Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the imp...Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the impulse observability and impulse controllability of the system are obtained. This research is theoretically important for studying the design of the degenerate evolution system.展开更多
The uniform convergence of the solutions of a parameterized family of Riccati differential equations which arise in the context of optimal control problems for systems described by a family of linear time-varying evol...The uniform convergence of the solutions of a parameterized family of Riccati differential equations which arise in the context of optimal control problems for systems described by a family of linear time-varying evolution equations is considered on the infinite time interval in Hilbert space.Some sufficient conditions and an illustrative example are given for uniform convergence of the solutions of a family of the Riccati differential equations.The uniform convergence of the solutions of the Riccati differential equations with respect to parameters is important for applications to problems in adaptive control of stochastic evolution systems.展开更多
Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space, Necessary and sufficient conditions conce...Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space, Necessary and sufficient conditions concerning the exact controllability are given. Relations between exact controllability and stability of singular distributed parameter system are specified.展开更多
Exact(approximate)controllability and exact(approximate)observability of stochastic singular systems in Banach spaces are discussed.Firstly,the condition for the existence and uniqueness of the mild solution to stocha...Exact(approximate)controllability and exact(approximate)observability of stochastic singular systems in Banach spaces are discussed.Firstly,the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces.Secondly,the necessary and sufficient conditions for the exact(approximate)controllability and exact(approximate)observability of the systems considered are derived in terms of GE-semigroup,and the dual principle is given.Thirdly,an illustrative example is given.展开更多
Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are obtained.These general results are used to examine the exact controllabi...Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are obtained.These general results are used to examine the exact controllability and approximate controllability of the Dzektser equation in the theory of seepage.展开更多
This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems i...This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform.Secondly,the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory.Finally,an example is given to illustrate the effectiveness of the obtained theoretical results.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61174081
文摘Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the impulse observability and impulse controllability of the system are obtained. This research is theoretically important for studying the design of the degenerate evolution system.
基金supported by the National Natural Science Foundation of China under Grant No.61174081.
文摘The uniform convergence of the solutions of a parameterized family of Riccati differential equations which arise in the context of optimal control problems for systems described by a family of linear time-varying evolution equations is considered on the infinite time interval in Hilbert space.Some sufficient conditions and an illustrative example are given for uniform convergence of the solutions of a family of the Riccati differential equations.The uniform convergence of the solutions of the Riccati differential equations with respect to parameters is important for applications to problems in adaptive control of stochastic evolution systems.
基金Supported by the National Natural Science Foundation of China (Grant No. 60674018)
文摘Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space, Necessary and sufficient conditions concerning the exact controllability are given. Relations between exact controllability and stability of singular distributed parameter system are specified.
基金supported by the National Natural Science Foundation of China under Grant Nos.11926402 and 61973338。
文摘Exact(approximate)controllability and exact(approximate)observability of stochastic singular systems in Banach spaces are discussed.Firstly,the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces.Secondly,the necessary and sufficient conditions for the exact(approximate)controllability and exact(approximate)observability of the systems considered are derived in terms of GE-semigroup,and the dual principle is given.Thirdly,an illustrative example is given.
基金supported by the National Natural Science Foundation of China under Grant Nos.61174081and 61273135。
文摘Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are obtained.These general results are used to examine the exact controllability and approximate controllability of the Dzektser equation in the theory of seepage.
基金supported by the National Natural Science Foundation of China under Grant Nos.11926402and 61973338。
文摘This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform.Secondly,the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory.Finally,an example is given to illustrate the effectiveness of the obtained theoretical results.