In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced couple...In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced coupled system, under certain conditions of compatibility, the exact synchronization, the exact synchronization by groups, and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.展开更多
This paper studies exact synchronization and asymptotic synchronization problems for a controlled linear system of ordinary differential equations. In this paper, we build up necessary and sufficient conditions for ex...This paper studies exact synchronization and asymptotic synchronization problems for a controlled linear system of ordinary differential equations. In this paper, we build up necessary and sufficient conditions for exact synchronization and asymptotic synchronization problems. When a system is not controllable but exactly synchronizable, it can be asymptotically synchronized in any given rate and the state of exact synchronization is given. However, when a system is not controllable and can be asymptotically synchronized in any given rate,it may not be exactly synchronizable.展开更多
In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations...In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations,and will be connected with the control theory via boundary controls in a finite time interval. More precisely,various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman's type are obtained. Finally, some prospects will be given.展开更多
Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronizatio...Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronization matrix,this paper introduces two kinds of induced generalized exact boundary synchronizations to better determine its generalized exactly synchronizable states.展开更多
This paper deals with the exact boundary controllability and the exact boundary synchronization for a 1-D system of wave equations coupled with velocities.These problems can not be solved directly by the usual HUM met...This paper deals with the exact boundary controllability and the exact boundary synchronization for a 1-D system of wave equations coupled with velocities.These problems can not be solved directly by the usual HUM method for wave equations,however,by transforming the system into a first order hyperbolic system,the HUM method for 1-D first order hyperbolic systems,established by Li-Lu(2022)and Lu-Li(2022),can be applied to get the corresponding results.展开更多
In this paper the exact internal controllability for a coupled system of wave equations with arbitrarily given coupling matrix is established.Based on this result,the exact internal synchronization and the exact inter...In this paper the exact internal controllability for a coupled system of wave equations with arbitrarily given coupling matrix is established.Based on this result,the exact internal synchronization and the exact internal synchronization by p-groups are successfully considered.展开更多
In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups...In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups. Moreover, the determination of the state of synchronization by groups is discussed with details for the synchronization and for the synchronization by 3-groups, respectively.展开更多
This paper deals with the generalized exact boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls in the framework of weak solutions.A necessary and sufficient condition for ...This paper deals with the generalized exact boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls in the framework of weak solutions.A necessary and sufficient condition for the generalized exact boundary synchronization is obtained,and some results for its generalized exactly synchronizable states are given.展开更多
For a coupled system of wave equations with Dirichlet boundary controls,this paper deals with the possible choice of its generalized synchronization matrices so that the admissible generalized exact boundary synchroni...For a coupled system of wave equations with Dirichlet boundary controls,this paper deals with the possible choice of its generalized synchronization matrices so that the admissible generalized exact boundary synchronizations for this system are obtained.展开更多
In this paper,the synchronizable system is defined and studied for a coupled system of wave equations with the same wave speed or with different wave speeds.
文摘In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced coupled system, under certain conditions of compatibility, the exact synchronization, the exact synchronization by groups, and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.
基金supported by National Natural Science Foundation of China (Grant Nos.11771344 and 11701138)Natural Science Foundation of Hebei Province of China (Grant No. A2020202033)。
文摘This paper studies exact synchronization and asymptotic synchronization problems for a controlled linear system of ordinary differential equations. In this paper, we build up necessary and sufficient conditions for exact synchronization and asymptotic synchronization problems. When a system is not controllable but exactly synchronizable, it can be asymptotically synchronized in any given rate and the state of exact synchronization is given. However, when a system is not controllable and can be asymptotically synchronized in any given rate,it may not be exactly synchronizable.
基金supported by National Basic Research Program of China(Grant No.2013CB834100)National Natural Science Foundation of China(Grant No.111211101)
文摘In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations,and will be connected with the control theory via boundary controls in a finite time interval. More precisely,various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman's type are obtained. Finally, some prospects will be given.
文摘Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronization matrix,this paper introduces two kinds of induced generalized exact boundary synchronizations to better determine its generalized exactly synchronizable states.
基金supported by the National Natural Science Foundation of China (Nos. 11831011,11901082)the Natural Science Foundation of Jiangsu Province (No. BK20190323)the Fundamental Research Funds for the Central Universities of China
文摘This paper deals with the exact boundary controllability and the exact boundary synchronization for a 1-D system of wave equations coupled with velocities.These problems can not be solved directly by the usual HUM method for wave equations,however,by transforming the system into a first order hyperbolic system,the HUM method for 1-D first order hyperbolic systems,established by Li-Lu(2022)and Lu-Li(2022),can be applied to get the corresponding results.
基金supported by the National Natural Science Foundation of China(No.11831011)。
文摘In this paper the exact internal controllability for a coupled system of wave equations with arbitrarily given coupling matrix is established.Based on this result,the exact internal synchronization and the exact internal synchronization by p-groups are successfully considered.
基金supported by the National Natural Science Foundation of China(No.11121101)the National Basic Research Program of China(No.2013CB834100)
文摘In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups. Moreover, the determination of the state of synchronization by groups is discussed with details for the synchronization and for the synchronization by 3-groups, respectively.
基金the National Natural Science Foundation of China(No.11831011)。
文摘This paper deals with the generalized exact boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls in the framework of weak solutions.A necessary and sufficient condition for the generalized exact boundary synchronization is obtained,and some results for its generalized exactly synchronizable states are given.
文摘For a coupled system of wave equations with Dirichlet boundary controls,this paper deals with the possible choice of its generalized synchronization matrices so that the admissible generalized exact boundary synchronizations for this system are obtained.
基金Project supported by the National Natural Science Foundation of China(Nos.11831011,11725102).
文摘In this paper,the synchronizable system is defined and studied for a coupled system of wave equations with the same wave speed or with different wave speeds.
