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 aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on...The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.展开更多
This paper focused on a class of linear state-delayed systems with or without uncertainty. As for uncertain systems, dissipative uncertainty description contains norm-bounded and positive real uncertainties as special...This paper focused on a class of linear state-delayed systems with or without uncertainty. As for uncertain systems, dissipative uncertainty description contains norm-bounded and positive real uncertainties as special cases. The paper is concerned with the design of dissipative static state feedback controllers such that the closed-loop system is (robustly) asymptotically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative state feedback controllers are obtained by using a linear matrix inequality (LMI) approach. It is shown that the solvability of dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H ∞ control and passive control.展开更多
In this paper, a set of detailed numerical simulations of pulsating solitons in certain regions, where the pulsating solitons exist, have been carried out. The results show that the transformation between pulsating so...In this paper, a set of detailed numerical simulations of pulsating solitons in certain regions, where the pulsating solitons exist, have been carried out. The results show that the transformation between pulsating soliton and fronts can be realised through a series of period-doubling bifurcations, while there exist many kinds of special solutions. The complete transformation diagram has been obtained when the value of nonlinear gain varies within a definite range. The detailed analysis of the diagram reveals that the pulsating soliton experiences period-doubling bifurcations for smaller values of the nonlinear gain. For larger values of it, the pulsating solitons show chaotic behaviour and complex pulse splitting except for some special bifurcations. With the value of nonlinear gain increasing further, the pulse profiles resume pulsating, but the pulse energy are much higher than before and the pulse centre may move along the propagation direction.展开更多
A dissipative-based adaptive neural control scheme was developed for a class of nonlinear uncertain systems with unknown nonlinearities that might not be linearly parameterized. The major advantage of the present work...A dissipative-based adaptive neural control scheme was developed for a class of nonlinear uncertain systems with unknown nonlinearities that might not be linearly parameterized. The major advantage of the present work was to relax the requirement of matching condition, i.e., the unknown nonlinearities appear on the same equation as the control input in a state-space representation, which was required in most of the available neural network controllers. By synthesizing a state-feedback neural controller to make the closed-loop system dissipative with respect to a quadratic supply rate, the developed control scheme guarantees that the L2-gain of controlled system was less than or equal to a prescribed level. And then, it is shown that the output tracking error is uniformly ultimate bounded. The design scheme is illustrated using a numerical simulation.展开更多
By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipat...By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative.展开更多
In this paper we develop a kind of dissipative discrete scheme for the computation of homoclinic orbits near TB-point in Hamiltonian systems. It is proved by using continuation method that when the dissipative term an...In this paper we develop a kind of dissipative discrete scheme for the computation of homoclinic orbits near TB-point in Hamiltonian systems. It is proved by using continuation method that when the dissipative term and its coefficient are suitably chosen, this scheme possesses discrete homoclinic orbits, which approximate the continuous homoclinic orbits with second order accuracy w.r. to time-step size.展开更多
More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtain...More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their for- malism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restric- tions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.展开更多
In this paper we consider the existence of a global periodic attractor for a class of infinite dimensional dissipative equations under homogeneous Dirichlet boundary conditions. It is proved that in a certain paramete...In this paper we consider the existence of a global periodic attractor for a class of infinite dimensional dissipative equations under homogeneous Dirichlet boundary conditions. It is proved that in a certain parameter, for an arbitrary timeperiodic driving force, the system has a unique periodic solution attracting any bounded set exponentially in the phase space, which implies that the system behaves exactly as a one-dimensional system. We mention, in particular, that the obtained result can be used to prove the existence of the global periodic attractor for abstract parabolic problems.展开更多
The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved i...The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .展开更多
This paper investigates a parameterization method of adaptive H∞ controllers for dissipative Hamiltonian systems with disturbances and unknown parameters.The family of adaptive H∞ controllers with full information i...This paper investigates a parameterization method of adaptive H∞ controllers for dissipative Hamiltonian systems with disturbances and unknown parameters.The family of adaptive H∞ controllers with full information is obtained by interconnecting an adaptive H∞ controller with a generalized zero-energy-gradient (ZEG) detectable,free generalized Hamiltonian system.The present parameterization method avoids solving Hamilton-Jacobi-Issacs equations and thus the controllers obtained are easier in operation as compared to some existing ones.Simulations show the effectiveness and feasibility of the adaptive control strategy proposed in this paper.展开更多
In this paper, an upper bound of fractal dimension of the compact kernel sections for the dissipative non-autonomous Klein-Gordon-Schr<span style="white-space:nowrap;">ö</span>dinger lat...In this paper, an upper bound of fractal dimension of the compact kernel sections for the dissipative non-autonomous Klein-Gordon-Schr<span style="white-space:nowrap;">ö</span>dinger lattice system is obtained, by applying a criterion for estimating fractal dimension of a family of compact subsets of a separable Hilbert space.展开更多
A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed bas...A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent (RSSWDD) and strictly (Q, S, R)-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality (LMI). And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.展开更多
