This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along wit...This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.展开更多
A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vert...A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vertex.This concept was introduced by Tutte as an extension of face colorings,and Tutte in 1954 conjectured that every bridgeless graph admits a nowhere-zero 5-flow,known as the 5-Flow Conjecture.This conjecture is verified for some graph classes and remains unresolved as of today.In this paper,we show that every bridgeless graph of Euler genus at most 20 admits a nowhere-zero 5-flow,which improves several known results.展开更多
Direct Thrust Control(DTC) is effective in dealing with the mismatch between thrust and rotor speed in traditional engine control. Among the DTC architecture, model-based thrust estimation method has less arithmetic c...Direct Thrust Control(DTC) is effective in dealing with the mismatch between thrust and rotor speed in traditional engine control. Among the DTC architecture, model-based thrust estimation method has less arithmetic consumption and better real-time performance. In this paper,a direct thrust controller design approach for gas turbine engine based on parameter dependent model is proposed. In order to ensure the stability of DTC control system based on parameter dependent model, there are usually conservatism detects. For the purpose of reducing the conservatism in the solution process of filter and controller, an Equilibrium Manifold Expansion(EME) model with bounded parameter variation of engine is established. The design conditions of Kalman filter for discrete-time EME system are introduced, and the proposed conditions have a certain suppression effect on the input noise of the system with bounded parameter variation.The engine thrust estimator stability and H∞filtering problems are solved by the polytopic quadratic Lyapunov function based on the Linear Matrix Inequalities(LMIs). To meet the performance requirements of thrust control, the Grey Wolf Optimization(GWO) algorithm is applied to optimize the PID control parameters. The proposed method is verified on a Hardware-in-Loop(HIL) platform. The simulation results demonstrate that the DTC framework can ensure the stability of engine closed-loop system in large range deviation tests. The filter and controller solution method considering the parameter variation boundary can obtain a solution that makes the system have better performance parameters. Moreover, the proposed filter has better thrust estimation performance than the traditional Kalman filter under the condition of sensor noise. Compared with Augmented Linear Quadratic Regulator(ALQR) controller, the PID controller optimized by GWO has a faster response in simulation.展开更多
Delay aware routing is now widely used to provide efficient network transmission. However, for newly developing or developed mobile communication networks(MCN), only limited delay data can be obtained. In such a netwo...Delay aware routing is now widely used to provide efficient network transmission. However, for newly developing or developed mobile communication networks(MCN), only limited delay data can be obtained. In such a network, the delay is with epistemic uncertainty, which makes the traditional routing scheme based on deterministic theory or probability theory not applicable. Motivated by this problem, the MCN with epistemic uncertainty is first summarized as a dynamic uncertain network based on uncertainty theory, which is widely applied to model epistemic uncertainties. Then by modeling the uncertain end-toend delay, a new delay bounded routing scheme is proposed to find the path with the maximum belief degree that satisfies the delay threshold for the dynamic uncertain network. Finally, a lowEarth-orbit satellite communication network(LEO-SCN) is used as a case to verify the effectiveness of our routing scheme. It is first modeled as a dynamic uncertain network, and then the delay bounded paths with the maximum belief degree are computed and compared under different delay thresholds.展开更多
For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case ...For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.展开更多
Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_...Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).展开更多
This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution un...This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution under some conditions.展开更多
In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forci...In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forcing function andαis a real parameter.Inspired by this special discontinuous oscillator,we study a more general discontinuous oscillator x′′+ω^(2)x+ϕ(x)=p(t),whereω∈R^(+)\N andϕ(x)has one discontinuous point.We show that every solution of this general discontinuous oscillator is bounded when some conditions are satisfied.展开更多
