We investigate feedback control for infinite horizon optimal control
problems for partial differential equations. The method is based
on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and
model reduction techniques. It is well-known that HJB equations suffer
the so called curse of dimensionality and, therefore, a reduction
of the dimension of the system is mandatory. In this report we focus
on the infinite horizon optimal control problem with quadratic cost
functionals. We compare several model reduction methods such as Proper
Orthogonal Decomposition, Balanced Truncation and a new algebraic
Riccati equation based approach. Finally, we present numerical examples
and discuss several features of the different methods analyzing advantages
and disadvantages of the reduction methods.
%0 Book Section
%1 alla2017model
%A Alla, Alessandro
%A Schmidt, Andreas
%A Haasdonk, Bernard
%B Model Reduction of Parametrized Systems
%C Cham
%D 2017
%E Benner, Peter
%E Ohlberger, Mario
%E Patera, Anthony
%E Rozza, Gianluigi
%E Urban, Karsten
%I Springer International Publishing
%K from:mhartmann ians imported vorlaeufig
%P 333--347
%R 10.1007/978-3-319-58786-8_21
%T Model Order Reduction Approaches for Infinite Horizon Optimal Control
Problems via the HJB Equation
%U https://doi.org/10.1007/978-3-319-58786-8_21
%X We investigate feedback control for infinite horizon optimal control
problems for partial differential equations. The method is based
on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and
model reduction techniques. It is well-known that HJB equations suffer
the so called curse of dimensionality and, therefore, a reduction
of the dimension of the system is mandatory. In this report we focus
on the infinite horizon optimal control problem with quadratic cost
functionals. We compare several model reduction methods such as Proper
Orthogonal Decomposition, Balanced Truncation and a new algebraic
Riccati equation based approach. Finally, we present numerical examples
and discuss several features of the different methods analyzing advantages
and disadvantages of the reduction methods.
%@ 978-3-319-58786-8
@inbook{alla2017model,
abstract = {We investigate feedback control for infinite horizon optimal control
problems for partial differential equations. The method is based
on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and
model reduction techniques. It is well-known that HJB equations suffer
the so called curse of dimensionality and, therefore, a reduction
of the dimension of the system is mandatory. In this report we focus
on the infinite horizon optimal control problem with quadratic cost
functionals. We compare several model reduction methods such as Proper
Orthogonal Decomposition, Balanced Truncation and a new algebraic
Riccati equation based approach. Finally, we present numerical examples
and discuss several features of the different methods analyzing advantages
and disadvantages of the reduction methods.},
added-at = {2018-07-20T10:54:30.000+0200},
address = {Cham},
author = {Alla, Alessandro and Schmidt, Andreas and Haasdonk, Bernard},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2d3c4dfa7f1388b5fec6d177e9e786e8c/mathematik},
booktitle = {Model Reduction of Parametrized Systems},
doi = {10.1007/978-3-319-58786-8_21},
editor = {Benner, Peter and Ohlberger, Mario and Patera, Anthony and Rozza, Gianluigi and Urban, Karsten},
interhash = {ece8c28ee37fdc9c9c9935f3393befbc},
intrahash = {d3c4dfa7f1388b5fec6d177e9e786e8c},
isbn = {978-3-319-58786-8},
keywords = {from:mhartmann ians imported vorlaeufig},
owner = {schmidta},
pages = {333--347},
publisher = {Springer International Publishing},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {Model Order Reduction Approaches for Infinite Horizon Optimal Control
Problems via the HJB Equation},
url = {https://doi.org/10.1007/978-3-319-58786-8_21},
year = 2017
}
