A scheme for optimal control problem formulation of a class of nonviscously damped system using pseudo-state-space formulation is presented in this paper.Taking the exponentially damped system of nonviscously damped s...A scheme for optimal control problem formulation of a class of nonviscously damped system using pseudo-state-space formulation is presented in this paper.Taking the exponentially damped system of nonviscously damped system as an example,a new state space representation is applied to the n-order exponentially damped system.The necessary conditions for the optimality of the exponentially damped system are obtained.A numerical example of a single degree of freedom exponentially damped system is considered to illustrate the methodology and technique.展开更多
The numerical solutions of two-dimensional(2D)and three-dimensional(3D)nonlinear viscous and nonviscous wave equations via the unified alternating direction implicit(ADI)finite difference methods(FDMs)are obtained in ...The numerical solutions of two-dimensional(2D)and three-dimensional(3D)nonlinear viscous and nonviscous wave equations via the unified alternating direction implicit(ADI)finite difference methods(FDMs)are obtained in this paper.By making use of the discrete energy method,it is proven that their numerical solutions converge to exact solutions with an order of two in both time and space with respect to H^(1)-norm.Numerical results confirm that they are relatively accurate and high-resolution,and more successfully simulate the conservation of the energy for nonviscous equations,and the dissipation of the energy for viscous equation.展开更多
The purpose is to design the control method for a single-degree-of-freedom(SDOF)exponentially damped oscillator.Based on the Lyapunov stability theory,sliding mode control and adaptive sliding mode control have been p...The purpose is to design the control method for a single-degree-of-freedom(SDOF)exponentially damped oscillator.Based on the Lyapunov stability theory,sliding mode control and adaptive sliding mode control have been proposed.Sliding control laws and adaptive sliding laws are designed for exponentially damped oscillator respectively in cases that the bound of the external exciting force is known or unknown.The viability and effectiveness of the above control designs have been validated by numerical simulations.展开更多
基金National Natural Science Foundation of China(No.11802338)。
文摘A scheme for optimal control problem formulation of a class of nonviscously damped system using pseudo-state-space formulation is presented in this paper.Taking the exponentially damped system of nonviscously damped system as an example,a new state space representation is applied to the n-order exponentially damped system.The necessary conditions for the optimality of the exponentially damped system are obtained.A numerical example of a single degree of freedom exponentially damped system is considered to illustrate the methodology and technique.
基金partially supported by the National Natural Science Foundation of China Grant Nos.11861047 and 11871393.
文摘The numerical solutions of two-dimensional(2D)and three-dimensional(3D)nonlinear viscous and nonviscous wave equations via the unified alternating direction implicit(ADI)finite difference methods(FDMs)are obtained in this paper.By making use of the discrete energy method,it is proven that their numerical solutions converge to exact solutions with an order of two in both time and space with respect to H^(1)-norm.Numerical results confirm that they are relatively accurate and high-resolution,and more successfully simulate the conservation of the energy for nonviscous equations,and the dissipation of the energy for viscous equation.
基金National Natural Science Foundation of China(No.11802338)
文摘The purpose is to design the control method for a single-degree-of-freedom(SDOF)exponentially damped oscillator.Based on the Lyapunov stability theory,sliding mode control and adaptive sliding mode control have been proposed.Sliding control laws and adaptive sliding laws are designed for exponentially damped oscillator respectively in cases that the bound of the external exciting force is known or unknown.The viability and effectiveness of the above control designs have been validated by numerical simulations.
