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
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system ...This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system is first proposed,and the adomian decomposition method(ADM)is employed to resolve this fractional-order system.The stability of equilibrium points and the corresponding control schemes are assessed,and several classical tools such as Lyapunov exponents(LE),bifurcation diagrams,complexity analysis(CA),and 0–1 test are further extended to analyze the dynamical behaviors of FOFR.Then the global Mittag–Leffler attractive set(MLAS)and Mittag–Leffler positive invariant set(MLPIS)for the proposed financial risk(FR)system are discussed.Finally,a proficient reservoir-computing(RC)method is applied to forecast the temporal evolution of the complex dynamics for the proposed system,and some simulations are carried out to show the effectiveness and feasibility of the present scheme.展开更多
In this paper, the problem of cubature Kalman fusion filtering(CKFF) is addressed for multi-sensor systems under amplify-and-forward(AaF) relays. For the purpose of facilitating data transmission, AaF relays are utili...In this paper, the problem of cubature Kalman fusion filtering(CKFF) is addressed for multi-sensor systems under amplify-and-forward(AaF) relays. For the purpose of facilitating data transmission, AaF relays are utilized to regulate signal communication between sensors and filters. Here, the randomly varying channel parameters are represented by a set of stochastic variables whose occurring probabilities are permitted to exhibit bounded uncertainty. Employing the spherical-radial cubature principle, a local filter under AaF relays is initially constructed. This construction ensures and minimizes an upper bound of the filtering error covariance by designing an appropriate filter gain. Subsequently, the local filters are fused through the application of the covariance intersection fusion rule. Furthermore, the uniform boundedness of the filtering error covariance's upper bound is investigated through establishing certain sufficient conditions. The effectiveness of the proposed CKFF scheme is ultimately validated via a simulation experiment concentrating on a three-phase induction machine.展开更多
In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total vari...In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.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
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 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
In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We p...In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We prove that if■then there exists a unique time-globally classical solution(u,v)for all n≥1,such a solution is bounded and satisfies u≥0,v>0.Moreover,we show that the above solution will convergence to the steady state(1,1)exponentially in L^(∞)as t→∞.展开更多
In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults.First, a novel augmented plant is co...In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults.First, a novel augmented plant is constructed by fusing the system state and the reference trajectory, which aims to transform the optimal fault-tolerant tracking control design with actuator faults into the optimal regulation problem of the conventional nonlinear error system. Subsequently, in order to ensure the normal execution of the online learning algorithm, a stability criterion condition is created to obtain an initial admissible tracking policy. Then, the constructed model neural network(NN) is pretrained to recognize the system dynamics and calculate trajectory control. The critic and action NNs are constructed to output the approximate cost function and approximate tracking control,respectively. The Hamilton-Jacobi-Bellman equation of the error system is solved online through the action-critic framework. In theoretical analysis, it is proved that all concerned signals are uniformly ultimately bounded according to the Lyapunov principle.The tracking control law can approach the optimal tracking control within a finite approximation error. Finally, two experimental examples are conducted to indicate the effectiveness and superiority of the developed fault-tolerant tracking control scheme.展开更多
It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cy...It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.展开更多
Missile acceleration saturation in a practical terminal guidance process may significantly reduce the interception performance.To solve this problem,this paper presents an anti-saturation guidance law with finite-time...Missile acceleration saturation in a practical terminal guidance process may significantly reduce the interception performance.To solve this problem,this paper presents an anti-saturation guidance law with finite-time convergence for a three dimensional maneuvering interception.The finite time boundedness(FTB)theory and the input-output finite time stability(IO-FTS)theory are used,as well as the long short-term memory(LSTM)network.A sufficient condition for FTB and IO-FTS of a class of nonlinear systems is given.Then,an anti-acceleration saturation missile terminal guidance law based on LSTM,namely LSTM-ASGL,is designed.It can effectively suppress the effect of acceleration saturation to track the maneuvering target more accurately in the complex dynamic environment.The excellent performance of LSTM-ASGL in different maneuvering target scenarios is verified by simulation.The simulation results show that the guidance law successfully prevents acceleration saturation and improves the tracking ability of the missile system to the maneuvering target.It is also shown that LSTM-ASGL has good generalization and anti-jamming performance,and consumes less energy than the anti-acceleration saturation terminal guidance law.展开更多
In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asympt...In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asymptotic behaviors of the Jost solutions as|λ|→∞andλ→0 are given.Considering that the scattering coefficients have simple zeros,the matrix RH problem,reconstruction formulas and corresponding trace formulas are also derived.Further,the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants.The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed.In particular,the asymptotic expressions of two-soliton solutions as|t|→∞are obtained,which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts.In addition,three types of bounded states for two-soliton solutions are presented with certain parametric conditions.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
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
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.
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
基金Project jointly supported by the National Natural Science Foundation of China(Grant No.12372013)Program for Science and Technology Innovation Talents in Universities of Henan Province,China(Grant No.24HASTIT034)+3 种基金the Natural Science Foundation of Henan Province,China(Grant No.232300420122)the Humanities and Society Science Foundation from the Ministry of Education of China(Grant No.19YJCZH265)China Postdoctoral Science Foundation(Grant No.2019M651633)First Class Discipline of Zhejiang-A(Zhejiang University of Finance and Economics Statistics),the Collaborative Innovation Center for Data Science and Big Data Analysis(Zhejiang University of Finance and Economics-Statistics).
