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 pr...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.展开更多
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 discontinuou...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.展开更多
We show that the volume of the projection bodyΠ(Z)of an n-dimensional zonotope Z with n+1 generators and of volume 1 is always exactly 2^(n).Moroever,we point out that an upper bound on the volume ofΠ(K)of a central...We show that the volume of the projection bodyΠ(Z)of an n-dimensional zonotope Z with n+1 generators and of volume 1 is always exactly 2^(n).Moroever,we point out that an upper bound on the volume ofΠ(K)of a centrally symmetric n-dimensional convex body of volume 1 is at least 2^(n)(9/8)^([n/3]).展开更多
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 ti...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.展开更多
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 differentia...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.展开更多
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 comba...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.展开更多
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 ...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.展开更多
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 uncertaintie...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.展开更多
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 ...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.展开更多
The robust controller design problem for switched polytopic systems under asynchronous switching is addressed.These systems exist in many aviation applications, such as dynamical systems involving rapid variations.A s...The robust controller design problem for switched polytopic systems under asynchronous switching is addressed.These systems exist in many aviation applications, such as dynamical systems involving rapid variations.A switched polytopic system is established to describe the highly maneuverable technology vehicle within the full flight envelope and a robust dynamic output feedback control method is designed for the switched polytopic system.Combining the Lyapunov-like function method and the average dwell time method, a sufficient condition is derived for the switched polytopic system with asynchronous switching and data dropout to be globally,uniformly and asymptotically stable in terms of linear matrix inequality.The robust dynamic output feedback controller is then applied to the highly maneuverable technology vehicle to illustrate the effectiveness of the proposed approach.The simulation results show that the angle of attack tracking performance is acceptable over the time history and the control surface responses are all satisfying along the full flight trajectory.展开更多
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 ...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.展开更多
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 ...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.展开更多
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 filteri...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.展开更多
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 ...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.展开更多
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 uncertai...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.展开更多
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 differen...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.展开更多
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-ti...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.展开更多
Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis...Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in [1]. Our approach is based on the use of linear programming and is solvable in polynomial time. The algorithm we developed can be implemented and parallelized in a very easy way.展开更多
基金supported in part by the National Science Foundation Grant DMS-1620016supported in parts by HKSAR grant Q81Q and JRI of The Hong Kong Polytechnic University.
文摘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.
基金M.Cui was supported in part by the National Natural Science Foundation of China(Grant No.11571026)the Beijing Municipal Natural Science Foundation of China(Grant No.1192003)Xiu Ye was supported in part by the National Science Foundation Grant DMS-1620016.
文摘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.
文摘We show that the volume of the projection bodyΠ(Z)of an n-dimensional zonotope Z with n+1 generators and of volume 1 is always exactly 2^(n).Moroever,we point out that an upper bound on the volume ofΠ(K)of a centrally symmetric n-dimensional convex body of volume 1 is at least 2^(n)(9/8)^([n/3]).
基金Supported by the National Natural Science Foundation of China(60811120024)Aeronautical Scienceand Technology Innovation Foundation of China(08C52001)~~
文摘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.
基金The Major Program of National Natural Science Foundation of China(No.11190015)the National Natural Science Foundation of China(No.61374006)
文摘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.
基金supported by Major Projects for Science and Technology Innovation 2030(Grant No.2018AA0100800)Equipment Pre-research Foundation of Laboratory(Grant No.61425040104)in part by Jiangsu Province“333”project under Grant BRA2019051.
文摘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.
基金the Scientific Innovation Team Project of Hubei Provincial Department of Education (T200809)the Science Foundationof Education Commission of Hubei Province (No. D20081306)the Doctoral Pre-research Foundation of Three Gorges University
文摘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.
文摘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.
文摘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.
基金co-supported by the National Natural Science Foundation of China (No.61374032)the Aeronautical Science Foundation of China (No.20130753005)
文摘The robust controller design problem for switched polytopic systems under asynchronous switching is addressed.These systems exist in many aviation applications, such as dynamical systems involving rapid variations.A switched polytopic system is established to describe the highly maneuverable technology vehicle within the full flight envelope and a robust dynamic output feedback control method is designed for the switched polytopic system.Combining the Lyapunov-like function method and the average dwell time method, a sufficient condition is derived for the switched polytopic system with asynchronous switching and data dropout to be globally,uniformly and asymptotically stable in terms of linear matrix inequality.The robust dynamic output feedback controller is then applied to the highly maneuverable technology vehicle to illustrate the effectiveness of the proposed approach.The simulation results show that the angle of attack tracking performance is acceptable over the time history and the control surface responses are all satisfying along the full flight trajectory.
文摘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.
基金Project(61074074)supported by the National Natural Science Foundation,ChinaProject(KT2012C01J0401)supported by the Group Innovation Fund,China
文摘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.
基金supported by the Major Program of National Natural Science Foundation of China(60710002)the Program for Changjiang Scholars and Innovative Research Team in University.
文摘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.
基金partially supported by Major Program of National Natural Science Foundation of China(60710002)Program for Changjiang Scholar and Innovative Research Team in University(PCSIRT).
文摘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.
基金This work was supported by the Chinese National Natural Science Foundation (No. 60374024) and Program for Changjiang Scholars and Innovative Research Team in University.
文摘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.
基金the National Natural Science Foundation of China (29872034) and the Natural Science Foundation of Henan Province for the financi
文摘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.
基金Projects(51205253,11272205)supported by the National Natural Science Foundation of ChinaProject(2012AA7052005)supported by the National High Technology Research and Development Program of China
文摘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.
文摘Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in [1]. Our approach is based on the use of linear programming and is solvable in polynomial time. The algorithm we developed can be implemented and parallelized in a very easy way.
