Mathematical Systems Theory Research Group

The Mathematical Systems Theory Research Group specializes in analysis and control of mathematical models of real-world dynamical phenomena.

Research focus and goals

In general, mathematical control theory concentrates on influencing the behaviour of dynamical models and it plays an important role in a wide range of modern technologies, such as energy efficient buildings, production of renewable energy, and self-driving cars. The theoretical part of the research belongs to the fields of Functional Analysis, Operator Theory, and Analysis of Partial Differential Equations.

Our research utilises state-of-the-art mathematical methods in the study of models arising from a wide range of engineering and industrial applications. Our main focus is in the highly challenging analysis of models involving Partial Differential Equations which are essential in modeling of flexible and vibrating structures, fluid flows, as well as diffusion of heat or materials.

Our research group especially specialises on robust control structures which tolerate uncertainty, modeling errors, and changes in the controlled systems. Tolerance to uncertainty is an important quality in any practical control designs in technology, and robustness is also an essential part in many control structures encountered in natural organisms.

The research is funded by Academy of Finland grants 298182 (2016-2019) and 310489 (2017-2021).

Some of our current research directions are listed in the following:

Robust control of partial differential equation models, especially disturbance cancellation for flexible and vibrating structures and control of fluid flows.
Analysis of large formations of autonomous agents, such as long queues of self-driving cars.
Model Predictive Control of partial differential equation models.
Stability theory of abstract differential equations.
Applications of mathematical systems theory in computational neuroscience.
Biomedical applications of robust tracking control.