Approximation of Large Scale Riccati Equations
by
Miroslav Stoyanov
Virginia Tech
Coauthors: Dr. Jeff Borggaard

Riccati equations are considered for high dimensional problems arising from

feedback control of PDE systems. The large number of dimensions prohibit us

from solving the Riccati equations directly and we are forced to consider

alternative approaches. We consider both Galerkin and Petrov-Galerkin

projection methods to reduce the size of the system. The projections are

applied to both the high dimensional Riccati equation and the Chandrasekhar

equation associated with it. The objective of these projection

methods is to obtain low rank approximations to the Riccati solution

(and the optimal gain) when the number of control inputs is low. We demonstrate

how our methods work using numerical examples arising from the heat equation

and an advection diffusion reaction equation (linearized Burgers equation).

Date received: September 27, 2007