Lecture Notes on Hybrid Systems & Games
نویسنده
چکیده
Hybrid systems have so far served us well throughout this course as a model for cyberphysical systems [Pla08, Pla10b]. Most definitely, hybrid systems can also serve as models for other systems that are not cyber-physical per se, i.e. they are not built as a combination of cyber and computing capabilities with physical capabilities. Some biological systems can be understood as hybrid systems, because they combine discrete and continuous dynamics. Or physical processes in which things happen at very different speeds, so where there is a slow process about which a continuous understanding is critical as well as a very fast process in which a discrete abstraction might be sufficient. Neither of those examples are particularly cyber-physical. Yet, nevertheless, they can have natural models as hybrid systems, because their fundamental characteristics is the interaction of discrete and continuous dynamics, which is exactly what hybrid systems are good for. Hence, despite their good match, not all hybrid systems are cyber-physical systems. The converse is not true either, though. Not all cyber-physical systems are hybrid systems. The reason for that is usually not that cyber-physical systems would not involve both discrete and continuous dynamics, but, rather, that, in addition to those, they involve also other dynamical aspects. It is a common phenomenon in cyberphysical systems that they involve several dynamical aspects, which is why they are best understood as multi-dynamical systems, i.e. systems with multiple dynamical features [Pla12c, Pla12b, Pla11, Pla13]. And this does not only happen for cyber-physical systems but also for other systems. Some applications imply require more dynamical features than just discrete and continuous dynamics. It is not going to be feasible to understand all those multi-dynamical system aspects at once in today’s lecture. But today’s lecture is going to introduce one very fundamen-
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تاریخ انتشار 2013