By Arjan J. van der Schaft, Hans Schumacher
This ebook is set dynamical structures which are "hybrid" within the feel that they include either non-stop and discrete nation variables. lately there was elevated learn curiosity within the learn of the interplay among discrete and non-stop dynamics. the current quantity presents a primary try out in booklet shape to collect thoughts and strategies facing hybrid platforms from numerous parts, and to examine those from a unified perspective.
The authors have selected a style of exposition that's mostly in keeping with illustrative examples instead of at the summary theorem-proof layout as the systematic examine of hybrid structures continues to be in its infancy. The examples are taken from many various software components, starting from strength converters to conversation protocols and from chaos to mathematical finance.
Subjects lined comprise the next: definition of hybrid structures; description codecs; lifestyles and specialty of strategies; specific subclasses (variable-structure platforms, complementarity systems); reachability and verification; balance and stabilizability; regulate layout tools. The ebook should be of curiosity to scientists from a variety of disciplines together with: desktop technology, regulate concept, dynamical procedure idea, structures modeling and simulation, and operations research.
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Additional resources for An introduction to hybrid dynamical systems
Below we shall apply this rule in a situation where multiple impact occurs (as it was done in ); of course one may debate whether such an extension is "correct". 14) V2 ~--- V3 ~ 0. How do we model this case with the above impact rule? The problem is t h a t not only the left mass is colliding with the middle mass, but that also the middle mass is in contact with the right mass; we thus encounter a multiple collision. 2. 13) for single collisions, and these two ways lead to different answers!
3 , " of this resulting discrete-event system may have a very complicated structure. Analogously, the projection of the hybrid behavior on the behavior of the continuous variables defines a continuous-time behavior defined on the time axis ~ minus the event times and their accumulation points. 6 Event-flow formulas In this section we provide an alternative framework for modeling hybrid systems, which is equation-based and which is therefore in some sense closer to the usual modeling frameworks for continuous systems than to the graph-related representations that are often used for discrete systems.
For flow conditions, such a composition m a y be based simply on conjunction (logical "and"), to express the intuition t h a t the time we are dealing with here is physical time so t h a t it should be c o m m o n to all subsystems. Things are different however in the case of event conditions. If an event occurs in one subsystem, there are not necessarily events in all other subsystems; or it m a y h a p p e n t h a t at the same physical time instant there are unrelated events, perhaps of different multiplicities, in several subsystems.
An introduction to hybrid dynamical systems by Arjan J. van der Schaft, Hans Schumacher