Linear Quadratic Optimal Control of a Wave Equation with Boundary Damping and Pointwise Control Input

The linear quadratic optimal regulator problem on a wave equation in a bounded subset of Rn 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 defined which allows us to investigate the regularity of the solution of the generalized wave equation under pointwise control. Finally, the linear quadratic optimal control problem is solved in the infinite time interval and, the existence and the regularity of the solution of the Riccati operator equation are obtained.