By Arjan J. van der Schaft, Hans Schumacher
This e-book is set dynamical structures which are "hybrid" within the feel that they comprise either non-stop and discrete nation variables. lately there was elevated study curiosity within the learn of the interplay among discrete and non-stop dynamics. the current quantity offers a primary test in publication shape to assemble techniques and techniques facing hybrid platforms from numerous parts, and to examine those from a unified perspective.
The authors have selected a style of exposition that's principally in keeping with illustrative examples instead of at the summary theorem-proof layout as the systematic research of hybrid structures continues to be in its infancy. The examples are taken from many various software parts, starting from energy converters to conversation protocols and from chaos to mathematical finance.
Subjects lined comprise the next: definition of hybrid platforms; description codecs; lifestyles and distinctiveness of suggestions; particular subclasses (variable-structure structures, complementarity systems); reachability and verification; balance and stabilizability; keep watch over layout equipment. The publication might be of curiosity to scientists from a variety of disciplines together with: machine technology, keep an eye on thought, dynamical approach conception, platforms modeling and simulation, and operations research.
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Additional info for An introduction to hybrid dynamical systems
14) as above, this gives rise to an event with multiplicity equal to c~. In fact, we obtain the following distribution of velocities at the subsequents stages t ~ t ~, t ~ , t ~ , ... of the time event at time t: Vl V2 V3 t~ 1 0 0 ~ i 1 0 t~ i 1 i ~ ~ Chapter 2. 4 1 1 1 ~ Hence the outcome of this event with multiplicity co is the same as the outcome derived by the first method, with an event of multiplicity 1. Interesting variations of both modeling approaches may be obtained by considering e.
Sometimes a system description can be considerably simplified by using what might be called a persistent-mode convention, which enforces that mode changes will occur only when they are necessary to prevent violation of flow conditions. Typically the involved conditions are expressed as inequality constraints on the continuous state variables. In the mechanics literature the persistent-mode convention is sometimes known as "Kilmister's principle" , . Formally, a P M C solution for a given event-flow formula is a solution having the property that, for each to, there is no solution of the same E F F t h a t coincides with the given solution for t < to, t h a t is defined for t < tl for some tl > to, and t h a t has no event at to.
Needless to say that many valuable aspects and/or approaches covered in the literature will not be addressed in the presentation of hybrid systems in this text. The terminology "hybrid systems" for this class of systems seems to have been first used by Witsenhausen . A recent introduction to various approaches in the theory of concurrent processes, in particular CSP, can be found in ; see this book for further references. For temporal logic we refer to  and . For an interesting discussion on the similarities and differences between the view points of on the one hand computer science and discrete event systems (automata) and on the other hand systems and control theory we refer to .
An introduction to hybrid dynamical systems by Arjan J. van der Schaft, Hans Schumacher