3 PhD Students/Postdocs at Slovak University of Technology

Topic #1: Set-based control of nonlinear systems

As the computers and algorithms get generally faster, many new control concepts become tractable and can be developed. Set-based control is one of these, where the primary use of sets is in enveloping a space of possible evolutions of variables of a system over time. If these envelopes can be obtained in reasonable time, many properties of dynamic systems such as stability or robustness can be reasoned about. The first goal of the thesis is to build a novel type of multi-base set arithmetics that combines elements such as interval analysis, convex-set theory, and polynomial-functions theory to achieve the best trade-off between accuracy of representation and the burden associated with the underlying calculations to obtain the envelopes. The second goal of the thesis is to develop methods of synthesis of controllers that can be used for safe and reliable control of nonlinear systems. The project of the thesis will be finished with a successful demonstration of the developed techniques on a laboratory plant.

Topic #2: Modelling, Optimal Design and Optimal Operation of Membrane Processes

Membrane processes are crucial in various industrial sectors, including water purification, pharmaceuticals, and food processing, due to their efficiency and sustainability. This proposed research aims to develop an integrative framework that combines advanced mathematical modeling techniques with optimization algorithms to achieve optimal design and operation of membrane processes. The study will involve the development of comprehensive mathematical models that capture the complex phenomena involved in membrane processes, considering factors such as mass transfer, fluid dynamics, and membrane fouling. Furthermore, the research will focus on optimizing the design parameters of membrane systems to enhance performance, minimize energy consumption, and reduce environmental impact. Finally, the proposed framework will facilitate real-time optimization strategies for the optimal operation of membrane processes, ensuring efficient and sustainable operation under varying operating conditions. Overall, this research will contribute to the advancement of membrane technology and its widespread adoption in industrial applications.

Topic #3: Development of reliable and explainable models for industrial monitoring, optimization, and control

Safe and sustainable process systems, which constitute the backbone of a modern, developed society, require sensing of key process variables, estimation of unmeasured variables, and application of actions that steer the systems towards desired goals. Automation of human decisions in such tasks would make these decisions become fast, reliable, and error-free. A key technology on the rise in this context is the use of combined mathematical modelling and statistical learning to gather information through software (soft) sensors to monitor, assess, and steer the behaviour of dynamic systems (e.g., industrial processing plants, water, gas and energy networks, or manmade machines and vehicles) into desired operating regimes. The delivered tools will exploit domain knowledge – making the designed mathematical models explainable – and assess and improve the information content of the data – making the models reliable and fit for industrial needs.