Cover picture with the lettering "CACSD" and stylized illustrations of a swinging pendulum and the quasi-stationary and periodic flow configuration in the cylinder wake.

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, data science, and scientific computing.

Primarily, we develop, analyse, and implement numerical algorithms for robust control and stabilization of (partial) differential equations. A particular focus lies on large-scale descriptor systems that play a role in the control of flows.

Within the vast research field of numerical methods for control systems, we pursue the so-called H-infinity controller design. In view of performant and reliable implementations, we also investigate related concepts like the computation of system norms or stability indices.

Where a model is insufficient or not even available, CACSD may rely on data. So called data-driven have been used since long and have found new traction with the emergence of neural networks. To ensure both performance and a sound theoretical basis of data-based approaches, we investigate the connections of control theory, classical system identification, and machine learning.


Swingup and stabilization of an inverted triple pendulum
Stabilizing a pendulum in upright position is a common control benchmark. Controlling a double or triple pendulum requires powerful hardware and a sophisticated and well-tuned software. Our triple pendulum is used to test new approaches and to showcase the potential of control algorithms. more


Illustration of the classification of configurations in the cylinder wake by "clusters" in reduced coordinates projected into the two-dimensional plane

Convolutional neural networks in controller design for PDEs

Partners: OvGU
Funded by: MPI, DFG (MathCoRe)
Funding Period: since 11/2021
Contact: Jan Heiland, Anahita Iravanizad, Yongho Kim, Vipin Kumar
Velocity field in the wake of a double cylinder

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
Schematic illustration of a closed-loop control system

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
MOR for control systems with uncertainties

MOR for control systems with uncertainties

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

Concluded Projects

Analysis of SPDE control problems

Analysis of SPDE control problems

Partners: U Halle
Funded by: MPI, IMPRS
Funding Period: 2015—2018
Numerical solution of optimal control problems with DAE constraints

Numerical solution of optimal control problems with DAE constraints

Partners: Augsburg U
Funded by: MPI
Funding Period: since 12/2013
Contact: Jan Heiland
Optimization of parameter dependent mechanical systems

Optimization of parameter dependent mechanical systems

Partners: U Split, Strossmayer U Osijek
Funded by: Croatian Science Foundation
Funding Period: 2015–2019

Featured Publications

Heiland, J.: Convergence of Coprime Factor Perturbations for Robust Stabilization of Oseen Systems. Mathematical Control and Related Fields 12 (3), pp. 747 - 761 (2022)
Bremer, J.; Heiland, J.; Benner, P.; Sundmacher, K.: Non-intrusive Time Galerkin POD for Optimal Control of a Fixed-Bed Reactor for CO2 Methanation. 16th IFAC Symposium on Advanced Control of Chemical Processes - ADCHEM 2021, Venice, Italy, June 13, 2021 - June 16, 2021. IFAC-PapersOnLine 54 (3), pp. 122 - 127 (2021)
Mitchell, T.: Fast Interpolation-based Globality Certificates for Computing Kreiss Constants and the Distance to Uncontrollability. SIAM Journal on Matrix Analysis and Applications 42 (2), pp. 578 - 607 (2021)
Benner, P.; Heiland, J.; Werner, S. W. R.: Robust Controller versus Numerical Model Uncertainties for Stabilization of Navier-Stokes Equations. 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations, Oaxaca, Mexico, May 20, 2019 - May 24, 2019. IFAC-PapersOnLine 52 (2), pp. 25 - 29 (2019)
Go to Editor View