Solving the linear quadratic optimal control problem for infinite-dimensional systems

Calculation of the solutions to linear quadratic optimal control problems for infinite-dimensional systems is considered. The sequence of solutions to a sequence of approximating finite-dimensional problems converges to the optimal control for the infinite-dimensional system if certain assumptions such as uniform stabilizability are satisfied. We use this result to calculate controllers for the infinite-dimensional system that are arbitrarily close to optimal. A one-dimensional heat equation and a problem of acoustic noise control are used to illustrate the algorithm. The numerical results are discussed.