Basis Construction for the Design of Boundary Feedback Controls From Reduced Order Models (Preprint)
AIR FORCE RESEARCH LAB WRIGHT-PATTERSON AFB OH AIR VEHICLES DIRECTORATE
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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. A weak formulation approach, in combination with proper orthogonal decomposition and Galerkin projection, is used to develop a reduced model of the distributed parameter system. Comparisons are done between reduced and full order solutions under open-loop boundary actuation to illustrate advantages gained by separate consideration of actuated dynamics in the reduced modeling process. A tracking control problem is specified for the full order system using a linear quadratic regulator formulation. Comparisons of feedback control effectiveness are done to demonstrate benefits in control effectiveness obtained from separate consideration of actuated dynamics during model reduction.
- Theoretical Mathematics