This work aims to reduce queries on big data to computations on small data,and hence make querying big data possible under bounded resources.A query Q is boundedly evaluable when posed on any big dataset D,there exist...This work aims to reduce queries on big data to computations on small data,and hence make querying big data possible under bounded resources.A query Q is boundedly evaluable when posed on any big dataset D,there exists a fraction DQ of D such that Q(D)=Q(DQ),and the cost of identifying DQ is independent of the size of D.It has been shown that with an auxiliary structure known as access schema,many queries in relational algebra(RA)are boundedly evaluable under the set semantics of RA.This paper extends the theory of bounded evaluation to RAaggr,i.e.,RA extended with aggregation,under the bag semantics.(1)We extend access schema to bag access schema,to help us identify DQ for RAaggr queries Q.(2)While it is undecidable to determine whether an RAaggr query is boundedly evaluable under a bag access schema,we identify special cases that are decidable and practical.(3)In addition,we develop an effective syntax for bounded RAaggr queries,i.e.,a core subclass of boundedly evaluable RAaggr queries without sacrificing their expressive power.(4)Based on the effective syntax,we provide efficient algorithms to check the bounded evaluability of RAaggr queries and to generate query plans for bounded RAaggr queries.(5)As proof of concept,we extend PostgreSQL to support bounded evaluation.We experimentally verify that the extended system improves performance by orders of magnitude.展开更多
We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
This note deals with some classes of bounded subsets in a quasi-metric space. We study and compare the bounded sets, totally-bounded sets and the Bourbaki-bounded sets on quasi metric spaces. For example, we show that...This note deals with some classes of bounded subsets in a quasi-metric space. We study and compare the bounded sets, totally-bounded sets and the Bourbaki-bounded sets on quasi metric spaces. For example, we show that in a quasi-metric space, a set may be bounded but not totally bounded. In addition, we investigate their bornologies as well as their relationships with each other. For example, given a compatible quasi-metric, we intend to give some necessary and sufficient conditions for which a quasi metric bornology coincides with the bornology of totally bounded sets, the bornology of bourbaki bounded sets and bornology of bourbaki bounded subsets.展开更多
In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge...In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge is introduced into the past tense operator, and then a new temporal epistemic logic LTLKP is obtained, so that LTLKP can naturally and precisely describe the system＇s reliability. Secondly, a set of prior algorithms are designed to calculate the maximal reachable depth and the length of the longest of loop free paths in the structure based on the graph structure theory. Finally, some theorems are proposed to show how to approximate the complete threshold with the diameter and recurrence diameter. The proposed work resolves the completeness threshold problem so that the completeness of bounded model checking can be guaranteed.展开更多
In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given.
In this paper, we give a criterion of the absolutely Cesàro bounded weighted backward shift in spirit of the comparison method. Our approach is to construct the proper product of weight functions <img src=&quo...In this paper, we give a criterion of the absolutely Cesàro bounded weighted backward shift in spirit of the comparison method. Our approach is to construct the proper product of weight functions <img src="Edit_7232e0dc-07ab-41c5-8657-a49f0463b47c.bmp" alt="" />by the fraction of two monomials of the indexes, then we apply proper scaling to give Cesàro boundedness. In particular, we present a new example of non Cesàro bounded weighted backward shift on <img src="Edit_799dadb7-40ab-48f9-bae3-191378f96164.bmp" alt="" />.展开更多
In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f...In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f(x)≠0,the system is non-Hamiltonian,so we have to introduce some reversibility assumptions to apply a suitable twist theorem,for reversible maps with small twist.Moreover,when the nonnegative parameterαdecreases to 0,the system becomes discontinuous.In this case,we need to introduce some suitable transformations to overcome the lack of regularity.We will prove that for any nonnegative parameterα,when p(t)is an odd periodic function satisfying∣∣∫2π0p(t)sintdift∣∣<4,all the solutions are bounded;when p(t)satisfies∣∣∫2π0p(t)sintdift∣∣>4,the SD oscillator has unbounded solutions,and when p(t)satisfies∣∣∫_(0)^(2π)p(t)sintdift∣∣≥4+|F|_(∞),all the solutions are unbounded.展开更多
In this paper,the flight formation control problem of a group of quadrotor unmanned aerial vehicles（UAVs） with parametric uncertainties and external disturbances is studied.Unitquaternions are used to represent the ...In this paper,the flight formation control problem of a group of quadrotor unmanned aerial vehicles（UAVs） with parametric uncertainties and external disturbances is studied.Unitquaternions are used to represent the attitudes of the quadrotor UAVs.Separating the model into a translational subsystem and a rotational subsystem,an intermediary control input is introduced to track a desired velocity and extract desired orientations.Then considering the internal parametric uncertainties and external disturbances of the quadrotor UAVs,the priori-bounded intermediary adaptive control input is designed for velocity tracking and formation keeping,by which the bounded control thrust and the desired orientation can be extracted.Thereafter,an adaptive control torque input is designed for the rotational subsystem to track the desired orientation.With the proposed control scheme,the desired velocity is tracked and a desired formation shape is built up.Global stability of the closed-loop system is proven via Lyapunov-based stability analysis.Numerical simulation results are presented to illustrate the effectiveness of the proposed control scheme.展开更多
Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.
