Abstract:
For large scale optimal control problems related, for example, to coupled systems involving fluids interacting with its environment, model reduction techniques may, be essential to arrive at computationally tractable problems. For certain classes of problems it was experienced that models of quite low dimension can provide suprisingly good approximations.
In this series of lectures the basis for proper orthogonal decomposition (POD) for model reduction will be derived. POD will be compared to other model reduction techniques, most notably to balanced trunction, a well-known method for reduction of linear systems. The construction principle for the POD basis from snap-shots and from alternative numerical methods will be explained. Galerkin schemes based on POD basis will be derived and their approximation properties will be analysed. The use of POD model reduction for both, open and closed loop parabolic optimal control problems will be described, computational and practical features will be high-ligthed. A recent development, OSPOD (optimality system POD) will be presented. It was introduced to overcome potential difficulties related to unmodelled dynamics in the POD approach to optimal control. The combination of POD with trust region methods as a means of deciding when to update the POD basis will be discussed. Examples from optimal control related to the Burgers and Navier Stokes equations will be demonstrate the effecivity of the methods.

Dispense

• Reduced Order Model Development and Control Design - Rome, January 06 (file PDF, 3624 Kb)
• Proper Orthogonal Decomposition: Introductory Remarks (file PDF, 160 Kb)
• References (file PDF, 26 Kb)

Orario del Corso
Le lezioni svolgeranno presso il Dipartimento di Matematica, Università di Roma "La Sapienza", P. Aldo Moro 2 secondo il seguente orario:

Martedì	24 Gennaio,	14.30-16.30	Aula Picone
Mercoledì	25 Gennaio,	10.00-12.00	Aula del Consiglio
Giovedì	26 Gennaio,	10.00-12.00	Aula del Consiglio

Le persone interessate sono invitate a registrarsi inviando un mail a falcone@mat.uniroma1.it entro il 15 Gennaio.

Thursday, 19-Jan-2006 12:48:18 CET