Summary of Study |
Summary of Branches |
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List of Roles |
Explanatory Notes
Instructions
Web page:
https://hurak.github.io/hys/
Anotation:
Course outlines:
| 1. | | Discrete-event systems (as a prequel to hybrid systems) and their models: (State) automata |
| 2. | | Discrete-event systems and their models: Petri nets |
| 3. | | Discrete-event systems and their models: Max-plus algebra and Max-plus systems as computational frameworks for a subclass of discrete-event systems |
| 4. | | Models of hybrid systems: Hybrid (state) automata |
| 5. | | Models of hybrid systems: Hybrid (state) equations |
| 6. | | Some special classes of hybrid systems: Reset systems, Switched systems, Piecewise affine (PWA) systems |
| 7. | | Solutions of hybrid systems: concepts, types, intricacies |
| 8. | | Stability of hybrid systems: Common Lyapunov Function approach using Linear Matrix Inequalities (LMI) and Sum of Squares (SOS) programming |
| 9. | | Stability of hybrid systems: Piecewise Lyapunov Function approach via LMI and SOS |
| 10. | | Complementarity dynamical systems: yet another framework for special classes of hybrid systems such as mechanical systems with impacts and electronic circuits with switching. Using complementarity optimization problems. |
| 11. | | Mixed logical dynamical (MLD) systems: yet another framework for modeling hybrid systems that turns the logical part into integer arithmetics making it suitable for optimization |
| 12. | | Model predictive control (MPC) for MLD systems: based on Mixed integer optimization |
| 13. | | Formal verification of hybrid systems: techniques based Reachability analysis, Barrier certificate function, and Temporal logics. |
Exercises outline:
The exercises will follow the lectures and will serve to develop some problem-solving skills.
Literature:
The field of hybrid systems is vast and spans several areas of science and engineering. It is therefore difficult, if not impossible, to find a single comprehensive reference to recommend to students for this subject. The more so that our choice of topics is inevitably determined by personal preferences. Therefore, the key learning resource will be the lecturer's own lecture notes. And we will always provide a list of recommended readings for further study when studying particular topics.
Among the texts that provide motivation for studying hybrid systems as well as some introduction into theoretical and computational frameworks, we recommend [1], which is also available on the author’s webpage. Yet another overview, which is also available online, is [2]. And yet another is [3], which is available on the author’s web page. The quartet of recommended online resources is concluded by [4].
Among the high-quality printed books, for which we are not aware of legally available online versions, the slim book [5] can be regarded as the classic. The handbook [6] contains a wealth of contributions from several authors (in fact two of the online resources linked above are chapters from this book). The latest textbook on the topic of hybrid systems is [7]. The book was probably the prime candidate for the book for this course, however we wanted a slightly different emphasis on each topic. Another relatively recent book is [8]. Although it is very well written and is certainly recommendable, it follows a particular framework that is not the most common one in the literature on hybrid systems – the framework of hybrid equations. But we are certainly going to introduce their approach in our course. The more so that it is supported by a freely available Matlab toolbox. The book [9] can be regarded as a predecessor and/or complement of the just mentioned [8]. Although the book is not available online, a short version appears as an article [10] in the popular IEEE Control Systems magazine. Last but not least, MPC methodology is specialized to hybrid systems in [11]. Unlike the other books in this list, this one is freely available on the authors’ webpage.
| [1] | | W. P. M. H. Heemels, D. Lehmann, J. Lunze, and B. De Schutter, “Introduction to hybrid systems,” in Handbook of Hybrid Systems Control: Theory, Tools, Applications, J. Lunze and F. Lamnabhi-Lagarrigue, Eds., Cambridge University Press, 2009, pp. 3–30. doi: 10.1017/CBO9780511807930.002. |
| [2] | | K. H. Johansson, “Hybrid control systems,” in UNESCO Encyclopedia of Life Support Systems (EOLSS), UNESCO, 2004. Accessed: Jun. 02, 2022. [Online]. Available: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-90411 |
| [3] | | B. De Schutter, W. P. M. H. Heemels, J. Lunze, and C. Prieur, “Survey of modeling, analysis, and control of hybrid systems,” in Handbook of Hybrid Systems Control: Theory, Tools, Applications, F. Lamnabhi-Lagarrigue and J. Lunze, Eds., Cambridge: Cambridge University Press, 2009, pp. 31–56. doi: 10.1 017/CBO9780511807930.003. |
| [4] | | J. Lygeros, Lecture Notes on Hybrid Systems. 2004. Available: https://people.eecs.berkeley.edu/~sastry/ee291e/lygeros.pdf |
| [5] | | A. J. van der Schaft and H. Schumacher, An Introduction to Hybrid Dynamical Systems. in Lecture Notes in Control and Information Sciences, no. 251. London: Springer-Verlag, 2000. Accessed: Dec. 11, 2018. [Online]. Available: https://doi.org/10.1007/BFb0109998 |
| [6] | | J. Lunze and F. Lamnabhi-Lagarrigue, Eds., Handbook of Hybrid Systems Control: Theory, Tools, Applications, 1 edition. Cambridge, UK ; New York: Cambridge University Press, 2009. |
| [7] | | H. Lin and P. J. Antsaklis, Hybrid Dynamical Systems: Fundamentals and Methods. in Advanced Textbooks in Control and Signal Processing. Cham: Springer, 2022. Accessed: Jul. 09, 2022. [Online]. Available: https://doi.org/10.1007/978-3-030-78731-8 |
| [8] | | R. G. Sanfelice, Hybrid Feedback Control. Princeton University Press, 2021. Accessed: Sep. 23, 2020. [Online]. Available: https://press.princeton.edu/books/hardcover/9780691180229/hybrid-feedback-control |
| [9] | | R. Goebel, R. G. Sanfelice, and A. R. Teel, Hybrid Dynamical Systems: Modeling, Stability, and Robustness. Princeton University Press, 2012. Available: https://press.princeton.edu/books/hardcover/9780691153896/hybrid-dynamical-systems |
| [10] | | R. Goebel, R. G. Sanfelice, and A. R. Teel, “Hybrid dynamical systems,” IEEE Control Systems Magazine, vol. 29, no. 2, pp. 28–93, Apr. 2009, doi: 10.1109/MCS.2008.931718. |
| [11] | | F. Borrelli, A. Bemporad, and M. Morari, Predictive Control for Linear and Hybrid Systems. Cambridge, New York: Cambridge University Press, 2017. Available: http://cse.lab.imtlucca.it/~bemporad/publications/papers/BBMbook.pdf |
Requirements:
| 1) | | basics of the theory of dynamical systems: state-space models, solutions, stability; 2) basics of automatic feedback control: (state) feedback control. |
Keywords:
hybrid systems, hybrid control, cyberphysical systems, switched systems, piecewise affine systems
Subject is included into these academic programs:
| Page updated 24.5.2025 17:53:44, semester: L/2024-5, L/2026-7, L/2025-6, Z/2024-5, Z/2026-7, Z/2025-6, Send comments about the content to the Administrators of the Academic Programs |
Proposal and Realization: I. Halaška (K336), J. Novák (K336) |