Invertibility of an Operator Appearing in the Control Theory for Linear Systems
Invertibility of an Operator Appearing in the Control Theory for Linear Systems
复制标题
DOI：
10.1023/a:1010254808822
复制
发表时间：
2001-07
影响因子：
0.6
通讯作者：
G. Kurina
中科院分区：
文献类型：
--
作者：
G. Kurina
We give sufficient conditions for the existence of a bounded inverse operator for a linear operator appearing in the theory of optimal control of linear systems in Hilbert space and having a matrix representation of the form $$\left( \begin{gathered} F_1 {\text{ 0 }}F_2 \hfill \\ F_3 {\text{ }}--F_1^* {\text{ }}F_5 \hfill \\ - F_5^* {\text{ }}F_2^* {\text{ }} - F_4 \hfill \\ \end{gathered} \right)$$ , where F3, F4are nonnegative self-adjoint operators. The invertibility of the operator under study is used to prove the unique solvability of a certain two-point boundary-value problem that arises from conditions for optimal control.
We give sufficient conditions for the existence of a bounded inverse operator for a linear operator appearing in the theory of optimal control of linear systems in Hilbert space and having a matrix representation of the form $$\left( \begin{gathered} F_1 {\text{ 0 }}F_2 \hfill \\ F_3 {\text{ }}--F_1^* {\text{ }}F_5 \hfill \\ - F_5^* {\text{ }}F_2^* {\text{ }} - F_4 \hfill \\ \end{gathered} \right)$$ , where F3, F4are nonnegative self-adjoint operators. The invertibility of the operator under study is used to prove the unique solvability of a certain two-point boundary-value problem that arises from conditions for optimal control.