Space robotics is regarded as one of the most impressing approaches for space debris removal missions. Due to the residual momentum of debris, it is essential to stabilize the base rapidly after capture. This paper pr...Space robotics is regarded as one of the most impressing approaches for space debris removal missions. Due to the residual momentum of debris, it is essential to stabilize the base rapidly after capture. This paper presents a novel control strategy for stabilization of a space robot in postcapture considering actuator failures and bounded torques. In the control strategy, the motion of the manipulator is not regarded as a disturbance to the base; in contrast, it is utilized to compensate for the limitation of the control torques by means of an inverse dynamical model of the system. Different scenarios where actuators are external mechanisms or momentum exchange devices have been carried out, and for actuator failures, both single-and two-actuator failures have been considered. Regarding to the performance of actuators, control torques are bounded. In cases that either single or two actuators have failed, the base can be stabilized kinematically when actuators are external mechanisms, but can only be stabilized dynamically when only momentum exchange devices are used. Finally, a space robot with a seven-degree-of-freedom manipulator in postcapture is studied to verify the validity and feasibility of the proposed control scheme. Simulation results show that the whole system can be stabilized rapidly.展开更多
基金Sponsored by Foreign Expert Program of China(Grant No.DL2023041002L)Yulin City Industry University Research Project(Grant No.CXY-2022-59).
文摘This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.
文摘A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vertex.This concept was introduced by Tutte as an extension of face colorings,and Tutte in 1954 conjectured that every bridgeless graph admits a nowhere-zero 5-flow,known as the 5-Flow Conjecture.This conjecture is verified for some graph classes and remains unresolved as of today.In this paper,we show that every bridgeless graph of Euler genus at most 20 admits a nowhere-zero 5-flow,which improves several known results.
基金supported by the National Natural Science Foundation of China(No.52372371)the Science Center for Gas Turbine Project,China(Nos.P2022-B-V-002-001,P2022-B-V-001-001).
文摘Direct Thrust Control(DTC) is effective in dealing with the mismatch between thrust and rotor speed in traditional engine control. Among the DTC architecture, model-based thrust estimation method has less arithmetic consumption and better real-time performance. In this paper,a direct thrust controller design approach for gas turbine engine based on parameter dependent model is proposed. In order to ensure the stability of DTC control system based on parameter dependent model, there are usually conservatism detects. For the purpose of reducing the conservatism in the solution process of filter and controller, an Equilibrium Manifold Expansion(EME) model with bounded parameter variation of engine is established. The design conditions of Kalman filter for discrete-time EME system are introduced, and the proposed conditions have a certain suppression effect on the input noise of the system with bounded parameter variation.The engine thrust estimator stability and H∞filtering problems are solved by the polytopic quadratic Lyapunov function based on the Linear Matrix Inequalities(LMIs). To meet the performance requirements of thrust control, the Grey Wolf Optimization(GWO) algorithm is applied to optimize the PID control parameters. The proposed method is verified on a Hardware-in-Loop(HIL) platform. The simulation results demonstrate that the DTC framework can ensure the stability of engine closed-loop system in large range deviation tests. The filter and controller solution method considering the parameter variation boundary can obtain a solution that makes the system have better performance parameters. Moreover, the proposed filter has better thrust estimation performance than the traditional Kalman filter under the condition of sensor noise. Compared with Augmented Linear Quadratic Regulator(ALQR) controller, the PID controller optimized by GWO has a faster response in simulation.
