In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape ...In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.展开更多
The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is comp...The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.展开更多
The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected s...The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. Vector V-function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of interconnected system are given. The stability regions obtained here are much larger than those in previous papers. The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.展开更多
In this paper, we design a fault diagnosis scheme for a class of variable coefficient wave equation (an overhead crane system), which is composed of an observer and its output error is treated as residual signal. When...In this paper, we design a fault diagnosis scheme for a class of variable coefficient wave equation (an overhead crane system), which is composed of an observer and its output error is treated as residual signal. When the system is in a healthy state, the output residual signal decays exponentially. Due to the existence of external disturbance, the residual is not zero in the state without fault. Therefore, we further design a reasonable threshold which is based on the upper bound of the residual dynamics and external disturbance to reduce the influence of external disturbance and determine whether the system fault occurs. The convergence properties of partial differential equation (PDE) observer and residual signal are analyzed by Lyapunov stability theory. Finally, the effectiveness of this fault diagnosis is illustrated by simulation and we can judge whether this overhead crane system fails by this fault diagnosis scheme.展开更多
基金Sponsored by the NSFC (10531070)Research Foundation for Outstanding Young Teachers of China University of Geoscience (Wuhan) (0816)
文摘In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.
文摘The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.
基金supported by National Natural Science Foundation of China(11401123,11271095)Research Fund for the Doctoral Program of Higher Education of China(20124410110002)
文摘The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. Vector V-function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of interconnected system are given. The stability regions obtained here are much larger than those in previous papers. The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.
文摘In this paper, we design a fault diagnosis scheme for a class of variable coefficient wave equation (an overhead crane system), which is composed of an observer and its output error is treated as residual signal. When the system is in a healthy state, the output residual signal decays exponentially. Due to the existence of external disturbance, the residual is not zero in the state without fault. Therefore, we further design a reasonable threshold which is based on the upper bound of the residual dynamics and external disturbance to reduce the influence of external disturbance and determine whether the system fault occurs. The convergence properties of partial differential equation (PDE) observer and residual signal are analyzed by Lyapunov stability theory. Finally, the effectiveness of this fault diagnosis is illustrated by simulation and we can judge whether this overhead crane system fails by this fault diagnosis scheme.
