The linear quadratic optimal regulator problem on a wave equation in a bounded subset of R n for n = 2; 3 with boundary damping and pointwise control input is formulated as a linear quadratic control problem with unbounded input/output operators using a variational approach. A dual control system is deened which allows us to investigate the regularity of the solution of the generalized wave equ...

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furtherm...

The linear quadratic optimal regulator problem on a wave equation in a bounded subset of R for n = 2; 3 with boundary damping and pointwise control input is formulated as a linear quadratic control problem with unbounded input/output operators using a variational approach. A dual control system is de ned which allows us to investigate the regularity of the solution of the generalized wave equat...