As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many o...As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.展开更多
In order to study whether the intemal control of enterprises is effective, this paper studies the relationship between the quality of internal control and the performance of the company in 2012-2015, in which 61 liste...In order to study whether the intemal control of enterprises is effective, this paper studies the relationship between the quality of internal control and the performance of the company in 2012-2015, in which 61 listed companies in China＇s Shanghai traffic transportation industry are studied. The results show that the quality of internal control has a significant positive correlation with the financial performance of enterprises. In particular, the internal control is significantly correlated with the company＇s growth ability, and the internal control is positively correlated with the profitability of the company. This research provides empirical data and decision-making basis for the state to deepen the construction of internal control system and strengthen internal control management of enterprises.展开更多
This paper investigates the problem of global disturbance rejection for a class of switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances ...This paper investigates the problem of global disturbance rejection for a class of switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances are assumed to be sinusoidal with completely unknown frequencies, phases and amplitudes. First, as an extension of the classic concept of internal model for non-switched systems, a switched internal model is proposed. Second, in order to solve the problem under study, an adaptive control method is established on the basis of the multiple Lyapunov functions method. Also,adaptive state-feedback controllers of subsystems are designed and incorporated with a switching law to asymptotically reject the unknown disturbances. Finally, an example is provided to demonstrate the effectiveness of the proposed design method.展开更多
For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In partic...For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the local exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.展开更多
基金Supported by National Natural Science Foundation of China (No.10871144)the Seed Foundation of Tianjin University (No.60302023)
文摘As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.
文摘In order to study whether the intemal control of enterprises is effective, this paper studies the relationship between the quality of internal control and the performance of the company in 2012-2015, in which 61 listed companies in China＇s Shanghai traffic transportation industry are studied. The results show that the quality of internal control has a significant positive correlation with the financial performance of enterprises. In particular, the internal control is significantly correlated with the company＇s growth ability, and the internal control is positively correlated with the profitability of the company. This research provides empirical data and decision-making basis for the state to deepen the construction of internal control system and strengthen internal control management of enterprises.
基金supported by the National Natural Science Foundation of China under Grant Nos.61773100 and 61773098IAPI Fundamental Research Funds under Grant No.2013ZCX03-02Fundamental Research Funds for the Central Universities under Grant No.N150404024
文摘This paper investigates the problem of global disturbance rejection for a class of switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances are assumed to be sinusoidal with completely unknown frequencies, phases and amplitudes. First, as an extension of the classic concept of internal model for non-switched systems, a switched internal model is proposed. Second, in order to solve the problem under study, an adaptive control method is established on the basis of the multiple Lyapunov functions method. Also,adaptive state-feedback controllers of subsystems are designed and incorporated with a switching law to asymptotically reject the unknown disturbances. Finally, an example is provided to demonstrate the effectiveness of the proposed design method.
文摘For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the local exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.
