Reduced basis method for H2 optimal feedback control problems

Abstract

In this paper we examine the application of recently introduced parametric model reduction techniques to the H2 optimal feedback control problem. The H2 control problem provides a realistic framework for control applications, since it considers disturbances in the system and in the measurement outputs. Furthermore it employs state-estimation to reconstruct the unknown state from the noisy measurements. It turns out, that the controller is a dynamical system and two solutions of algebraic Riccati equations (AREs) are required to form it. We apply parametric model order reduction techniques to the AREs and to the state equation of the observer and show by numerical examples, that this approach can yield a significant speed-up in multi-query scenarios for large scale parametric problems for the control of partial differential equations (PDE).