We know that the total daily energy dissipation increases in complex organisms like the humans. It’s very probable that this increase in total energy dissipation is related to the progressive increase in mass. But we...We know that the total daily energy dissipation increases in complex organisms like the humans. It’s very probable that this increase in total energy dissipation is related to the progressive increase in mass. But we also know that day by day the dissipation of energy per unit mass decreases in these organisms. We intend to verify if this decrease is only an expression of the second law of thermodynamics, or if it is related to the increase in mass that occurs in these organisms. For this, we set ourselves the following objectives: verify the correlation between total energy dissipation and the evolution of body mass, and verify the correlation between the dissipation of energy per unit of mass and the evolution of body mass. As a result of the data analysis, we found a high degree of correlation between total energy dissipation and the evolution of body mass. And we also found a high correlation between the energy dissipated per unit of mass and the evolution of body mass. We can conclude that self-organization produces not only an increase in mass, but also a decline in energy dissipation per unit mass beyond what is expected by the second law of thermodynamics.展开更多
The definition and the previous measurements of a dynamics-relevant temperature-like quantity in granular media are reviewed for slow and fast particle systems. Especially, the validity of the fluctuation-dissipation ...The definition and the previous measurements of a dynamics-relevant temperature-like quantity in granular media are reviewed for slow and fast particle systems. Especially, the validity of the fluctuation-dissipation theorem in such an athermal system is explored. Experimental evidences for the fluctuation-dissipation theorem relevant effect temperature support the athermal statistical mechanics, which has been widely explored in recent years by physicists. Difficulties encountered in defining temperature or establishing thermodynamics or statistical mechanics in non-equilibrium situations are discussed.展开更多
This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton (gμHS2) system with viscous terms. Under the period boundary conditions and with t...This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton (gμHS2) system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative (gμHS2) system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative (gμHS2) system, we show that the semi-group of the solution operator {S(t)}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S(t)}t≥0 possesses a global attractor in the Sobolev space H2(S) × H2(S).展开更多
In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic (DHSP) solit...In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic (DHSP) solitons. The results reveal that, the evolution and the self-deflection of the bright and dark DHSP solitons are influenced by the system temperature. At a given temperature, for a stable DHSP soliton originally formed in the dissipative system, it attempts to evolve into another DHSP soliton when the temperature change is appropriately small, whereas it will become unstable or break down if the temperature departure is large enough. Moreover, the self-deflection degree of the solitary beam centre increases as temperature rises in some range, while it is decided by the system parameters and is slight under small-signal condition. The system temperature can be adjusted to change the formation and the self-deflection of the solitary beam in order to gain certain optical ends. In a word, the system temperature plays a role for the DHSP solitons in the dissipative system.展开更多
From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretica...From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series truncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.展开更多
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the National NSFC under grant No.50579022the Foundation of Pre-973 Program of China under grant No.2004CCA02500+1 种基金the SRF for the ROCS,SEMthe Talent Recruitment Foundation of HUST
文摘The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.
文摘This paper focused on a class of linear state-delayed systems with or without uncertainty. As for uncertain systems, dissipative uncertainty description contains norm-bounded and positive real uncertainties as special cases. The paper is concerned with the design of dissipative static state feedback controllers such that the closed-loop system is (robustly) asymptotically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative state feedback controllers are obtained by using a linear matrix inequality (LMI) approach. It is shown that the solvability of dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H ∞ control and passive control.
文摘In this paper, a set of detailed numerical simulations of pulsating solitons in certain regions, where the pulsating solitons exist, have been carried out. The results show that the transformation between pulsating soliton and fronts can be realised through a series of period-doubling bifurcations, while there exist many kinds of special solutions. The complete transformation diagram has been obtained when the value of nonlinear gain varies within a definite range. The detailed analysis of the diagram reveals that the pulsating soliton experiences period-doubling bifurcations for smaller values of the nonlinear gain. For larger values of it, the pulsating solitons show chaotic behaviour and complex pulse splitting except for some special bifurcations. With the value of nonlinear gain increasing further, the pulse profiles resume pulsating, but the pulse energy are much higher than before and the pulse centre may move along the propagation direction.
文摘A dissipative-based adaptive neural control scheme was developed for a class of nonlinear uncertain systems with unknown nonlinearities that might not be linearly parameterized. The major advantage of the present work was to relax the requirement of matching condition, i.e., the unknown nonlinearities appear on the same equation as the control input in a state-space representation, which was required in most of the available neural network controllers. By synthesizing a state-feedback neural controller to make the closed-loop system dissipative with respect to a quadratic supply rate, the developed control scheme guarantees that the L2-gain of controlled system was less than or equal to a prescribed level. And then, it is shown that the output tracking error is uniformly ultimate bounded. The design scheme is illustrated using a numerical simulation.
基金The Natural Science Foundation of Yun-nan Province of China (2001A0001M)
文摘By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative.
