MASTER ASSIGNMENT
Problem Description
In parallel with the developments in information science and technology, “data-driven” methods gained increasing popularity among the control community as well. A fundamental result by (Willems, Rapisarda, Markovskya, & De Moor, 2005) revealed how/when a system can be characterized by a finite set of trajectories (instead of a model). The seminal work of (De Persis & Tesi, 2020) provided solutions to the basic offline controller synthesis problems of state/ouput feedback stabilization and linear-quadratic regulation based on data-dependent linear matrix inequalities (LMIs). Further research by (Berberich, Scherer, & Allgöwer, 2023) led to the development of a framework that facilitates the combination of prior model knowledge with experimental data to design robust controllers. A recent MSc thesis by (Boer, 2023) proposed a more refined pertubation model, based on which robust state feedback controllers can be designed in a way to potentially reduce the inherent conservatism in synthesis.
It is well-known that robust estimator synthesis for uncertain systems can also be formulated as an LMI problem in a model-based setting; see e.g. (Sun & Packard, 2005). It seems that data-driven estimator synthesis has not been considered in the control literature yet. The use of dilated LMI conditions by (De Oliveira, Geromel, & Bernussou, 2002) can also be explored in this context. On the practical side, estimation of the contact force is a problem that is quite relevant for robotics applications since it might eliminate the need for using sensors. In a recent MSc assignment by (Holst, 2022), the force estimation problem was considered on a flexure based positioning mechanism (see the picture). It would be interesting to explore the potentials of data-driven estimator synthesis for force estimation in this mechanism.
Goals and Tentative Work
The goal of this MSc assignment is to develop a data-driven robust estimator synthesis method and explore its potential for force estimation. The assignment work is hence foreseen to contain the following parts:
- Study of basics of LMI optimization and LMI-based estimator synthesis
- Study of and practice with LMI optimization software (Matlab LMILAB, Yalmip, CVX)
- Literature survey and study on data-driven offline synthesis methods (based especially on LMI optimization)
- Development of a novel data-driven (offline) estimator synthesis method Exploration of the potential of the proposed method in a flexure-based positioning mechanism
Desired Qualifications
- Good knowledge of control theory (via CSD4R and System Identification; Robust/Optimal Control would be a plus)
- Strong experience with Matlab (Control System Toolbox) and Simulink
- Basic knowledge of optimization and linear algebra
- Passion for understanding and reproducing complicated mathematical derivations Interest and ability to do experimental work
References
- Berberich, J., Koch, A., Scherer, C. W., & Allgöwer, F. (2020). Robust data-driven state-feedback design. Proc. American Control Conference, (pp. 1532-1538). Denver, CO, USA.
- Berberich, J., Scherer, C. W., & Allgöwer, F. (2023). Combining Prior Knowledge and Data for Robust Controller Design. IEEE Transactions on Automatic Control, 4618-4633.
- Boer, R. d. (2023). Robust data-driven state-feedback synthesis from data corrupted by perturbations with bounded norms and rates-of-variation. MSc Thesis, University of Twente, Enschede.
- De Oliveira, M. C., Geromel, J. C., & Bernussou, J. (2002). Extended H-two and H-infinity norm characterizations and controller parametrizations for discrete-time systems. International Journal of Control, 75(9), 666-679.
- De Persis, C., & Tesi, P. (2020, March). Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness. IEEE Transactions on Automatic Control, 65(3), 909-924.
- Holst, T. H. (2022). External force estimation on a non-linear compliant 2DOF manipulator system. MSc Thesis, University of Twente, Enschede.
- Sun, K., & Packard, A. (2005). Robust H_two and H_infinity Filters for Uncertain LFT Systems. IEEE Transactions on Automatic Control, 715-720.
- Willems, J. C., Rapisarda, P., Markovskya, I., & De Moor, B. L. (2005). A note on persistency of excitation. Systems and Control Letters, 54, 325 – 329.
Contact persons
