The dynamic interaction between maglev vehicle and three-span continuous guideway is discussed. With the consideration of control system, the dynamic interaction model has been developed. Numerical simulation has been...The dynamic interaction between maglev vehicle and three-span continuous guideway is discussed. With the consideration of control system, the dynamic interaction model has been developed. Numerical simulation has been performed to study dynamic characteristics of the guideway. The results show that bending rigidity, vehicle speed, span ratio and primary frequency all have important influences on the dynamic characteristics of the guideway and there is no distinct trend towards resonance vibration when fl/（v/l） equals 1.0. The definite way is to control impact coefficient and acceleration of the guideway. The conclusions can serve the design of high-speed maglev three-span continuous guideway.展开更多
This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows.General formulation of the continuous ...This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows.General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived.With the adjoint method,the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function,regardless of the number of design parameters.An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method.Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil,wing,and wing-body configuration,and the aerodynamic performance improvement of turbine and compressor blade rows.The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.展开更多
COVID-19 epidemic models with constant transmission rate cannot capture the patterns of the infection data in the presence of pharmaceutical and non-pharmaceutical interventions during a pandemic.Because of this,a new...COVID-19 epidemic models with constant transmission rate cannot capture the patterns of the infection data in the presence of pharmaceutical and non-pharmaceutical interventions during a pandemic.Because of this,a new modification of SIR model that contain the vaccination compartment with time dependent coefficients and weak/lossimmunity is explored.Literature review confirms that the effect of vaccination on the time dependent transmission rate is still an open problem.This study answers this open problem.In this study,we first prove the well-posedness and investigate the model dynamics to show their continuous dependence on the model parameters.We then provide an algorithm to derive the time-dependent transmission function for the epidemiologic model and the data of the infected cases.The derived coupled nonlinear differential equations show the effect of vaccination on the transmission rate.Unlike previous studies,we first filter the published data and solve the nonlinear coupled differential equations using the finite difference technique,where the coefficient of the coupled nonlinear differential equations is a function of given data.We then show that time-dependent transmission function can be represented by linear combinations of Gaussian radial base function.We then validate the prediction of our models using numerical simulations,where we used the published data of COVID-19 confirmed cases by the Ministries of Health in Saudi Arabia and Poland.Finally,the numerical solutions of a SIRVI model with time dependent transmission rate show that the waves for currently active cases are in good agreement with the data of Saudi Arabia and Poland.展开更多
This paper investigates imitation dynamics with continuously distributed delay.In realistic technological,economic,and social environments,individuals are involved in strategic interactions simultaneously while the in...This paper investigates imitation dynamics with continuously distributed delay.In realistic technological,economic,and social environments,individuals are involved in strategic interactions simultaneously while the influences of their decision-making may not be observable instantaneously.It shows that there exists a time delay effect.Different distributions of delay are further considered to efficiently lucubrate the stability of interior equilibrium in the imitation dynamics with continuous distributions of delay in the two-strategy game contexts.Precisely,when the delay follows the uniform distributions and Gamma distributions,the authors present that interior equilibrium can be asymptotically stable.Furthermore,when the probability density of the delay is general density,the authors also determine a sufficient condition for stability derived from the expected delay.Last but not least,the interested but uncomplicated Snowdrift game is utilized to demonstrate our theoretical results.展开更多
The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier c...The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.展开更多
In this paper, adaptive linear quadratic regulator(LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses inputoutput data along the system trajectory to conti...In this paper, adaptive linear quadratic regulator(LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses inputoutput data along the system trajectory to continuously adapt and converge to the optimal controller. The result differs from previous results in that the adaptive optimal controller is designed without the knowledge of the system dynamics and an initial stabilizing policy. Further, the controller is updated continuously using input-output data, as opposed to the commonly used switched/intermittent updates which can potentially lead to stability issues. An online state derivative estimator facilitates the design of a model-free controller. Gradient-based update laws are developed for online estimation of the optimal gain. Uniform exponential stability of the closed-loop system is established using the Lyapunov-based analysis, and a simulation example is provided to validate the theoretical contribution.展开更多
基金Project (No. 2005AA505440) supported by the Hi-Tech Researchand Development Program (863) of China
文摘The dynamic interaction between maglev vehicle and three-span continuous guideway is discussed. With the consideration of control system, the dynamic interaction model has been developed. Numerical simulation has been performed to study dynamic characteristics of the guideway. The results show that bending rigidity, vehicle speed, span ratio and primary frequency all have important influences on the dynamic characteristics of the guideway and there is no distinct trend towards resonance vibration when fl/（v/l） equals 1.0. The definite way is to control impact coefficient and acceleration of the guideway. The conclusions can serve the design of high-speed maglev three-span continuous guideway.
