Approximations and Mesh Independence for LQR Optimal Control

The development of practical computational schemes for optimization and control of non-normal distributed parameter systems requires that one builds certain computational efficiencies (such as mesh independence) into the approximation scheme. We consider the issues of convergence and mesh independence for the Kleinman-Newton algorithm for solving the operator Riccati equation defined by the linear quadratic regulator (LQR) problem. We show that dual convergence and preservation of exponential stability (POES) play central roles in both convergence and mesh independence and we present numerical results to illustrate the theory