Convergence of infinite dimensional sampled LQR problems: theory and numerical results

A theory for convergence of the closed-loop solution to infinite-dimensional discrete-time linear quadratic regulator (LQR) problems on the infinite time interval to the solution of a corresponding continuous-time LQR problem as the length of the sampling interval tends toward zero is discussed. Convergence of solutions to the operator algebraic Riccati equation and corresponding optimal feedback control gains is guaranteed under appropriate uniform stabilizability and detectability conditions and consistent sampling. Some numerical results involving the optimal LQ control of a heat or diffusion equation, a hereditary or delay differential equation, and a hybrid system of ordinary and partial differential equations describing the transverse vibration of a cantilevered Voigt-Kelvin viscoelastic beam with tip mass are also presented