A Snapshot Decomposition Method for Reduced Order Modeling and Boundary Feedback Control

Abstract

In this paper, we develop a reduced basis construction method that allows for separate consideration of baseline and actuated dynamics in the reduced modeling process. A prototype initial boundary value problem, governed by the two-dimensional Burgers equation, is formulated to demonstrate the utility of the method in a boundary control setting. Comparisons are done between reduced and full order solutions under open-loop boundary actuation to illustrate advantages gained by separate consideration of actuated dynamics. A tracking control problem is specifled using a linear quadratic regulator formulation. Comparisons of feedback control efiectiveness are done to demonstrate beneflts in control efiectiveness obtained from separate consideration of actuated dynamics during model reduction.