Computer-aided Control System Design
Computer-aided control system design refers to numerical and analytical methods for the design of controllers and on modeling, discretization, and simulation of systems with controls and observations. Work on effective control setups combines methods from the fields of nonlinear control, dynamical systems, 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.
Showcase
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.
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Projects
Partners: OvGU
Funded by: DFG
Funding Period: 2020-2023
Contact: Alexander Zuyev
Partners: OvGU
Funded by: MPI, DFG (MathCoRe)
Funding Period: since 11/2021
Contact: Jan Heiland, Yongho Kim
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
Partners: NUST Islamabad, TU Delft, PSE Group
Funded by: MPI
Funding Period: since 06/2016
Contact: Jan Heiland
Concluded Projects
Partners: New York U, TU Berlin, Lehigh U, Aquila U, MIT
Funded by: MPI, NYU
Funding Period: 2015-2022
Partners: U Halle
Funded by: MPI, IMPRS
Funding Period: 2015—2018
Partners: Augsburg U
Funded by: MPI
Funding Period: since 12/2013
Contact: Jan Heiland
Partners: U Split, Strossmayer U Osijek
Funded by: Croatian Science Foundation
Funding Period: 2015–2019
Featured Publications
Zuyev, A.; Feng, L.; Benner, P.: Estimates of the Kolmogorov n-Width for Nonlinear Transformations with Application to Distributed-Parameter Control Systems. IEEE Control Systems Letters 8, pp. 1877 - 1882 (2024)
Yevgenieva, Y.; Zuyev, A.; Benner, P.; Seidel-Morgenstern, A.: Periodic Optimal Control of a Plug Flow Reactor Model with an Isoperimetric Constraint. Journal of Optimization Theory and Applications 202, pp. 582 - 604 (2024)
Grushkovskaya, V.; Zuyev, A.: Motion Planning and Stabilization of Nonholonomic Systems using Gradient Flow Approximations. Nonlinear Dynamics 111, pp. 21647 - 21671 (2023)
Benner, P.; Chuiko, S.; Zuyev, A.: A Periodic Boundary Value Problem with Switchings under Nonlinear Perturbations. Boundary Value Problems, 50, 12 pages (2023)
Heiland, J.: Convergence of Coprime Factor Perturbations for Robust Stabilization of Oseen Systems. Mathematical Control and Related Fields 12 (3), pp. 747 - 761 (2022)
Misra, R.; Wisniewski, R.; Zuyev, A.: Attitude Stabilization of a Satellite Having Only Electromagnetic Actuation Using Oscillating Controls. Aerospace 9 (8), 444 (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)
