Course Details

1. Develop the general formulation for hybrid systems and explain the formalisms used in hybrid systems and special classes of hybrid systems.
2. Implement several hybrid computer modelling and analysis tools
3. Develop the framework for stability analysis of hybrid systems.
4. Explain the concepts of temporal logics and model checking, and implement appropriate tools for verification.
5. List and explain various verification methods, like deductive verification, simulation based methods, barrier certificates and sum of squares techniques.
6. Describe various approaches used for controller design and synthesis for hybrid systems, including optimal contro,l, invariant control, game theoretic design, mixed integer programming, model predictive control and supervisory control.
7. Explain stochastic processes and implement discrete and continuous time Markov chains and SDEs to model SHS.
8. Implement verification techniques for SHS including probabilistic model checking, reachability analysis, simulation techniques and barrier certificates.

�      Review of systems theory: Continuous Systems theory, Discrete event systems.

�      Modelling: General formulation, Trajectories, Languages, Special classes.

�      Analysis & Abstractions: Stability, Reachability, Simulation, Bisimulation.

�      Verification: Temporal Logic, Model Checking, Tools, Deductive verification, Simulation based methods, Barrier certificates, Sums Of Squares

�      Control: Logic based optimal control, Game theoretic methods, Symbolic control.

�     Stochastic Hybrid Systems: Modelling, Verification.

• A.J. van der Schaft, J.M. Schumacher, An Introduction to hybrid dynamical systems, Lecture Notes in Control and Information Sciences, Vol. 251, Springer-Verlag, London, 2000.
• P. Tabuada, Verification and Control of Hybrid Systems: A Symbolic Approach, Springer, 2009.

• D. Liberzon, Switching in systems and control, Birkhauser, 2003
• E.M. Clarke, O. Grumberg, D. Peled, Model Checking. MIT Press, 2000

• The teaching of this course is based on lectures (3 hours per week) in a classroom, using a combination of traditional teaching with notes on a white board and slide presentations using a projector for the presentation of the more complicated diagrams and graphs.
• Several examples regarding the material presented during the lectures are discussed and solved and further questions related to particular topic issues are compiled by the students and answered, during the lecture or assigned as homework. Due to the level and type of the course the students are urged to participate in discussing the various topics and provide their opinion. Topic notes are compiled by students, during the lecture which serve to cover the main issues under consideration. Students are also required to heavily use the textbook assigned to the course in addition to other sources found in the library and elsewhere to broaden their perspective on the various issues presented in class and in the textbook.
• Homework problems are assigned from the textbook and elsewhere as a turn in assignment or for homework practice. Also, students are advised to use the reference books for further reading and practice in solving related exercises. Tutorial problems are also submitted as homework and these are solved during lectures or the solutions are posted on the class webpage. Further literature search is encouraged by assigning students to identify a specific problem related to some issue, gather relevant scientific information about how others have addressed the problem.
• Students are assessed continuously and their knowledge is checked through tests with their assessment weight, date and time being set at the beginning of the semester via the course outline. They are prepared for final exam, by revision on the matter taught, problem solving and concept testing and are also trained to be able to deal with time constraints and revision timetable. The final assessment of the students is formative and summative and is assured to comply with the subject’s expected learning outcomes and the quality of the course.