文摘In this paper we develop a kind of dissipative discrete scheme for the computation of homoclinic orbits near TB-point in Hamiltonian systems. It is proved by using continuation method that when the dissipative term and its coefficient are suitably chosen, this scheme possesses discrete homoclinic orbits, which approximate the continuous homoclinic orbits with second order accuracy w.r. to time-step size.
文摘More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their for- malism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restric- tions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.
文摘In this paper we consider the existence of a global periodic attractor for a class of infinite dimensional dissipative equations under homogeneous Dirichlet boundary conditions. It is proved that in a certain parameter, for an arbitrary timeperiodic driving force, the system has a unique periodic solution attracting any bounded set exponentially in the phase space, which implies that the system behaves exactly as a one-dimensional system. We mention, in particular, that the obtained result can be used to prove the existence of the global periodic attractor for abstract parabolic problems.
文摘The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .
基金supported by National Natural Science Foundation of China (No. 61074189)
文摘This paper investigates a parameterization method of adaptive H∞ controllers for dissipative Hamiltonian systems with disturbances and unknown parameters.The family of adaptive H∞ controllers with full information is obtained by interconnecting an adaptive H∞ controller with a generalized zero-energy-gradient (ZEG) detectable,free generalized Hamiltonian system.The present parameterization method avoids solving Hamilton-Jacobi-Issacs equations and thus the controllers obtained are easier in operation as compared to some existing ones.Simulations show the effectiveness and feasibility of the adaptive control strategy proposed in this paper.
文摘In this paper, an upper bound of fractal dimension of the compact kernel sections for the dissipative non-autonomous Klein-Gordon-Schr<span style="white-space:nowrap;">ö</span>dinger lattice system is obtained, by applying a criterion for estimating fractal dimension of a family of compact subsets of a separable Hilbert space.
基金supported in part by the National Natural Science Foundation of China (60874045 60904030)+1 种基金the Foundation of the Education Bureau of Jiangsu Province (09KJB510019)the Natural Science Foundation of Jiangsu Province (BK2009184)
文摘A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent (RSSWDD) and strictly (Q, S, R)-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality (LMI). And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.
文摘We know that the total daily energy dissipation increases in complex organisms like the humans. It’s very probable that this increase in total energy dissipation is related to the progressive increase in mass. But we also know that day by day the dissipation of energy per unit mass decreases in these organisms. We intend to verify if this decrease is only an expression of the second law of thermodynamics, or if it is related to the increase in mass that occurs in these organisms. For this, we set ourselves the following objectives: verify the correlation between total energy dissipation and the evolution of body mass, and verify the correlation between the dissipation of energy per unit of mass and the evolution of body mass. As a result of the data analysis, we found a high degree of correlation between total energy dissipation and the evolution of body mass. And we also found a high correlation between the energy dissipated per unit of mass and the evolution of body mass. We can conclude that self-organization produces not only an increase in mass, but also a decline in energy dissipation per unit mass beyond what is expected by the second law of thermodynamics.
基金supported by the Key Program of the National Natural Science Foundation of China (Grant No. 11034010)the National Natural Science Foundation of China (Grant No. 11274354)+1 种基金the Special Fund for Earthquake Research of China (Grant No. 201208011)the Chinese Academy of Sciences "Strategic Priority Research Program -SJ-10" (Grant No. XDA04020200)
文摘The definition and the previous measurements of a dynamics-relevant temperature-like quantity in granular media are reviewed for slow and fast particle systems. Especially, the validity of the fluctuation-dissipation theorem in such an athermal system is explored. Experimental evidences for the fluctuation-dissipation theorem relevant effect temperature support the athermal statistical mechanics, which has been widely explored in recent years by physicists. Difficulties encountered in defining temperature or establishing thermodynamics or statistical mechanics in non-equilibrium situations are discussed.
基金partially supported by NNSF of China(11571126,11701198)China Postdoctoral Science Foundation funded project(2017M622397)
文摘This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton (gμHS2) system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative (gμHS2) system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative (gμHS2) system, we show that the semi-group of the solution operator {S(t)}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S(t)}t≥0 possesses a global attractor in the Sobolev space H2(S) × H2(S).
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10574051 and 10174025)
文摘In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic (DHSP) solitons. The results reveal that, the evolution and the self-deflection of the bright and dark DHSP solitons are influenced by the system temperature. At a given temperature, for a stable DHSP soliton originally formed in the dissipative system, it attempts to evolve into another DHSP soliton when the temperature change is appropriately small, whereas it will become unstable or break down if the temperature departure is large enough. Moreover, the self-deflection degree of the solitary beam centre increases as temperature rises in some range, while it is decided by the system parameters and is slight under small-signal condition. The system temperature can be adjusted to change the formation and the self-deflection of the solitary beam in order to gain certain optical ends. In a word, the system temperature plays a role for the DHSP solitons in the dissipative system.
文摘From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series truncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.