is proposed and analyzed.The Caputo time-fractional derivative(of orderα,with 0<α<1)is approximated by a finite difference method with an accuracy of order3-α,and the space discretization is based on the LDG method.For the finite difference method,we summarize and supplement some previous work by others,and apply it to the analysis of the convergence and stability of the proposed scheme.The optimal error estimate is obtained in the L2norm,indicating that the scheme has temporal(3-α)th-order accuracy and spatial(k+1)th-order accuracy,where k denotes the highest degree of a piecewise polynomial in discontinuous finite element space.The numerical results are also provided to verify the accuracy and efficiency of the considered scheme.

Mechanics analysis of a wheelchair robot with wheel-track coupling mechanism

A barrier-free wheelchair robot with a mechanism coupled by wheel and track is presen- ted in this paper. Using the wheelchair, the lower limb disabled persons could be more relaxed to take part in outdoor activities whether on flat ground or stairs and obstacles in the city. The wheel- track coupling mechanism is designed and the stability of the bodywork of the wheelchair robot on the stairs is analyzed. In order to obtain the stability of wheelchair robot when it climbs obstacles, centroid projection method is applied to analyze the static stability, stability margin is proposed to provide the stability under some dynamic forces, and the push rod rotation angle in terms of the guaranteed stability margin is given. Finally, the dynamic model of the wheelchair robot based on Lagrange equation is established, which can be a theoretical foundation for the wheelchair control system design.

Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lya-punov＇s stability theory, linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an Hoe-norm constraint. Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.

Stability of equivariant bifurcation problems with two types of state variables and their unfoldings in presence of parameter symmetry

Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter symmetry is discussed. Some basic results are obtained. Transversality condition is used to characterize the stability of equavariant bifurcation problems.

High-entropy(La_(0.2)Nd_(0.2)Sm_(0.2)Gd_(0.2)Yb_(0.2))_(2)(Zr_(0.75)Ce_(0.25))_(2)O_(7)thermal barrier coating material with significantly enhanced fracture toughness

Poor fracture toughness leads to premature failure of La_(2)(Zr_(0.75)Ce_(0.25))_(2)O_(7)(LCZ)ther-mal barrier coatings in an elevated temperature service environment.A novel coating material,namely(La_(0.2)Nd_(0.2)Sm_(0.2)Gd_(0.2)Yb_(0.2))_(2)(Zr_(0.75)Ce_(0.25))_(2)O_(7)(LNSGY)based on the high-entropy con-cept,was successfully fabricated by solid-state sintering.The microstructure of LCZ and LNSGY was investigated by X-Ray Diffraction(XRD),Raman Spectrometer(RS),Transmission Electronic Microscopy(TEM)and Scanning Electron Microscopy(SEM).The fracture toughness of the LCZ and LNSGY ceramics was evaluated.The LNSGY has excellent high-temperature phase stability,and the grain size of LNSGY ceramic is smaller than that of LCZ ceramic at an elevated temper-ature due to the sluggish diffusion effect.Compared with LCZ(fracture toughness is(1.4±0.1)MPa·m^(1/2)),the fracture toughness of LNSGY is significantly enhanced(fracture toughness is(2.0±0.3)MPa·m^(1/2)).Therefore,the LNSGY can be a promising advanced thermal barrier coat-ing material in the future.

Invariant Subspace and Exact Solutions to the Generalized Kudryashov-Sinelshchikov Equation

In this research,invariant subspaces and exact solutions for the governing equation are obtained through the invariant subspace method,and the generalized second-order Kudryashov-Sinelshchikov equation is used to describe pressure waves in a liquid with bubbles.The governing equations are classified and transformed into a system of ordinary differential equations,and the exact solutions of the classified equation are obtained by solving the system of ordinary differential equations.The method gives logarithmic,polynomial,exponential,and trigonometric solutions for equations.The primary accomplishments of this work are displaying how to obtain the exact solutions of the classified equations and giving the stability analysis of reduced ordinarydifferential equations.

Model Predictive Control Synthesis Approach of Electrode Regulator System for Electric Arc Furnace

In electric are furnace smelting, electrode regulator system is a key link. A good electrode control algorithm will reduce energy consumption effectively and shorten smelting time greatly. The offline design online synthesis model predictive control algorithm is proposed for electrode regulator system with input and output constraints. On the offline computation, the continuum of terminal constraint sets will be constructed. On the online synthesis, the time-varying terminal constraint sets will be adopted and at least one free control variable will be introduced to solve the min-max optimization control problem. Then Lyapunov method will be adopted to analyze closed-loop system stability. Simulation and field trial results show that the proposed offline design online synthesis model predictive control method is effective.

STABILITY OF LOTKA-VOLTERRA COOPERATION SYSTEM WITH SINGLE FEEDBACK CONTROL

In this paper, a Lotka-Volterra cooperation system with single feedback control is proposed and studied. We investigate the local stability and the global stability of the system. Our study shows that with suitable restriction on the coefficients of the feedback control variable, the system can still remain globally stable or become extinct, which shows that the feedback control variable plays a very important role in the dynamics behaviors of the system.

Robust Self-tuning Control Based on Discrete-time Sliding Mode for Auto-regressive Mathematical Model in the Presence of Unmodelled Dynamics

In this paper, we propose a new robust selfbtuning control, called the generalized minimum variance a/-equivalent self- tuning control （GMVSTC-a/） for the linear timevarying （LTV） systems, which can be described by the discrete-time auto-regressive exogenous （ARX） mathematical model in the presence of unmodelled dynamics. The estimation of the parameters contained in this mathematical model is made on the basis of the proposed modified recursive least squares （m-RLS） parametric estimation algorithm with dead zone and forgetting factor. The stability analysis of the proposed parametric estimation algorithm m-RLS is treated on the basis of a Lyapunov function. A numerical simulation example is used to prove the performances and the effectiveness of the explicit scheme of the proposed robust self-tuning control GMVSTC-a/.

Efficient Numerical Computation of Time-Fractional Nonlinear Schrodinger Equations in Unbounded Domain

The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded domain.We first derive absorbing boundary conditions for the fractional system by using the unified approach introduced in[47,48]and a linearization procedure.Then,the initial boundary-value problem for the fractional system with ABCs is discretized,a stability analysis is developed and the error estimate O(h^(2)+τ)is stated.To accel-erate the L1-scheme in time,a sum-of-exponentials approximation is introduced to speed-up the evaluation of the Caputo fractional derivative.The resulting algorithm is highly efficient for long time simulations.Finally,we end the paper by reporting some numerical simulations to validate the properties(accuracy and efficiency)of the derived scheme.

ROBUST STABILITY FOR DEGENERATE NEUTRAL SYSTEMS WITH MIXED TIME-VARYING DELAYS

This paper concerns the stability and robust stability criteria for degenerate neu-tral systems with mixed time-varying delays. A method based on the stability of a new operator D and the linear matrix inequalities is presented that makes it easy to calculate both the upper stability bounds and the free weighting matrices. Since the criteria take the time-varying delays and degenerate neutral systems into account, they are less conservative than previous methods. The Matlab LMI toolbox illustrates the impro...