Reduced Basis Approximation for the Discrete-time Parametric Algebraic Riccati Equation

In this work we study the application of the reduced basis (RB) approximation method for parametric discrete-time algebraic Riccati equations (DARE). The DARE is very challenging to solve in large dimensions and parametric problems for large-scale applications are therefore often infeasible. We thus propose to apply the low-rank factor greedy (LRFG) algorithm to build a suitable low-dimensional subspace for the model reduction approach. Furthermore, we perform a rigorous error estimation, including an effectivity analysis and show how the RB-DARE procedure can be implemented efficiently. Numerical examples for an application in feedback control prove the benefits, in particular excellent speedups and reliability of the error estimators.