Page 374 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 374
TIONAL APPROXIMATION FOR DATA-DRIVEN MODELING AND COMPLEXITY
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
[3] R. V. Polyuga and A. J. van der Schaft, "Effort- and flow-constraint reduction methods for
structure preserving model reduction of port-Hamiltonian systems," Systems & Control
Letters, vol. 61, no. 3, pp. 412-421, 2012.
Spurious poles
Nick Trefethen, trefethen@maths.ox.ac.uk
Oxford University, United Kingdom
Spurious poles of rational approximations are fascinating in theory and troublesome in practice.
This talk reviews the mathematical and computational sides of this subject and explores the use
of the two-step method of AAA-least squares approximation for avoiding the problem.
Interpolatory Model Reduction in H∞-Controller Design
Matthias Voigt, mvoigt@math.tu-berlin.de
TU Berlin, Germany
In engineering problems, it is often desired to attenuate the influence of external noise and to
deal with uncertainties in a dynamical system. Classically, this amounts to the design of so-
called H∞-controllers which results in very difficult nonconvex and nonsmooth optimization
problems. The corresponding numerical methods require multiple evaluations of the H∞-norm
and its gradient with respect to the controller variables. In this talk we address new efficient
methods for the computation of the H∞-norm of large-scale dynamical systems with possibly
irrational transfer functions. We discuss a subspace projection approach for solving this problem
using interpolatory techniques that are well-known in model reduction. More precisely, after
performing the reduction, we compute the H∞-norm of the reduced transfer function and choose
the point at which the H∞-norm is attained as a new interpolation point to update the projection
matrices. We will discuss convergence properties of this procedure and illustrate it by various
examples. One focus of this talk will be on delay systems which are reduced by employing the
Loewner framework, This is useful in order to get a sequence of linear reduced models whose
H∞-norm can be evaluated more efficiently. Finally, we show how to apply these techniques in
the context of controller design.
372
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
[3] R. V. Polyuga and A. J. van der Schaft, "Effort- and flow-constraint reduction methods for
structure preserving model reduction of port-Hamiltonian systems," Systems & Control
Letters, vol. 61, no. 3, pp. 412-421, 2012.
Spurious poles
Nick Trefethen, trefethen@maths.ox.ac.uk
Oxford University, United Kingdom
Spurious poles of rational approximations are fascinating in theory and troublesome in practice.
This talk reviews the mathematical and computational sides of this subject and explores the use
of the two-step method of AAA-least squares approximation for avoiding the problem.
Interpolatory Model Reduction in H∞-Controller Design
Matthias Voigt, mvoigt@math.tu-berlin.de
TU Berlin, Germany
In engineering problems, it is often desired to attenuate the influence of external noise and to
deal with uncertainties in a dynamical system. Classically, this amounts to the design of so-
called H∞-controllers which results in very difficult nonconvex and nonsmooth optimization
problems. The corresponding numerical methods require multiple evaluations of the H∞-norm
and its gradient with respect to the controller variables. In this talk we address new efficient
methods for the computation of the H∞-norm of large-scale dynamical systems with possibly
irrational transfer functions. We discuss a subspace projection approach for solving this problem
using interpolatory techniques that are well-known in model reduction. More precisely, after
performing the reduction, we compute the H∞-norm of the reduced transfer function and choose
the point at which the H∞-norm is attained as a new interpolation point to update the projection
matrices. We will discuss convergence properties of this procedure and illustrate it by various
examples. One focus of this talk will be on delay systems which are reduced by employing the
Loewner framework, This is useful in order to get a sequence of linear reduced models whose
H∞-norm can be evaluated more efficiently. Finally, we show how to apply these techniques in
the context of controller design.
372