基金National Natural Science Foundation of China (61773044,62073009)National key Laboratory of Science and Technology on Reliability and Environmental Engineering(WDZC2019601A301)。
文摘Delay aware routing is now widely used to provide efficient network transmission. However, for newly developing or developed mobile communication networks(MCN), only limited delay data can be obtained. In such a network, the delay is with epistemic uncertainty, which makes the traditional routing scheme based on deterministic theory or probability theory not applicable. Motivated by this problem, the MCN with epistemic uncertainty is first summarized as a dynamic uncertain network based on uncertainty theory, which is widely applied to model epistemic uncertainties. Then by modeling the uncertain end-toend delay, a new delay bounded routing scheme is proposed to find the path with the maximum belief degree that satisfies the delay threshold for the dynamic uncertain network. Finally, a lowEarth-orbit satellite communication network(LEO-SCN) is used as a case to verify the effectiveness of our routing scheme. It is first modeled as a dynamic uncertain network, and then the delay bounded paths with the maximum belief degree are computed and compared under different delay thresholds.
基金partially supported by the research grant of Macao University of Science and Technology(FRG-22-075-MCMS)the Macao Government Research Funding(FDCT0128/2022/A)+2 种基金the Science and Technology Development Fund of Macao SAR(005/2022/ALC)the Science and Technology Development Fund of Macao SAR(0045/2021/A)Macao University of Science and Technology(FRG-20-021-MISE)。
文摘For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.
文摘Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).
基金Supported by the National Natural Science Foundation of China(11301419)the Research and innovation Team of China West Normal University(CXTD2020-5)。
文摘This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution under some conditions.
基金Supported by Key Research Funds for the Universities of Henan Province(Grant No.19A110018)Foundation for Key Teacher of Henan Polytechnic University(Grant No.2022XQG-09).
文摘In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forcing function andαis a real parameter.Inspired by this special discontinuous oscillator,we study a more general discontinuous oscillator x′′+ω^(2)x+ϕ(x)=p(t),whereω∈R^(+)\N andϕ(x)has one discontinuous point.We show that every solution of this general discontinuous oscillator is bounded when some conditions are satisfied.
基金supported in part by Royal Society YVolfson Research Merit Award WRM/R1/180014,ERC 652976,EPSRC EP/M025268/1,Shenzhen Institute of Computing Sciences,and Beijing Advanced Innovation Center for Big Data and Brain Computing.
文摘This work aims to reduce queries on big data to computations on small data,and hence make querying big data possible under bounded resources.A query Q is boundedly evaluable when posed on any big dataset D,there exists a fraction DQ of D such that Q(D)=Q(DQ),and the cost of identifying DQ is independent of the size of D.It has been shown that with an auxiliary structure known as access schema,many queries in relational algebra(RA)are boundedly evaluable under the set semantics of RA.This paper extends the theory of bounded evaluation to RAaggr,i.e.,RA extended with aggregation,under the bag semantics.(1)We extend access schema to bag access schema,to help us identify DQ for RAaggr queries Q.(2)While it is undecidable to determine whether an RAaggr query is boundedly evaluable under a bag access schema,we identify special cases that are decidable and practical.(3)In addition,we develop an effective syntax for bounded RAaggr queries,i.e.,a core subclass of boundedly evaluable RAaggr queries without sacrificing their expressive power.(4)Based on the effective syntax,we provide efficient algorithms to check the bounded evaluability of RAaggr queries and to generate query plans for bounded RAaggr queries.(5)As proof of concept,we extend PostgreSQL to support bounded evaluation.We experimentally verify that the extended system improves performance by orders of magnitude.
文摘We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
文摘This note deals with some classes of bounded subsets in a quasi-metric space. We study and compare the bounded sets, totally-bounded sets and the Bourbaki-bounded sets on quasi metric spaces. For example, we show that in a quasi-metric space, a set may be bounded but not totally bounded. In addition, we investigate their bornologies as well as their relationships with each other. For example, given a compatible quasi-metric, we intend to give some necessary and sufficient conditions for which a quasi metric bornology coincides with the bornology of totally bounded sets, the bornology of bourbaki bounded sets and bornology of bourbaki bounded subsets.