基金supported by the National Natural Science Foundation of China(Grant Nos.51206003 and 51376009)the National Science Foundation for Post-doctoral Scientists of China(Grant Nos.2012M510267 and 2013T60035)
文摘This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows.General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived.With the adjoint method,the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function,regardless of the number of design parameters.An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method.Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil,wing,and wing-body configuration,and the aerodynamic performance improvement of turbine and compressor blade rows.The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.
基金funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University through Research Group no.RG-21-09-16.
文摘COVID-19 epidemic models with constant transmission rate cannot capture the patterns of the infection data in the presence of pharmaceutical and non-pharmaceutical interventions during a pandemic.Because of this,a new modification of SIR model that contain the vaccination compartment with time dependent coefficients and weak/lossimmunity is explored.Literature review confirms that the effect of vaccination on the time dependent transmission rate is still an open problem.This study answers this open problem.In this study,we first prove the well-posedness and investigate the model dynamics to show their continuous dependence on the model parameters.We then provide an algorithm to derive the time-dependent transmission function for the epidemiologic model and the data of the infected cases.The derived coupled nonlinear differential equations show the effect of vaccination on the transmission rate.Unlike previous studies,we first filter the published data and solve the nonlinear coupled differential equations using the finite difference technique,where the coefficient of the coupled nonlinear differential equations is a function of given data.We then show that time-dependent transmission function can be represented by linear combinations of Gaussian radial base function.We then validate the prediction of our models using numerical simulations,where we used the published data of COVID-19 confirmed cases by the Ministries of Health in Saudi Arabia and Poland.Finally,the numerical solutions of a SIRVI model with time dependent transmission rate show that the waves for currently active cases are in good agreement with the data of Saudi Arabia and Poland.
基金supported by the National Natural Science Foundation of China under Grant No.11271098Guizhou Provincial Science and Technology Fund under Grant No.[2019]1067the Fundamental Funds for Introduction of Talents of Guizhou University under Grant No.[2017]59。
文摘This paper investigates imitation dynamics with continuously distributed delay.In realistic technological,economic,and social environments,individuals are involved in strategic interactions simultaneously while the influences of their decision-making may not be observable instantaneously.It shows that there exists a time delay effect.Different distributions of delay are further considered to efficiently lucubrate the stability of interior equilibrium in the imitation dynamics with continuous distributions of delay in the two-strategy game contexts.Precisely,when the delay follows the uniform distributions and Gamma distributions,the authors present that interior equilibrium can be asymptotically stable.Furthermore,when the probability density of the delay is general density,the authors also determine a sufficient condition for stability derived from the expected delay.Last but not least,the interested but uncomplicated Snowdrift game is utilized to demonstrate our theoretical results.
文摘The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.
文摘In this paper, adaptive linear quadratic regulator(LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses inputoutput data along the system trajectory to continuously adapt and converge to the optimal controller. The result differs from previous results in that the adaptive optimal controller is designed without the knowledge of the system dynamics and an initial stabilizing policy. Further, the controller is updated continuously using input-output data, as opposed to the commonly used switched/intermittent updates which can potentially lead to stability issues. An online state derivative estimator facilitates the design of a model-free controller. Gradient-based update laws are developed for online estimation of the optimal gain. Uniform exponential stability of the closed-loop system is established using the Lyapunov-based analysis, and a simulation example is provided to validate the theoretical contribution.
