A Mixed Finite-Element Method on Polytopal Mesh

In this paper,we introduce new stable mixed finite elements of any order on polytopal mesh for solving second-order elliptic problem.We establish optimal order error estimates for velocity and super convergence for pressure.Numerical experiments are conducted for our mixed elements of different orders on 2D and 3D spaces that confirm the theory.

A Modified Weak Galerkin Finite Element Method for the Biharmonic Equation on Polytopal Meshes

A modified weak Galerkin(MWG)finite element method is developed for solving the biharmonic equation.This method uses the same finite element space as that of the discontinuous Galerkin method,the space of discontinuous polynomials on polytopal meshes.But its formulation is simple,symmetric,positive definite,and parameter independent,without any of six inter-element face-integral terms in the formulation of the discontinuous Galerkin method.Optimal order error estimates in a discrete H2 norm are established for the corresponding finite element solutions.Error estimates in the L^(2)norm are also derived with a sub-optimal order of convergence for the lowest-order element and an optimal order of convergence for all high-order of elements.The numerical results are presented to confirm the theory of convergence.

ROBUST FAULT DIAGNOSIS FOR HELICOPTER FCS BASED ON LINEAR PARAMETERVARYING ADAPTIVE OBSERVER

Based on the linear parameter-varying （LPV） adaptive observer, the robust fault diagnosis for a class of LPV systems with external disturbances is studied. Since the flight control system （FCS） is nonlinear and time-varying, the LPV technique is used for FCS. And then the adaptive fault estimation algorithm based on the LPV adaptive observer is proposed to estimate the fault. To minimize the effect of disturbances on the fault estimation, the H~ robust performance index is introduced to design the LPV adaptive fault diagnosis observer and the fault estimation algorithm. The result shows that the method has good estimation performance and is robust to external disturbances. The design method is presented in terms of linear matrix inequalities （LMIs）. Finally, a helicopter LPV FCS model with the actuator fault is used to illustrate the effectiveness of the proposed method.

Polytopic型不确定系统的鲁棒故障检测滤波器设计

研究了具有未知输入和Polytopic型不确定性线性离散时间系统的鲁棒故障检测滤波器(robustfaultdetectionfilter,RFDF)的设计问题.提出了H∞滤波方法及其在Polytopic型RFDF问题上的拓展,根据线性矩阵不等式得出了该设计问题解存在的充分条件以及独立参数RFDF解的参数化问题,并通过算例验证了算法的有效性.

基于电网扰动暂态响应分析的虚拟同步机黑箱建模

建模和仿真是研究储能系统控制应用的重要工具。针对储能变流器的虚拟同步机(virtualsynchronousgenerator,VSG)控制,提出了一种基于电网扰动暂态响应分析的黑箱建模方法。首先基于VSG二阶非线性模型及其在工作点附近的小信号摄动处理,分析电网运行条件和功率指令对黑箱参数的影响,由此确定了黑箱参数MPf辨识采用输出误差(outputerror,OE)模型,黑箱参数MQU辨识采用多中心(polytopic)模型,进一步分析了OE模型的适用条件,并给出了辨识和建模流程。然后通过电网扰动激励出功率振荡模态信息,利用最小二乘法辨识黑箱参数。最后根据实验数据建立了VSG黑箱模型并且验证了模型的有效性,同时在Matlab/Simulink里搭建仿真模型,通过对比详细仿真模型和黑箱模型的仿真速度与存储空间,验证了黑箱模型适用于系统层对大规模储能系统的仿真分析。

Air combat decision-making of multiple UCAVs based on constraint strategy games

Game theory can be applied to the air combat decision-making problem of multiple unmanned combat air vehicles(UCAVs).However,it is difficult to have satisfactory decision-making results completely relying on air combat situation information,because there is a lot of time-sensitive information in a complex air combat environment.In this paper,a constraint strategy game approach is developed to generate intelligent decision-making for multiple UCAVs in complex air combat environment with air combat situation information and time-sensitive information.Initially,a constraint strategy game is employed to model attack-defense decision-making problem in complex air combat environment.Then,an algorithm is proposed for solving the constraint strategy game based on linear programming and linear inequality(CSG-LL).Finally,an example is given to illustrate the effectiveness of the proposed approach.

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.

Stability analysis of time-varying systems via parameter-dependent homogeneous Lyapunov functions

This paper considers the stability analysis of linear continuous-time systems, and that the dynamic matrices are affected by uncertain time-varying parameters, which are assumed to be bounded, continuously differentiable, with bounded rates of variation. First, sufficient conditions of stability for time-varying systems are given by the commonly used parameter-dependent quadratic Lyapunov function. Moreover, the use of homogeneous polynomial Lyapunov functions for the stability analysis of the linear system subject to the time-varying parametric uncertainty is introduced. Sufficient conditions to determine the sought after Lyapunov function is derived via a suitable paramenterization of polynomial homogeneous forms. A numerical example is given to illustrate that the stability conditions are less conservative than similar tests in the literature.

Robust H_∞ Controller Design for Uncertain Neutral Systems via Dynamic Observer Based Output Feedback

In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.

Robust H-infinity estimation for continuous-time polytopic uncertain systems

The design of full-order robust H-infunity estimators is investigated for continuous-time polytopic uncertain systems, The main purpose is to obtain a stable and proper linear estimator such that the estimation error system remains robustly stable with a prescribed H-infinity attenuation level. Based on a recently proposed H-infinity performance criterion which exhibits a kind of decoupling between the Lyapunov matrix and the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.

