Design of data-driven Hamiltonian models for complex mechatronic systems and their application in energy-based control

Dr. Dmitry Gromov

In the recent decades, we have observed a significant shift in how we understand and address complex dynamical systems and phenomena. An intensive development of computational tools has allowed a transition from model-based to data-based approaches in modeling and analysis of complex technical systems and processes. The advantages of such a transition are manifold and range from taming the underlying complexity of the real objects and increasing the flexibility of the methods used to providing instruments for real-time decision-making under dynamically changing circumstances.

Specifically, the objectives of the envisaged project are the development of an approach to reconstruct port-Hamiltonian models of complex mechatronic systems based upon the observed data and the subsequent application of the derived models for the energy-based feedback control design. This approach will extend the existing methods, which are based upon the application of the infinite-dimensional linear Koopman operators, in that we will consider a special class of (potentially high-dimensional) nonlinear models possessing symplectic structure. We will thus solve the problem of determining the best possible approximation to the available measurements while preserving the physical properties of the system (invariants, vibrational modes etc.)

The obtained results will be tested on a physical model of an elastic gantry crane installed at the Clausthal University of Technology. This system is well-known for being prone to structural vibrations, and its real-time control presents a substantial challenge to the engineers. However, the potential applications of the suggested approach go far beyond a single application and hopefully will result in the development of a full-scale research program.

1. Lecture by Dr. Gromov at the Institute for Electrical Information Technology, Clausthal University of Technology, 10:30, 8 July 2024. The lecture will be open for all students and staff members of CUT.
2. Lecture by Prof. Palis and tutorial by A. Maksakov at the University of Latvia, 14-16 October 2024. Both the lecture and the tutorial will be open for all students and staff members of LU.

Direct: participants of the project.                             Number: 3

Indirect: members of the respective scientific groups,   current and prospective students of both groups.   Number: 40 (LU) + 30 (CUT)