A proper orthogonal decomposition approach to approximate balanced truncation of infinite dimensional linear systems

Abstract

We extend a method for approximate balanced reduced order model derivation for finite dimensional linear systems developed by Rowley (Int. J. Bifur. Chaos Appl. Sci. Eng. 15(3) (2005), pp. 997–1013) to infinite dimensional systems. The algorithm is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method can be also applied to nonlinear systems. Numerical results are presented for a convection diffusion system.

Keywords:

• balanced truncation
• proper orthogonal decomposition
• infinite dimensional systems

2000 AMS Subject Classification :

• 93-xx
• 65-xx
• 35-xx

Acknowledgements

This research was supported in part by the Air Force Office of Scientific Research under AFOSR grants FA9550-05-1-0041 and FA9550-07-1-0540.