This paper proposes a robust dichotomy-based model predictive control(DS-MPC)with a fixed switching frequency for the grid-connected inverter(GCI).The proposed fast dichotomy algorithm can select and deduce the optima...This paper proposes a robust dichotomy-based model predictive control(DS-MPC)with a fixed switching frequency for the grid-connected inverter(GCI).The proposed fast dichotomy algorithm can select and deduce the optimal voltage vector dynamically through the space vector plane.Therefore,the proposed DS-MPC strategy could ensure dynamic performance and steady-state performance as well.Also,the current control robustness can be improved through DS-MPC with disturbance observer(DO)based on the extended Kalman filter(EKF).The novelty of this control is that the current control with fast dynamic response can be realized in the weak grid,even if the grid voltages are greatly distorted.Simulation and hardware experiments on the weak grid validate the effectiveness of the proposed DS-MPC with the EKF observer approach.展开更多
We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ i...We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.展开更多
In this paper we construct, by using the theory of exponential dichotomies, a Melnikov-type function by which we can detect the existence of homoclinic orbits for the perturbed systems x = g(x) + epsilon h(t, x, epsil...In this paper we construct, by using the theory of exponential dichotomies, a Melnikov-type function by which we can detect the existence of homoclinic orbits for the perturbed systems x = g(x) + epsilon h(t, x, epsilon). Our result of this paper may be complementary to that of K.J.Palmer([3]).展开更多
In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△=A（t）x on time scales. Moreover, for the nonlinear perturbed equation x△= A（t）x ...In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△=A（t）x on time scales. Moreover, for the nonlinear perturbed equation x△= A（t）x ＋ f（t, x） we give the instability of the zero solution when f is sufficiently small.展开更多
In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In concl...In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In conclusion, we use the Banach contraction mapping principle and exponential dichotomy property to obtain our main results.展开更多
For time-varying non-regressive linear dynamic equations on a time scale with bounded graininess, we introduce the concept of the associative operator with linear systems on time scales. The purpose of this research i...For time-varying non-regressive linear dynamic equations on a time scale with bounded graininess, we introduce the concept of the associative operator with linear systems on time scales. The purpose of this research is the characterizations of the exponential dichotomy obtained in terms of Fredholm property of that associative operator. Particularly, we use Perron’s method, which was generalized on time scales by J. Zhang, M. Fan, H. Zhu in?[1], to show that if the associative operator is semi-Fredholm then the corresponding linear nonautonomous equation has an exponential dichotomy on both?T?+?and?T-.??Moreover, we also give the converse result that the linear systems have?an exponential dichotomy on both?T?+?andT-??then the associative operator is Fredholm on?T.展开更多
The sequential rock remote sensing information is a group of rocks that are correlative in space or in space and time. For the sake of plottiug them, someone had brought forward the optimization segn.entotion metkod. ...The sequential rock remote sensing information is a group of rocks that are correlative in space or in space and time. For the sake of plottiug them, someone had brought forward the optimization segn.entotion metkod. We have ased this method to plot the sequential rock remote sensing information at tbe remote sensing hyperspetral test field of Daqing mountain, Inner Mongolia Autonomous Region, China, and found some disadvantages of this method. Therefore, we put forward the optimization dichotomy to plot them, and get better results. Finally we make a conclusion.展开更多
In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cy...In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cycle. We improve some important results.展开更多
This paper will discuss the relation between the concepts of nature and culture and their intricate interdependency, focusing on modernity. Moreover, it will analyze the dichotomy that has historically emerged and its...This paper will discuss the relation between the concepts of nature and culture and their intricate interdependency, focusing on modernity. Moreover, it will analyze the dichotomy that has historically emerged and its implications. Human beings have had different conceptions about what is natural and what is non-natural throughout their history. Before Modernity we did not conceive nature as being a different ontological reality, we did not perceive it as being separated from us. After modernity everything changed, and we began to see nature as a mere object. Nature became, then, a representation, like a painting on a wall. Our contemporary world vision, Weltanschauung, was formed mainly during the 16th and 17th centuries. There was, at that time, a considerable change in the way we perceived and described the world. This new mentality and this new form of representing the cosmos provided the basis for our new way of thinking. They were the substrate upon which our modern paradigm was erected. The world＇s conversion in an image only became a reality thanks to technology. But this change happened only because of the paradigm shift originated in the 17th century. Technique always has been a way to articulate