The module gives an introduction to hybrid discrete-continuous systems, as arising by embedding digital hardware into physical environments, and it elaborates on state of the art methods for the mathematical modelling and the analysis of such systems. It thus provides central competences for understanding and designing reliable cyber-physical systems.
Professional competence
The students:

• characterise formal models of cyber-physical systems: hybrid automata, hybrid state transition systems
• name domain-specific system requirements: safety, stability, robustness
• name analysis methods: symbolic state-space exploration, abstraction and abstraction refinement, generalized Lyapunov-Methods
• use state-of-the-art analysis tools
• select and apply adequate modelling and analysis methods for concrete application scenarios
• apply methods to reduce large state spaces and reduce infinite-state systems by abstraction
• know the de-facto industry standards for system modelling and are able to apply the corresponding modelling framewortks and tools

Methodological competence
The students:

• mtdel heterogeneous dynamical systems with adequate modelling and design tools, in particular Simulink/Stateflow
• transfer modelling and analysis methods to other heterogeneous domains, e.g. socio-technical systems

Social competence
The students:

• work in teams
• solve complex modelling, design, and analysis tasks in teams

Self-competence
The students:

• reflect their actions and respect the scope of methods dedicated to hybrid systems

Embedded computer systems continuously interact with their environment, which generally comprises state- and time-continuous components.The coupling of the embedded system to its environment thus induces complex interleavings between discrete computational and decision processes and continuous processes. The resulting processes are neither amenable to the analytic techniques of continuous control nor of discrete mathematics. They instead require a broader, integrated theory: hybrid discrete-continuous systems.The lectures provide an in-depth introduction into a variety of analysis and design methods of these computer-based systems and their recent extensions to cyber-physical systems The accompanying hands-on-project enhances the lecture by developing and using design and verification tools.

• Luca P Carloni, Roberto Passerone, Allesandro Pinto & Alberto L Sangiovanni-Vincentelli: Languages and Tools for Hybrid System design.World Scientific, 2006.
• Wassim M. Haddad, VijaySekhar Chellaboina & Sergey G. Nersesov: Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control. Princeton University Press, 2006
• Daniel Liberzon: Switching in Systems and Control. Birkhauser, 2003
• Michael Huth, Mark Ryan: Logic in Computer Science: Modelling and Reasoning About Systems. Cambridge University Press, 2004.
• Christel Baier, Joost-Pieter Katoen: Principles of Model Checking. MIT Press, 2008.

At the end of the lecture period

Semester project including written work and final presentation