Impulsive stabilization of a class of nonlinear system with bounded gain error

Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.

A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter

The Unsteady Adaptive Stochastic Finite Elements(UASFE)approach is a robust and efficient uncertainty quantification method for resolving the effect of random parameters in unsteady simulations.In this paper,it is shown that the underlying Adaptive Stochastic Finite Elements(ASFE)method for steady problems based on Newton-Cotes quadrature in simplex elements is extrema diminishing(ED).It is also shown that the method is total variation diminishing(TVD)for one random parameter and for multiple random parameters for first degree Newton-Cotes quadrature.It is proven that the interpolation of oscillatory samples at constant phase in the UASFE method for unsteady problems results in a bounded error as function of the phase for periodic responses and under certain conditions also in a bounded error in time.The two methods are applied to a steady transonic airfoil flow and a transonic airfoil flutter problem.

Self-Sustained Boundedness of Logical and Quantal Error at Semantic Intelligence

It is demonstrated that the recently introduced semantic intelligence spontaneously maintains bounded logical and quantal error on each and every semantic trajectory, unlike its algorithmic counterpart which is not able to. This result verifies the conclusion about the assignment of equal evolutionary value to the motion on the set of all the semantic trajectories sharing the same homeostatic pattern. The evolutionary value of permanent and spontaneous maintenance of boundedness of logical and quantal error on each and every semantic trajectory is to make available spontaneous maintenance of the notion of a kind intact in the long run.

ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS

Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.

Generalized gap functions and error bounds for generalized variational inequalities

We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.

OPTIMAL ERROR BOUND IN A SOBOLEV SPACE OF REGULARIZED APPROXIMATION SOLUTIONS FOR A SIDEWAYS PARABOLIC EQUATION

The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i. e. , a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.

THE CRUCIAL CONSTANTS IN THE EXPONENTIAL-TYPE ERROR ESTIMATES FOR GAUSSIAN INTERPOLATION

It＇s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It＇s of the form｜f（x） - s（x）｜≤（Cd）c/d｜｜f｜｜h where C, c are constants, h is the Gaussian function, s is the interpolating function, and d is called fill distance which, roughly speaking, measures the spacing of the points at which interpolation occurs. This error bound gets small very fast as d → 0. The constants C and c are very sensitive. A slight change of them will result in a huge change of the error bound. The number c can be calculated as shown in [9]. However, C cannot be calculated, or even approximated. This is a famous question in the theory of radial basis functions. The purpose of this paper is to answer this question.

An Existent Condition of Error Bounds for Abstract Linear Inequality System

We consider the abstract linear inequality system （A, C, b） and give a sufficient condition for the system （A, C, b） to have an error bound, which extends the previous result.

Double sampling derivatives and truncation error estimates

This paper investigates double sampling series derivatives for bivariate functions defined on R2 that are in the Bernstein space. For this sampling series, we estimate some of the pointwise and uniform bounds when the function satisfies some decay conditions. The truncated series of this formula allow us to approximate any order of partial derivatives for function from Bernstein space using only a finite number of samples from the function itself. This sampling formula will be useful in the approximation theory and its applications, especially after having the truncation error well-established. Examples with tables and figures are given at the end of the paper to illustrate the advantages of this formula.

ERROR BOUNDS IN PERIODIC QUARTIC SPLINE INTERPOLATION

In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper is to establish that r=0,1,2,3.Also,the nanperiodic cases cannot be constructed empoly-ing the methodology of this paper because that will involve several other end conditions entirely different than(1,10).

Alternative Error Bounds for Some Numerical Quadrature Rules

Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

COMPUTING AREAS BOUNDED BYRATIONAL BEZIER CURVES

An approach is presented for computing integral values, such as areas and volumes of revo-lution . of regions bounded by rational plane B zier curves. The method approximates rational curveswith polynomial curves, and then computes the integral values on those polynomial curves. Errorbounds are provided. For high precision, this new algorithm performs much more quickly than con-ventional numerical methods.

Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD fows

The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics(MHD)flows.The time derivative is expressed by means of Caputo’s fractional derivative concept,while the model is solved via the full-spectral method(FSM)and the semi-spectral scheme(SSS).The FSM is based on the operational matrices of derivatives constructed by using higher-order orthogonal polynomials and collocation techniques.The SSS is developed by discretizing the time variable,and the space domain is collocated by using equal points.A detailed comparative analysis is made through graphs for various parameters and tables with existing literature.The contour graphs are made to show the behaviors of the velocity and magnetic fields.The proposed methods are reasonably efficient in examining the behavior of convection-diffusion equations arising in MHD flows,and the concept may be extended for variable order models arising in MHD flows.

