the programme of the joint third semester at UMLP covers a large variety of topics related to modelling, analysis, simulation and control of multiphysics systems.
All dynamical models from macroscopic physics (mechatronics, electromagnetism, hydraulics, chemical and process systems and thermodynamics in the broad sense) are described using unifying physical and mathematical theories.
Such a unifying framework will be presented in the courses of the programme.
Resulting model-based control designs (for controllers, observers, etc.) may be built upon this general structure of complex multiphysics systems. Those designs allow the design of robust structural controllers, observers or supervision algorithms, for instance.
Besides, structure preserving methods exist for the reduction, discretisation and simulation of multiphysics systems. Those methods preserve the structural properties of the original systems and lead to efficient long-range simulation or optimisation algorithms. The same ideas apply for spatio-temporal dynamics and allow us to cope with distributed parameter systems where variations, both with time and space, matter. This paves the way to a wide range of applications ranging from design, optimisation and simulation, to control, supervision, and maintenance.
The third semester is composed of 7 modules:
The objectives, content and associated pedagogical teams are detailed hereafter :
Coordinators: B. Maschke, S. Trenn
Teachers: B. Maschke, S. Trenn,T. Reis, Y. Le Gorrec, S. Stramigioli, A. van der Schaft
learn about fundamentals of port-based modelling of physical systems and technical systems.
Coordinators: A. Macchelli, H. Gernandt
Teachers: A. Macchelli, P. Borja, H.Gernandt, Y. Le Gorrec, Y. Wu, N. Liu
In this lecture, students will gain a deeper understanding of passivity as a fundamental
concept in the control of multiphysical systems and study its relation to port-Hamiltonian systems. We will explore extensions of passivity in the context of dissipativity, along with recently introduced generalised notions of passivity. In the second part of the lecture, we will demonstrate how these passivity concepts can be leveraged for control design through the framework of control-by-interconnection.
Finally, the students will learn about the roles of passivity and dissipativity in the domain of optimal control problems. Particular attention will be given to model predictive control (MPC), one of the most widely used advanced control strategies in industrial applications. We will illustrate how passivity and dissipativity can aid in establishing critical properties such as stability and the turnpike phenomenon.
Coordinators: Y. Le Gorrec, T. Reis
Teachers: Y. Le Gorrec, T. Reis, A. Macchelli, Y. Wu, N. Liu, H. Zwart
Students will acquire a solid understanding of the port-Hamiltonian formulation for
distributed parameter and multiphysical systems. They will learn the theoretical foundations and
practical applications of this formulation for modelling such systems using the specific properties of port-Hamiltonian structures. This includes gaining insights into the mathematical principles that underpin port-Hamiltonian models, such as energy-based descriptions and interconnection structures.
Students will explore how these principles can be applied to describe and analyse a wide variety of physical systems, including mechanical, electrical, thermal, and fluid systems. Moreover, they will understand how to leverage the port-Hamiltonian framework to design control strategies that utilise system properties like passivity. Through practical examples and case studies, students will also develop the skills to implement these methods, thereby bridging the gap between theory and practice.
Coordinators: S. Ahmed, T. Reis
Teachers: T. Reis, S. Ahmed, P. Kotyczka, T. Faulwasser, S. Glas
This course aims to equip students with a comprehensive understanding of numerical methods used in solving control, model reduction and optimisation problems. Students will explore the mathematical foundations of these techniques and gain the ability to apply them to practically motivated case studies.
The course focuses on formulating optimisation, model reduction and control problems in mathematical terms and solving them using appropriate numerical approaches. A strong emphasis will be placed on the development, analysis, and implementation of numerical algorithms tailored to challenges in control systems, model reduction and optimisation. By the end of the course, students will be able to apply the acquired skills to real-world problems.
Coordinators : Y. Le Gorrec, H. Gernandt
Teachers: D. Matignon, P. Kotyczka, L. Lefèvre, M. Fournié, G. Haine
This course provides students with the knowledge and skills to model and numerically simulate distributed parameter systems using finite element discretisation methods for spatial and temporal domains, emphasising the preservation of physical system properties. Through the use of vector calculus as a fundamental mathematical framework, students will explore the theoretical foundations of these methods. The course features three hands-on programming lab sessions, enabling practical application and reinforcing concepts. By the end of the course, students will be equipped with advanced numerical and modelling techniques for the design and analysis of control systems.
Coordinators: A. Macchelli, S. Ahmed
Teachers: A. Macchelli, B. Jayawardhana, D. Matignon, B. Maschke, T. Hélie, A. v. d Schaft, S. Ahmed
This course is designed to enable participants to apply the principles of port-Hamiltonian systems theory to advanced engineering applications in robotics, mechatronics, process control, and acoustics. Participants will gain a deep understanding of how port-Hamiltonian frameworks can be leveraged for modelling, passivity-based control, stability analysis, and optimisation in these diverse domains. By bridging theoretical insights with practical implementations, the course equips learners with the ability to design energy-efficient, robust, and stable systems that address complex interdisciplinary challenges.
Coordinators: Y. Wu, S. Trenn
Teachers: All
Solve real-world problems using the knowledge acquired during the master programme through the project-based approach.
In this module, a small group of students (ideally composed of at least one applied mathematics and one engineering student) will collaborate on a project based on real-world applications over the semester. The objective is to integrate and apply the diverse skills acquired during the master's programme - such as complex system modelling, numerical techniques, and control design methods - to solve practical challenges in fields including mechanical, electronic, and hydraulic systems. This interdisciplinary approach fosters teamwork and allows students to bridge theoretical concepts and practical implementation, equipping them to address challenges in advanced technological domains. The module involves at least two hours of weekly work, supplemented by two weeks of intensive project-focused activities during the semester. Evaluation will be based on a scientific report, a presentation, and the successful real-world implementation of the application.
The third semester will end with a scientific workshop gathering students and supervisors, as well as invited speakers to present the outcomes of the Multidisciplinary projects. A prize for the best project/presentation will be awarded at this occasion.
The lectures are partly based on the following related books from the EMJM participants and partners:
