Interpolation-Based Numerical Algorithms in Robust Control

• Applicant: Professor Dr. Matthias Voigt
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 424221635

• Final Report Year: 2023

Final Report Abstract

In this DFG project, optimization-based methods for model reduction, system identification, and H∞-controller synthesis of port-Hamiltonian (pH) systems have been developed. PH systems enable energybased modeling of complex dynamic processes from various engineering fields such as electrodynamics, thermodynamics, classical mechanics, and quantum mechanics, allowing for intuitive coupling of such systems. To leverage the advantageous properties of pH systems in optimizing complex networks, classical methods for model reduction, system identification, and controller synthesis need to be adapted. However, previous adaptations have resulted in accuracy and performance losses, respectively. Therefore, in this project a new approach has been developed that is based on formulating the problems as optimization problems for the transfer functions of pH systems. The proposed approach utilizes the possibility to easily parameterize pH systems to employ unconstrained optimization techniques. Initially, a pH system is chosen, where all entries of the system matrices depend on a parameter vector. Using a particular objective functional and adapted optimization strategy, either the H∞ -approximation error in model reduction, the sum of squared errors in system identification, or the H∞-norm of the transfer functions of the closed-loop system in H∞-controller synthesis is minimized. The presented methods have been compared with the current state of the art in pH system theory, demonstrating a significant improvement in terms of accuracy and performance. Moreover, the flexibility of these methods allows for their application to other problems such as reducing differential-algebraic equations or parametric systems. The results obtained using the optimization-based techniques can often significantly outperform previous approaches.

Publications

• Certifying Global Optimality for the L∞-Norm Computation of Large-Scale Descriptor Systems. IFAC-PapersOnLine, 53(2), 4279-4284.
  Schwerdtner, P.; Mengi, E. & Voigt, M.
  
• Adaptive Sampling for Structure-Preserving Model Order Reduction of Port-Hamiltonian Systems. IFAC-PapersOnLine, 54(19), 143-148.
  Schwerdtner, Paul & Voigt, Matthias
  
• Port-Hamiltonian System Identification from Noisy Frequency Response Data.
  P. Schwerdtner
  
• Structure-Preserving Model Order Reduction for Index One Port-Hamiltonian Descriptor Systems.
  P. Schwerdtner, T. Moser, V. Mehrmann & M. Voigt
  
• Structure-Preserving Model Order Reduction for Index Two Port-Hamiltonian Descriptor Systems
  T. Moser, P. Schwerdtner, V. Mehrmann & M. Voigt
  
• Fixed-order H-infinity controller design for port-Hamiltonian systems. Automatica, 152, 110918.
  Schwerdtner, Paul & Voigt, Matthias
  
• SOBMOR: Structured Optimization-Based Model Order Reduction. SIAM Journal on Scientific Computing, 45(2), A502-A529.
  Schwerdtner, Paul & Voigt, Matthias
  
• Structured Optimization-Based Reduction, Identification, and Control. Dissertation, Technische Universität Berlin, Institut für Mathematik, Januar 2023.
  P. Schwerdtner
  
• Structured Optimization-Based Model Order Reduction for Parametric Systems. SIAM Journal on Scientific Computing, 47(1), A72-A101.
  Schwerdtner, Paul & Schaller, Manuel