On model reduction via empirical balanced truncation

Empirical balanced truncation is considered as an approach for deriving reduced-order models of large-scale nonlinear systems that are of interest in the design of feedback control systems. Empirical balanced truncation is related to the widely-applied proper orthogonal decomposition (POD) methodology and yet may be better suited for closed-loop control because order reduction is based on the system's state-to-output interaction along with its input-to-state interaction, not just the latter. Refinements to the scheme originally proposed in the literature are presented leading to reduced data requirements that may become significant for applications such as aerodynamic flow control. Towards that end, the 1-dimensional Burgers' equation is used to validate the basic ideas, implementation details, and applicability to closed-loop control system design.