Computer Aided Control System Design

Computer Aided Control System Design

Computer aided control system design refers to numerical methods for the design of controllers and on modeling, discretization, and simulation of systems with controls and observations. The work on effective control setups combines methods from the fields of model order reduction, matrix equations, and scientific computing.

One of our core areas is the computer aided control of system governed by (partial) differential equations. Among others, we develop numerical algorithms for robust control and stabilization of descriptor systems that are obtained from the discretization of differential equations with additional constraints like the Navier-Stokes equations.

Within the vast research field of numerical methods for control systems, we 
focus on the construction of H-infinity controllers or the computation of system norms by using spectral information of certain structured matrix pencils. Apart from the developments in the theory, our algorithms are casted into efficient and robust software environments.

Projects

<h3>Stabilization and optimal control of flows</h3>

Stabilization and optimal control of flows

Partners: Shanghai U
Funded by: DFG, MPI, IMPRS, CDZ, Chinese High-end Foreign Experts program
Funding Period: DFG SPP1253 (until 10/2013), MPI (since 11/2013)
Contact: Jan Heiland


<h3>Numerical solution of optimal control problems with DAE constraints</h3>

Numerical solution of optimal control problems with DAE constraints

Partners: Augsburg U

Funded by: MPI

Funding Period: since 12/2013

Contact: Jan Heiland

<h3>Computational methods for robust control and optimization</h3>

Computational methods for robust control and optimization

Partners: New York U, TU Berlin, Lehigh U, Aquila U, MIT
Funded by: MPI, NYU
Funding Period: since 10/2015
Contact: Tim Mitchell

<h3>Optimization of parameter dependent mechanical systems</h3>

Optimization of parameter dependent mechanical systems

Partners: U Split, Strossmayer U Osijek
Funded by: Croatian Science Foundation
Funding Period: 07/2015 – 06/2019
Contact: Jonas Denißen

<h3>Analysis of SPDE control problems</h3>

Analysis of SPDE control problems

Partners: U Halle
Funded by: MPI, IMPRS
Funding Period: since 04/2015
Contact: Christoph Trautwein

<h3>MOR for control systems</h3>

MOR for control systems

Partners: NUST Islamabad, TU Delft, PSE Group
Funded by: MPI
Funding Period: since 06/2016
Contact: Jan Heiland

Concluded Projects

HPC domain decomposition for PDE constrained optimization

Funded by: CDS (01/2013-07/2013), NDS (08/2013-01/2014)
Researcher: Martin Stoll, Andrew Barker

Discontinuous Galerkin methods for PDE constrained optimization, in particular reaction diffusion systems

Funded by: MPI, CDS (since 10/2012)
Researcher: Peter Benner, Hamdullah Yücel, Martin Stoll

Featured Publications

F. E. Curtis, T. Mitchell, and M. L. Overton (2017)
A BFGS-SQP Method for Nonsmooth, Nonconvex, Constrained Optimization and its Evaluation using Relative Minimization Profiles
Optimization Methods and Software, 32(1), pp. 148-181, 2017
J. Heiland (2016)
A Differential-Algebraic Riccati Equation for Applications in Flow Control
SIAM Journal on Control and Optimization, 54(2), pp. 718-739 (2016)
P. Benner, M. Heinkenschloss, J. Saak, and H. K. Weichelt (2016)
An inexact low-rank Newton–ADI method for large-scale algebraic Riccati equations
Applied Numerical Mathematics, 108, pp. 125-142, 2016
P. Benner and J. Heiland (2015)
LQG-Balanced Truncation Low-Order Controller for Stabilization of Laminar Flows
Active Flow and Combustion Control 2014. Springer International Publishing, 365-379
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