LINEAR QUADRATIC OPTIMAL CONTROL OF A WAVE EQUATION WITH BOUNDARY DAMPING AND POINTWISE CONTROL INPUT by

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 equation under pointwise control. The regularity results for wave equations with Dirichlet boundary condition are generalized to the wave equation considere here. Finally, the linear quadratic optimal control problem is solved in the in nite time interval and the existence of the regularity of the solution of the Riccati operator equation are obtained. Research supported in prat under a grant from the Air Force O ce of Scienti c Research: AFOSR 90-0091