Model predictive control synthesis algorithm based on polytopic terminal region for Hammerstein-Wiener nonlinear systems

An improved model predictive control algorithm is proposed for Hammerstein-Wiener nonlinear systems.The proposed synthesis algorithm contains two parts:offline design the polytopic invariant sets,and online solve the min-max optimization problem.The polytopic invariant set is adopted to replace the traditional ellipsoid invariant set.And the parameter-correlation nonlinear control law is designed to replace the traditional linear control law.Consequently,the terminal region is enlarged and the control effect is improved.Simulation and experiment are used to verify the validity of the wind tunnel flow field control algorithm.

Robust dissipative filtering for continuous-time polytopic uncertain neutral systems

This article is concerned with the problem of robust dissipative filtering for continuous-time polytopic uncertain neutral systems. The main purpose is to obtain a stable and proper linear filter such that the filtering error system is strictly dissipative. A new criterion for the dissipativity of neutral systems is first provided in terms of linear matrix inequalities （LMI）. Then, an LMI sufficient condition for the existence of a robust filter is established and a design procedure is proposed for this type of systems. Two numerical examples are given. One illustrates the less conservativeness of the proposed criterion; the other demonstrates the validity of the filtering design procedure.

Analysis of finite-time practical stability for time-varying polytopic systems

The problem of finite-time practical stability （FTPS） for time-varying polytopic systems is discussed. Three equivalent conditions for FTPS are first proposed. To facilitate the system analysis, a sufficient linear matrix inequality （LMI） criterion on the FTPS is further provided. The definition of finite-time practical boundedness and a sufficient LMI criterion are also provided to overcome the exogenous disturbance. A numerical example is used to illustrate the effect of the proposed approach.

Enhanced LMI Representations for H2 Performance of Polytopic Uncertain Systems: Continuous-time Case

Based on two recent results, several new criteria of H2 performance for continuous-time linear systems are established by introducing two slack matrices. When used in robust analysis of systems with polytopic uncertainties, they can reduce conservatism inherent in the earlier quadratic method and the established parameter-dependent Lyapunov function approach. Two numerical examples are included to illustrate the feasibility and advantage of the proposed representations.

Parameter-dependent Lyapunov functional for systems with multiple time delays

The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional. The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between die terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results.

Studies on the Synthesis and Complexing Behavior of Crown Ethers with External Coordination Center

The synthesis, characterization of five ditopic or tritopic crown compounds were reported in this paper together with the preparation of the corresponding hetero-dinuclear and hetero-trinuclear complexes with different metal cations.

Robust H_∞ directional control for a sampled-data autonomous airship

A robust H∞ directional controller for a sampled-data autonomous airship with polytopic parameter uncertainties was proposed. By input delay approach, the linearized airship model was transformed into a continuous-time system with time-varying delay. Sufficient conditions were then established based on the constructed Lyapunov-Krasovskii functional, which guarantee that the system is mean-square exponentially stable with H∞ performance. The desired controller can be obtained by solving the obtained conditions. Simulation results show that guaranteed minimum H∞ performance γ=1.4037 and fast response of attitude for sampled-data autonomous airship are achieved in spite of the existence of parameter uncertainties.

Why Well Spread Probability Samples Are Balanced

When sampling from a finite population there is often auxiliary information available on unit level. Such information can be used to improve the estimation of the target parameter. We show that probability samples that are well spread in the auxiliary space are balanced, or approximately balanced, on the auxiliary variables. A consequence of this balancing effect is that the Horvitz-Thompson estimator will be a very good estimator for any target variable that can be well approximated by a Lipschitz continuous function of the auxiliary variables. Hence we give a theoretical motivation for use of well spread probability samples. Our conclusions imply that well spread samples, combined with the Horvitz- Thompson estimator, is a good strategy in a varsity of situations.

Fault diagnosis and accommodation for linear parameter-varying in flight control systems

The fault diagnosis and accommodation strategy for a class of linear parameter-varying (LPV) systems were investigated. A fast adaptive fault estimation (FAFE) algorithm for LPV systems module, based on an adaptive observer, proposed to enhance the performance of fault estimation including rapidity and accuracy. Then, the obtained fault estimate was used to construct the fault tolerant control (FTC) law. The design method was formulated as a convex linear matrix inequalities (LMIs) optimization problem. Once the faults are estimated, the fault tolerant controller is implemented as a dynamic output feedback controller. This controller can compensate for the effect of the faults by stabilizing the closed-loop systems. Finally, a helicopter model in a vertical flight with actuator fault was used to the effectiveness of the proposed approach.

Robust Predictive Control for Polytopic Uncertain Systems with Time-delay Subjected to Actuator Saturation

Robust predictive control algorithms were presented for polytopic uncertain linear discrete systems with time-delay subjected to actuator saturation. In the first algorithm, the parameter dependent state feedback model predictive control (MPC) law was obtained from minimizing the upper bound of the cost function subjected to several linear matrix inequality constraints. In order to reduce computation burden, a second robust MPC algorithm based on nominal performance cost was presented. The feasibility of the optimization problems guarantees that the algorithms are robustly stable. The simulation results verify the effectiveness of the proposed algorithms.