基于有限时间输出反馈的线性扩张状态观测器

为快速、准确地观测系统中的未知扰动及状态,提出一种有限时间线性扩张状态观测器(Finite-time linear extended state observer,FT-LESO),它具有期望的收敛性能且结构简单、易于设计.假设系统的状态无法量测,观测器设计问题转化为扰动下的输出反馈控制问题.针对该问题,提出一种扰动下的有限时间线性输出反馈控制方法,得到控制器参数与闭环系统状态向量2-范数间的解析关系.在此基础上,提出有限时间线性扩张状态观测器,得到观测器参数与观测误差收敛速度及稳态观测误差间的解析关系,给出一充分条件保证观测误差有限时间有界、且能以不低于指数收敛的速度收敛到给定范围内,为观测器参数设计提供理论依据.通过数值仿真验证提出的观测器,仿真结果与理论分析相符,提出的观测器是有效的.

Ellipsoidal bounding set-membership identification approach for robust fault diagnosis with application to mobile robots

A robust fault diagnosis approach is developed by incorporating a set-membership identification (SMI) method. A class of systems with linear models in the form of fault related parameters is investigated, with model uncertainties and parameter variations taken into account explicitly and treated as bounded errors. An ellipsoid bounding set-membership identification algorithm is proposed to propagate bounded uncertainties rigorously and the guaranteed feasible set of faults parameters enveloping true parameter values is given. Faults arised from abrupt parameter variations can be detected and isolated on-line by consistency check between predicted and observed parameter sets obtained in the identification procedure. The proposed approach provides the improved robustness with its ability to distinguish real faults from model uncertainties, which comes with the inherent guaranteed robustness of the set-membership framework. Efforts are also made in this work to balance between conservativeness and computation complexity of the overall algorithm. Simulation results for the mobile robot with several slipping faults scenarios demonstrate the correctness of the proposed approach for faults detection and isolation (FDI).

蛇形机器人跟踪误差预测的自适应轨迹跟踪控制器

为了满足蛇形机器人轨迹跟踪运动的精度需要,消除外界干扰对机器人跟踪误差的影响,提出了一种蛇形机器人跟踪误差预测的自适应轨迹跟踪控制器。所提出的控制器实现了机器人干扰变量、摩擦系数和控制参数的预测,并用预测值和虚拟控制函数来补偿系统的控制输入,抵消了蛇形机器人在轨迹跟踪过程中的侧滑角,避免了干扰变量对机器人带来的负面影响,提高了轨迹跟踪的误差稳定性与控制精度。在建立蛇形机器人模型后,利用积分形式的侧滑角补偿项改进了视线法,并设计了蛇形机器人的自适应轨迹跟踪控制器。使机器人的位置误差在10 s内实现收敛,角度误差小于0.03 rad,预测值误差在5 s内收敛。通过仿真实验,验证了所提出的控制器的有效性和优越性。

A New Type of Solution Method for the Generalized Linear Complementarity Problem over a Polyhedral Cone

This paper addresses the generalized linear complementarity problem （GLCP） over a polyhedral cone. To solve the problem, we first equivalently convert the problem into an affine variational inequalities problem over a closed polyhedral cone, and then propose a new type of method to solve the GLCP based on the error bound estimation. The global and R-linear convergence rate is established. The numerical experiments show the efficiency of the method.

Analysis for MIMO correlated frequency-selective channel in the presence of interference

The space time spreading, superimposed training sequences, and space-time coding are used to present a multiple input and multiple output （MIMO） systems model, and a closed-form of average error probability upper bound expression for MIMO correlated frequency-selective channel in the presence of interference （co-channel interference and jamming signals） is derived. Moreover, the correlation at both ends of the wireless link that can be incorporated equivalently into correlation at the transmit end is also derived, which is significant to analyze space-time link algorithm of MIMO systems.

Space-time spreading and space-time coding for correlated frequency-selective channel in the presence of interference

The space-time spreading （SIS）, superimposed training sequences and space-time coding （STC） are adopted to obtain a closed-form of average error probability upper bound and maximum likelihood esti- mation expression for multiple input and multiple output （MIMO） correlated frequency-selective channel in the presence of interference （colored interference）. Moreover, the correlation at both ends of the wire- less link that can be incorporated equivalently into correlation at the transmit end is derived. Finally, the mean square error （MSE） of the maximum likelihood estimate is also derived.