Title page for ETD etd-05212009-155950

Type of Document Dissertation
Author Stoyanov, Miroslav
URN etd-05212009-155950
Title Reduced Order Methods for Large Scale Riccati Equations
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Borggaard, Jeffrey T. Committee Chair
Burns, John A. Committee Member
Gugercin, Serkan Committee Member
Zietsman, Lizette Committee Member
  • Large Scale
  • High Rank
  • Navier-Stokes
  • Riccati Equations
Date of Defense 2009-05-05
Availability unrestricted
Solving the linear quadratic regulator (LQR) problem for partial differential equa-

tions (PDEs) leads to many computational challenges. The primary challenge comes

from the fact that discretization methods for PDEs typically lead to very large sys-

tems of differential or differential algebraic equations. These systems are used to form

algebraic Riccati equations involving high rank matrices. Although we restrict our

attention to control problems with small numbers of control inputs, we allow for po-

tentially high order control outputs. Problems with this structure appear in a number

of practical applications yet no suitable algorithm exists. We propose and analyze so-

lution strategies based on applying model order reduction methods to Chandrasekhar

equations, Lyapunov/Sylvester equations, or combinations of these equations. Our nu-

merical examples illustrate improvements in computational time up to several orders of

magnitude over standard tools (when these tools can be used). We also present exam-

ples that cannot be solved using existing methods. These cases are motivated by flow

control problems that are solved by computing feedback controllers for the linearized


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