基金The National Natural Science Foundation of China (No.10974093)the Scientific Research Foundation for Senior Personnel of Jiangsu University (No.07JDG014)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province (No.08KJD520015)
文摘In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge is introduced into the past tense operator, and then a new temporal epistemic logic LTLKP is obtained, so that LTLKP can naturally and precisely describe the system＇s reliability. Secondly, a set of prior algorithms are designed to calculate the maximal reachable depth and the length of the longest of loop free paths in the structure based on the graph structure theory. Finally, some theorems are proposed to show how to approximate the complete threshold with the diameter and recurrence diameter. The proposed work resolves the completeness threshold problem so that the completeness of bounded model checking can be guaranteed.
基金partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge
文摘In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given.
文摘In this paper, we give a criterion of the absolutely Cesàro bounded weighted backward shift in spirit of the comparison method. Our approach is to construct the proper product of weight functions <img src="Edit_7232e0dc-07ab-41c5-8657-a49f0463b47c.bmp" alt="" />by the fraction of two monomials of the indexes, then we apply proper scaling to give Cesàro boundedness. In particular, we present a new example of non Cesàro bounded weighted backward shift on <img src="Edit_799dadb7-40ab-48f9-bae3-191378f96164.bmp" alt="" />.
基金supported by the Key Research Funds for the Universities of Henan Province(No.19A110018)the Foundation for Key Teachers of Henan Polytechnic University(No.2022XQG-09)。
文摘In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f(x)≠0,the system is non-Hamiltonian,so we have to introduce some reversibility assumptions to apply a suitable twist theorem,for reversible maps with small twist.Moreover,when the nonnegative parameterαdecreases to 0,the system becomes discontinuous.In this case,we need to introduce some suitable transformations to overcome the lack of regularity.We will prove that for any nonnegative parameterα,when p(t)is an odd periodic function satisfying∣∣∫2π0p(t)sintdift∣∣<4,all the solutions are bounded;when p(t)satisfies∣∣∫2π0p(t)sintdift∣∣>4,the SD oscillator has unbounded solutions,and when p(t)satisfies∣∣∫_(0)^(2π)p(t)sintdift∣∣≥4+|F|_(∞),all the solutions are unbounded.
基金supported by the National Natural Science Foundation of China(No.61374048)
文摘In this paper,the flight formation control problem of a group of quadrotor unmanned aerial vehicles（UAVs） with parametric uncertainties and external disturbances is studied.Unitquaternions are used to represent the attitudes of the quadrotor UAVs.Separating the model into a translational subsystem and a rotational subsystem,an intermediary control input is introduced to track a desired velocity and extract desired orientations.Then considering the internal parametric uncertainties and external disturbances of the quadrotor UAVs,the priori-bounded intermediary adaptive control input is designed for velocity tracking and formation keeping,by which the bounded control thrust and the desired orientation can be extracted.Thereafter,an adaptive control torque input is designed for the rotational subsystem to track the desired orientation.With the proposed control scheme,the desired velocity is tracked and a desired formation shape is built up.Global stability of the closed-loop system is proven via Lyapunov-based stability analysis.Numerical simulation results are presented to illustrate the effectiveness of the proposed control scheme.
文摘Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.
基金co-supported by the National Natural Science Foundation of China (Nos. 11402200 and 11502203)the China Scholarship Council (CSC)
文摘Space robotics is regarded as one of the most impressing approaches for space debris removal missions. Due to the residual momentum of debris, it is essential to stabilize the base rapidly after capture. This paper presents a novel control strategy for stabilization of a space robot in postcapture considering actuator failures and bounded torques. In the control strategy, the motion of the manipulator is not regarded as a disturbance to the base; in contrast, it is utilized to compensate for the limitation of the control torques by means of an inverse dynamical model of the system. Different scenarios where actuators are external mechanisms or momentum exchange devices have been carried out, and for actuator failures, both single-and two-actuator failures have been considered. Regarding to the performance of actuators, control torques are bounded. In cases that either single or two actuators have failed, the base can be stabilized kinematically when actuators are external mechanisms, but can only be stabilized dynamically when only momentum exchange devices are used. Finally, a space robot with a seven-degree-of-freedom manipulator in postcapture is studied to verify the validity and feasibility of the proposed control scheme. Simulation results show that the whole system can be stabilized rapidly.
