The networking of multi-physics systems (mechanical, electical, hydraulic, biochemical, ...) with computational (control systems, signal processing, logical inferencing, planning, ...) processes, interacting with often uncertain environments, with human actors, in a socio-economic context, leads to so-called Cyber-Physical Systems (CPS). The CPS that are engineered today are reaching a hitherto unseen level of complexity.

To date, no unifying theory nor systematic design methods, techniques and tools exist for such systems. Individual (mechanical, electrical, network, or software) engineering disciplines only offer partial solutions.

Multi-paradigm Modelling (MPM) proposes to model every part and aspect of such complex systems explicitly, at the most appropriate level(s) of abstraction, using the most appropriate modelling formalism(s). This includes the explicit modelling of the often complex engineering workflows.

Due to the specialization required in different disciplines, difficulties arise when knowledge about the different parts, views and workflow phases of the development of CPS have to be communicated. Current Electrical/Mechanical/Control... Engineering and Computer Science, education do not cover all of the above, which hampers understanding of the development of CPS at a "systems" level.

To tackle this challenge, the training school will provide an overview of the formalisms, techniques, methods and tools, as well as common workflows used for the development of complex systems. The students will get the opportunity to apply the freshly acquired knowledge hands-on in the development of a line-following robot. This case, though simple, exhibits all the aspects of complexity found in far more complex CPS.

The main intended audience are researchers (such as PhD students) with a background in software development who want to understand the other (physics, deployment, ...) aspects of CPS development. Others, with a background in for example mechanical engineering, will conversely learn about the software aspects of CPS development.
More advanced MPM topics such as modelling language engineering and model transformation will not be covered: we believe that first a good understanding of the diverse formalisms, methods and techniques used in CPS development, must be developed. For language engineering and other topics, see for example the Domain-Specific Modelling, Theory and Practice (DSM-TP) Summer Schools.

The Training School topics include:

• Industrial needs and causes of complexity;
• Workflow modelling;
• SysML;
• Model checking of requirements;
• Causal Block Diagrams (aka Synchronous Data Flow);
• Modelling physical systems using power-flow lumped-parameter models (Bond Graphs);
• Mathematical modelling with computationally causal and a-causal (Modelica) languages;
• Calibration of models using physical experiments;
• Basics of (PID) controller design;
• Co-simulation;
• System architecture and (software) deployment in real-time, resource constrained systems; and
• Design Space Exploration;