Grammian Based Model Reduction of Large-Scale Systems

2:45 PM-3:00 PM

*Room: Rio Mar 5*

*Chair: Danny Sorensen, Rice University, USA*

We describe model reduction techniques for large scale dynamical systems, modeled via systems of equations of the type

{ | F(x (t), x(t), u(t)) = 0 |

y(t) = H(x(t), u(t)), |

as encountered in the study of control systems with input u(t) Î R^{m}, state x(t) ^{Î} R^{N} and output y(t) ^{Î} R^{p}. These models arise from the discretization of continuum problem and correspond to
sparse systems of equations F(. , ., ..) and H(. , ..). The state dimension *N* is typically very large, while *m* and *p* are usually reasonably small. Although the numerical simulation of such systems may still be viable for large state dimensions *N*, most control problems of such systems are of such high complexity that they require
model reduction techniques, i.e. techniques that construct a lower order model via a projection P(.) on a state space of l lower dimension. We survey such techniques and put emphasis on the case where F(. , . , .) and H(. , .) are linear time-invariant or linear time-varying. We also show that the use of reduced order models is not restricted to control systems design : interesting applications are found in e.g. circuit simulation and weather prediction.

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Created 4/12/00; Updated 4/12/00