文摘This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system is first proposed,and the adomian decomposition method(ADM)is employed to resolve this fractional-order system.The stability of equilibrium points and the corresponding control schemes are assessed,and several classical tools such as Lyapunov exponents(LE),bifurcation diagrams,complexity analysis(CA),and 0–1 test are further extended to analyze the dynamical behaviors of FOFR.Then the global Mittag–Leffler attractive set(MLAS)and Mittag–Leffler positive invariant set(MLPIS)for the proposed financial risk(FR)system are discussed.Finally,a proficient reservoir-computing(RC)method is applied to forecast the temporal evolution of the complex dynamics for the proposed system,and some simulations are carried out to show the effectiveness and feasibility of the present scheme.
基金supported in part by the National Natural Science Foundation of China(12171124,61933007)the Natural Science Foundation of Heilongjiang Province of China(ZD2022F003)+2 种基金the National High-End Foreign Experts Recruitment Plan of China(G2023012004L)the Royal Society of UKthe Alexander von Humboldt Foundation of Germany
文摘In this paper, the problem of cubature Kalman fusion filtering(CKFF) is addressed for multi-sensor systems under amplify-and-forward(AaF) relays. For the purpose of facilitating data transmission, AaF relays are utilized to regulate signal communication between sensors and filters. Here, the randomly varying channel parameters are represented by a set of stochastic variables whose occurring probabilities are permitted to exhibit bounded uncertainty. Employing the spherical-radial cubature principle, a local filter under AaF relays is initially constructed. This construction ensures and minimizes an upper bound of the filtering error covariance by designing an appropriate filter gain. Subsequently, the local filters are fused through the application of the covariance intersection fusion rule. Furthermore, the uniform boundedness of the filtering error covariance's upper bound is investigated through establishing certain sufficient conditions. The effectiveness of the proposed CKFF scheme is ultimately validated via a simulation experiment concentrating on a three-phase induction machine.
基金Supported in part by NSFC(No.11971005)the Fundamental Research Funds for the Central Universities(Nos.GK202101008,GK202102012)。
文摘In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.
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.
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.
基金supported by the Jilin Scientific and Technological Development Program(20210101466JC).
文摘In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We prove that if■then there exists a unique time-globally classical solution(u,v)for all n≥1,such a solution is bounded and satisfies u≥0,v>0.Moreover,we show that the above solution will convergence to the steady state(1,1)exponentially in L^(∞)as t→∞.
基金supported in part by the National Natural Science Foundation of China(62222301,62373012,62473012,62021003)the National Science and Technology Major Project(2021ZD0112302,2021ZD0112301)the Beijing Natural Science Foundation(JQ19013)
文摘In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults.First, a novel augmented plant is constructed by fusing the system state and the reference trajectory, which aims to transform the optimal fault-tolerant tracking control design with actuator faults into the optimal regulation problem of the conventional nonlinear error system. Subsequently, in order to ensure the normal execution of the online learning algorithm, a stability criterion condition is created to obtain an initial admissible tracking policy. Then, the constructed model neural network(NN) is pretrained to recognize the system dynamics and calculate trajectory control. The critic and action NNs are constructed to output the approximate cost function and approximate tracking control,respectively. The Hamilton-Jacobi-Bellman equation of the error system is solved online through the action-critic framework. In theoretical analysis, it is proved that all concerned signals are uniformly ultimately bounded according to the Lyapunov principle.The tracking control law can approach the optimal tracking control within a finite approximation error. Finally, two experimental examples are conducted to indicate the effectiveness and superiority of the developed fault-tolerant tracking control scheme.
基金Supported by the National Natural Science Foundation of China(12201446)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(22KJB110005)the Shuangchuang Program of Jiangsu Province(JSSCBS20220898)。
文摘It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.
文摘Missile acceleration saturation in a practical terminal guidance process may significantly reduce the interception performance.To solve this problem,this paper presents an anti-saturation guidance law with finite-time convergence for a three dimensional maneuvering interception.The finite time boundedness(FTB)theory and the input-output finite time stability(IO-FTS)theory are used,as well as the long short-term memory(LSTM)network.A sufficient condition for FTB and IO-FTS of a class of nonlinear systems is given.Then,an anti-acceleration saturation missile terminal guidance law based on LSTM,namely LSTM-ASGL,is designed.It can effectively suppress the effect of acceleration saturation to track the maneuvering target more accurately in the complex dynamic environment.The excellent performance of LSTM-ASGL in different maneuvering target scenarios is verified by simulation.The simulation results show that the guidance law successfully prevents acceleration saturation and improves the tracking ability of the missile system to the maneuvering target.It is also shown that LSTM-ASGL has good generalization and anti-jamming performance,and consumes less energy than the anti-acceleration saturation terminal guidance law.
基金supported by the National Natural Science Foundation of China(Grant Nos.12475003 and11705284)by the Natural Science Foundation of Beijing Municipality(Grant Nos.1232022 and 1212007)。
文摘In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asymptotic behaviors of the Jost solutions as|λ|→∞andλ→0 are given.Considering that the scattering coefficients have simple zeros,the matrix RH problem,reconstruction formulas and corresponding trace formulas are also derived.Further,the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants.The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed.In particular,the asymptotic expressions of two-soliton solutions as|t|→∞are obtained,which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts.In addition,three types of bounded states for two-soliton solutions are presented with certain parametric conditions.
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.