how （and what） we think. With the Greek, technique （technd） was, at first, an extension of the physis. Thus, the technique was a way of being instead of a way of thinking. After the paradigm shift in the 17th century （a metaphysical change, in the very way we connected to the world）, the human being left his former place. Perhaps would be even better if we talked about nature and culture as being as a hybrid. What, at the source, was natural, through the flows of production and consumption, undergoes transformations and becomes something that is not natural anymore but, at the same time, not completely artificial either. Our world, once divided between the social and the natural, becomes a space where a constant process, a continuous flow, is constantly happening. From that dichotomy between something good and something bad arises a dialectic, in which we no longer can see any division whatsoever.展开更多
Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address th...Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address the paradoxes. Among the paradoxes, two of the most famous ones are Zeno’s Room Walk and Zeno’s Achilles. Lie Tsu’s pole halving dichotomy is also discussed in relation to these paradoxes. These paradoxes are first-order nonlinear phenomena, and we expressed them with the concepts of linear and nonlinear variables. In the new nonlinear concepts, variables are classified as either linear or nonlinear. Changes in linear variables are simple changes, while changes in nonlinear variables are nonlinear changes relative to their asymptotes. Continuous asymptotic curves are used to describe and derive the equations for expressing the relationship between two variables. For example, in Zeno’s Room Walk, the equations and curves for a person to walk from the initial wall towards the other wall are different from the equations and curves for a person to walk from the other wall towards the initial wall. One walk has a convex asymptotic curve with a nonlinear equation having two asymptotes, while the other walk has a concave asymptotic curve with a nonlinear equation having a finite starting number and a bottom asymptote. Interestingly, they have the same straight-line expression in a proportionality graph. The Appendix of this discussion includes an example of a second-order nonlinear phenomenon. .展开更多
The property of dichotomy of interconnected second-order pendulum-like systems with multiple equilibria is investigated. This interconnection can be viewed as harmonic control of independent sub-systems. Linear interc...The property of dichotomy of interconnected second-order pendulum-like systems with multiple equilibria is investigated. This interconnection can be viewed as harmonic control of independent sub-systems. Linear interconnections and a class of input and output interconnections are considered in this paper. The effects of input and output interconnections are shown through a permutation matrix. Frequency domain and linear matrix inequality (LMI) conditions of dichotomy of interconnected pendulum-like systems are derived. It is shown that global properties of two coupled systems can be changed significantly through interconnections. Examples are given to illustrate the results.展开更多
Oscar Wilde is mainly famous for being the representative figure of Aesthetic Movement and the steadfast advocate of"art for art's sake". Although being influenced by the traditional dichotomy of women, ...Oscar Wilde is mainly famous for being the representative figure of Aesthetic Movement and the steadfast advocate of"art for art's sake". Although being influenced by the traditional dichotomy of women, Wilde does try to add some personal elements during this process. In one of his social comedies, An Ideal Husband, this wildean characteristic is more obvious. This essay attempts to reveal those hidden images which are employed by Wilde to represent his female characters and tries to show the Wilde's improvement of the traditional dichotomy.展开更多
文摘This paper proposes a robust dichotomy-based model predictive control(DS-MPC)with a fixed switching frequency for the grid-connected inverter(GCI).The proposed fast dichotomy algorithm can select and deduce the optimal voltage vector dynamically through the space vector plane.Therefore,the proposed DS-MPC strategy could ensure dynamic performance and steady-state performance as well.Also,the current control robustness can be improved through DS-MPC with disturbance observer(DO)based on the extended Kalman filter(EKF).The novelty of this control is that the current control with fast dynamic response can be realized in the weak grid,even if the grid voltages are greatly distorted.Simulation and hardware experiments on the weak grid validate the effectiveness of the proposed DS-MPC with the EKF observer approach.
文摘We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.
文摘In this paper we construct, by using the theory of exponential dichotomies, a Melnikov-type function by which we can detect the existence of homoclinic orbits for the perturbed systems x = g(x) + epsilon h(t, x, epsilon). Our result of this paper may be complementary to that of K.J.Palmer([3]).
文摘In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△=A（t）x on time scales. Moreover, for the nonlinear perturbed equation x△= A（t）x ＋ f（t, x） we give the instability of the zero solution when f is sufficiently small.
基金The Undergraduate Research Training Program Grant(J1030101)the NSF(11271151)of China
文摘In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In conclusion, we use the Banach contraction mapping principle and exponential dichotomy property to obtain our main results.
