In this paper,we delve into the problem of exponential stability for a coupled system of a one-dimensional(1-D)N-root wave network with boundary delays.Our aim is to establish a universal controller design strategy,wh...In this paper,we delve into the problem of exponential stability for a coupled system of a one-dimensional(1-D)N-root wave network with boundary delays.Our aim is to establish a universal controller design strategy,where the designed controller must guarantee the stability of the closed-loop system.The research approach undertaken in this paper assumes that the system state is known.We employ an integral-type feedback controller to achieve system stability,where the integral kernel function serves as a parameter.We attempt to select the corresponding exponentially stable system as the target system,and then construct a bounded linear transformation to demonstrate the equivalence between the target system and the original system,thereby eliminating the adverse effects of time delays on the system.The crux lies in determining the equation that the kernel function must satisfy.Herein,we primarily present a methodology for selecting the parameter function within this transformation,to achieve an exponentially stable feedback controller.展开更多
This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpola...This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta(ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν +1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.展开更多
This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicate...This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor are designed:The state of system is estimated with available observation and then predicted without observation.After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method.The equivalent system together with the design of observer and predictor give the estimated output feedback.It is shown that the closed-loop system is exponentially stable.Numerical simulations are presented to illustrate the effect of the stabilizing controller.展开更多
基金supported by the National Natural Science Foundation of China(No.12301579)the Fundamental Research Funds for the Central Universities of Civil Aviation University of China(No.3122019140).
文摘In this paper,we delve into the problem of exponential stability for a coupled system of a one-dimensional(1-D)N-root wave network with boundary delays.Our aim is to establish a universal controller design strategy,where the designed controller must guarantee the stability of the closed-loop system.The research approach undertaken in this paper assumes that the system state is known.We employ an integral-type feedback controller to achieve system stability,where the integral kernel function serves as a parameter.We attempt to select the corresponding exponentially stable system as the target system,and then construct a bounded linear transformation to demonstrate the equivalence between the target system and the original system,thereby eliminating the adverse effects of time delays on the system.The crux lies in determining the equation that the kernel function must satisfy.Herein,we primarily present a methodology for selecting the parameter function within this transformation,to achieve an exponentially stable feedback controller.
基金supported by the National Natural Science Foundation of China(Grant No.12471379).
文摘This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta(ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν +1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.
基金supported by the National Natural Science Foundation of China under Grant No.61203058the Training Program for Outstanding Young Teachers of North China University of Technology under Grant No.XN131+1 种基金the Construction Plan for Innovative Research Team of North China University of Technology under Grant No.XN129the Laboratory construction for Mathematics Network Teaching Platform of North China University of Technology under Grant No.XN041
文摘This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor are designed:The state of system is estimated with available observation and then predicted without observation.After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method.The equivalent system together with the design of observer and predictor give the estimated output feedback.It is shown that the closed-loop system is exponentially stable.Numerical simulations are presented to illustrate the effect of the stabilizing controller.
