The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well...The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value problem.The exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method,which reduces the global exact boundary controllability problem to a local one.The proof is carried out in line with [2,15].Then a constructive method that has been developed in [13] is used to study the local problem.Especially when the region is star-complemented,it is obtained that the control function only need to be applied on a relatively open subset of the boundary.For the cubic Klein-Gordon equation,similar results of the global exact boundary controllability are proved by such an idea.展开更多
This paper discusses the properties of the storage functions for a class of nonlinear stochastic systems. Some necessary and sufficient conditions for a function to be a storage function are derived. As applications, ...This paper discusses the properties of the storage functions for a class of nonlinear stochastic systems. Some necessary and sufficient conditions for a function to be a storage function are derived. As applications, the finite and infinite horizon nonlinear stochastic H∞ controls for systems with state, control, and external disturbance dependent noise are investigated, which generalize the previous results.展开更多
基金supported by the National Natural Science Foundation of China (No. 10728101)the 973 Project ofthe Ministry of Science and Technology of China+1 种基金the Doctoral Program Foundation of the Ministry of Ed-ucation of Chinathe "111" Project and the Postdoctoral Science Foundation of China (No. 20070410160)
文摘The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value problem.The exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method,which reduces the global exact boundary controllability problem to a local one.The proof is carried out in line with [2,15].Then a constructive method that has been developed in [13] is used to study the local problem.Especially when the region is star-complemented,it is obtained that the control function only need to be applied on a relatively open subset of the boundary.For the cubic Klein-Gordon equation,similar results of the global exact boundary controllability are proved by such an idea.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 10921101 and 60874032, the National Basic Research Program of China （973 Program） under Grant No. 2007CB814904, the Key Project of Natural Science Foundation of Shandong Province under Grant No. ZR2009GZ001, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20103718110006.
文摘This paper discusses the properties of the storage functions for a class of nonlinear stochastic systems. Some necessary and sufficient conditions for a function to be a storage function are derived. As applications, the finite and infinite horizon nonlinear stochastic H∞ controls for systems with state, control, and external disturbance dependent noise are investigated, which generalize the previous results.