文摘For time-varying non-regressive linear dynamic equations on a time scale with bounded graininess, we introduce the concept of the associative operator with linear systems on time scales. The purpose of this research is the characterizations of the exponential dichotomy obtained in terms of Fredholm property of that associative operator. Particularly, we use Perron’s method, which was generalized on time scales by J. Zhang, M. Fan, H. Zhu in?[1], to show that if the associative operator is semi-Fredholm then the corresponding linear nonautonomous equation has an exponential dichotomy on both?T?+?and?T-.??Moreover, we also give the converse result that the linear systems have?an exponential dichotomy on both?T?+?andT-??then the associative operator is Fredholm on?T.
文摘The sequential rock remote sensing information is a group of rocks that are correlative in space or in space and time. For the sake of plottiug them, someone had brought forward the optimization segn.entotion metkod. We have ased this method to plot the sequential rock remote sensing information at tbe remote sensing hyperspetral test field of Daqing mountain, Inner Mongolia Autonomous Region, China, and found some disadvantages of this method. Therefore, we put forward the optimization dichotomy to plot them, and get better results. Finally we make a conclusion.
文摘In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cycle. We improve some important results.
文摘This paper will discuss the relation between the concepts of nature and culture and their intricate interdependency, focusing on modernity. Moreover, it will analyze the dichotomy that has historically emerged and its implications. Human beings have had different conceptions about what is natural and what is non-natural throughout their history. Before Modernity we did not conceive nature as being a different ontological reality, we did not perceive it as being separated from us. After modernity everything changed, and we began to see nature as a mere object. Nature became, then, a representation, like a painting on a wall. Our contemporary world vision, Weltanschauung, was formed mainly during the 16th and 17th centuries. There was, at that time, a considerable change in the way we perceived and described the world. This new mentality and this new form of representing the cosmos provided the basis for our new way of thinking. They were the substrate upon which our modern paradigm was erected. The world＇s conversion in an image only became a reality thanks to technology. But this change happened only because of the paradigm shift originated in the 17th century. Technique always has been a way to articulate how （and what） we think. With the Greek, technique （technd） was, at first, an extension of the physis. Thus, the technique was a way of being instead of a way of thinking. After the paradigm shift in the 17th century （a metaphysical change, in the very way we connected to the world）, the human being left his former place. Perhaps would be even better if we talked about nature and culture as being as a hybrid. What, at the source, was natural, through the flows of production and consumption, undergoes transformations and becomes something that is not natural anymore but, at the same time, not completely artificial either. Our world, once divided between the social and the natural, becomes a space where a constant process, a continuous flow, is constantly happening. From that dichotomy between something good and something bad arises a dialectic, in which we no longer can see any division whatsoever.
文摘Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address the paradoxes. Among the paradoxes, two of the most famous ones are Zeno’s Room Walk and Zeno’s Achilles. Lie Tsu’s pole halving dichotomy is also discussed in relation to these paradoxes. These paradoxes are first-order nonlinear phenomena, and we expressed them with the concepts of linear and nonlinear variables. In the new nonlinear concepts, variables are classified as either linear or nonlinear. Changes in linear variables are simple changes, while changes in nonlinear variables are nonlinear changes relative to their asymptotes. Continuous asymptotic curves are used to describe and derive the equations for expressing the relationship between two variables. For example, in Zeno’s Room Walk, the equations and curves for a person to walk from the initial wall towards the other wall are different from the equations and curves for a person to walk from the other wall towards the initial wall. One walk has a convex asymptotic curve with a nonlinear equation having two asymptotes, while the other walk has a concave asymptotic curve with a nonlinear equation having a finite starting number and a bottom asymptote. Interestingly, they have the same straight-line expression in a proportionality graph. The Appendix of this discussion includes an example of a second-order nonlinear phenomenon. .
基金Supported by National Natural Science Foundation of P. R. China (60334030, 60204007, 60474029, 60404007)
文摘The property of dichotomy of interconnected second-order pendulum-like systems with multiple equilibria is investigated. This interconnection can be viewed as harmonic control of independent sub-systems. Linear interconnections and a class of input and output interconnections are considered in this paper. The effects of input and output interconnections are shown through a permutation matrix. Frequency domain and linear matrix inequality (LMI) conditions of dichotomy of interconnected pendulum-like systems are derived. It is shown that global properties of two coupled systems can be changed significantly through interconnections. Examples are given to illustrate the results.
文摘Oscar Wilde is mainly famous for being the representative figure of Aesthetic Movement and the steadfast advocate of"art for art's sake". Although being influenced by the traditional dichotomy of women, Wilde does try to add some personal elements during this process. In one of his social comedies, An Ideal Husband, this wildean characteristic is more obvious. This essay attempts to reveal those hidden images which are employed by Wilde to represent his female characters and tries to show the Wilde's improvement of the traditional dichotomy.
