To study the Schneider's projection problem, Lutwak, Yang and Zhang recently introduced a new .affine invariant functional U(P) for convex polytopes in R^n. In the paper, we obtain the analytic expression of the af...To study the Schneider's projection problem, Lutwak, Yang and Zhang recently introduced a new .affine invariant functional U(P) for convex polytopes in R^n. In the paper, we obtain the analytic expression of the affine-invariant U(P) defined on a specific subclass of origin-symmetric convex polytopes in Rn and give an application of U(P) to the Lp-Minkowski problem.展开更多
The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain syst...The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality (LMI) conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.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
Given two disjoint 3-dimensional convex polytopes P and Q and a straight direction along Which P moves in translation, this paper presents a linear algorithm for determining Whether P collides with Q, and the possible...Given two disjoint 3-dimensional convex polytopes P and Q and a straight direction along Which P moves in translation, this paper presents a linear algorithm for determining Whether P collides with Q, and the possible collision positions on P and Q. This result is achieved by using the hierarchicat representation of polytopes, of which the preprocessing time is linear with space.展开更多
In a previous work, we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical variet...In a previous work, we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we summarize the results of the previous work and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs(X, Δ) when X is a projective horospherical variety.展开更多
The logarithmic capacitary Minkowski problem asks for necessary and sufficient conditions on a finite Borel measure on the unit sphere so that it is the logarithmic capacitary measure of a convex body.This article com...The logarithmic capacitary Minkowski problem asks for necessary and sufficient conditions on a finite Borel measure on the unit sphere so that it is the logarithmic capacitary measure of a convex body.This article completely solves the case of discrete measures whose support sets are in general position.展开更多
In this paper we study the cubical stuctures and fundamental groups of real toric spaces.We give an explicit presentation of the fundamental group of the real toric space over a simple polytope.Then using this present...In this paper we study the cubical stuctures and fundamental groups of real toric spaces.We give an explicit presentation of the fundamental group of the real toric space over a simple polytope.Then using this presentation,we give a description of the existence of non-degenerate colourings on a simple polytope from a homotopy point of view.展开更多
In this paper a triangulation of continuous and arbitrary refinement of grid sizes is proposed for simplicial homotopy algorithms to compute zero points on a polytope P. The proposed algorithm generates a piecewise li...In this paper a triangulation of continuous and arbitrary refinement of grid sizes is proposed for simplicial homotopy algorithms to compute zero points on a polytope P. The proposed algorithm generates a piecewise linear path in P × [1,∞) from any chosen interior point x0 of P on level {1} to a solution of the underlying problem. The path is followed by making linear programming pivot steps in a linear system and replacement steps in the triangnlation.The starting point x0 is left in a direction to one vertex of P. The direction in which x0 leaves depends on the function value at x0 and the polytope P. Moreover, we also give a new equivalent form of the Brouwer fixed point theorem on polytopes. This form has many important applications in mathematical programming and the theory of differential equations.展开更多
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 tha...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.展开更多
We first characterize a polytope we prove some properties for the operator Г-2 whose new ellipsoid is a ball. Furthermore 2 and obtain some inequalities.
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
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
基金Project supported by the National Natural Science Foundation of China (No.10671119)
文摘To study the Schneider's projection problem, Lutwak, Yang and Zhang recently introduced a new .affine invariant functional U(P) for convex polytopes in R^n. In the paper, we obtain the analytic expression of the affine-invariant U(P) defined on a specific subclass of origin-symmetric convex polytopes in Rn and give an application of U(P) to the Lp-Minkowski problem.
基金supported by the National Natural Science Foundation of China (6090405161021002)
文摘The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality (LMI) conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.
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.
文摘Given two disjoint 3-dimensional convex polytopes P and Q and a straight direction along Which P moves in translation, this paper presents a linear algorithm for determining Whether P collides with Q, and the possible collision positions on P and Q. This result is achieved by using the hierarchicat representation of polytopes, of which the preprocessing time is linear with space.
文摘In a previous work, we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we summarize the results of the previous work and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs(X, Δ) when X is a projective horospherical variety.
文摘The logarithmic capacitary Minkowski problem asks for necessary and sufficient conditions on a finite Borel measure on the unit sphere so that it is the logarithmic capacitary measure of a convex body.This article completely solves the case of discrete measures whose support sets are in general position.
基金Partially supported by the NSFC(Grant No.11971112)the China Scholarship Council(Grant No.202106100095)。
文摘In this paper we study the cubical stuctures and fundamental groups of real toric spaces.We give an explicit presentation of the fundamental group of the real toric space over a simple polytope.Then using this presentation,we give a description of the existence of non-degenerate colourings on a simple polytope from a homotopy point of view.
文摘In this paper a triangulation of continuous and arbitrary refinement of grid sizes is proposed for simplicial homotopy algorithms to compute zero points on a polytope P. The proposed algorithm generates a piecewise linear path in P × [1,∞) from any chosen interior point x0 of P on level {1} to a solution of the underlying problem. The path is followed by making linear programming pivot steps in a linear system and replacement steps in the triangnlation.The starting point x0 is left in a direction to one vertex of P. The direction in which x0 leaves depends on the function value at x0 and the polytope P. Moreover, we also give a new equivalent form of the Brouwer fixed point theorem on polytopes. This form has many important applications in mathematical programming and the theory of differential equations.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Nos.10671117,30771709)the Science and Technology Research Item of Zhejiang Provincial Department of Education (No.20070935)
文摘We first characterize a polytope we prove some properties for the operator Г-2 whose new ellipsoid is a ball. Furthermore 2 and obtain some inequalities.
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.