An introduction to hybrid dynamical systems by Arjan J. van der Schaft, Hans Schumacher

By Arjan J. van der Schaft, Hans Schumacher

This publication is ready dynamical platforms 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 presents a primary try out in e-book shape to assemble ideas and techniques facing hybrid platforms from a variety of parts, and to examine those from a unified perspective.
The authors have selected a method of exposition that's mostly in accordance with illustrative examples instead of at the summary theorem-proof layout as the systematic research of hybrid platforms remains to be in its infancy. The examples are taken from many alternative software components, starting from energy converters to communique protocols and from chaos to mathematical finance.
Subjects coated comprise the subsequent: definition of hybrid structures; description codecs; life and area of expertise of options; precise subclasses (variable-structure platforms, complementarity systems); reachability and verification; balance and stabilizability; regulate layout tools. The publication may be of curiosity to scientists from quite a lot of disciplines together with: machine technology, regulate concept, dynamical method concept, platforms modeling and simulation, and operations research.

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This becomes especially clear in an object-oriented modeling approach, where the interconnection (or composition) of hybrid automata may easily lead to a rapid growth in number of locations, and a rather elaborate (re-)specification of the resulting hybrid automaton model obtained by interconnection. Thus from the user's point of view an interesting alternative for efficiently specifying "physical" hybrid systems is to look for possibilities of specifying such systems primarily by means of equations, as in the framework of event-flow formulas.

6. A comma is used to indicate logical conjunction between several expressions on one line, a vertical bar is used to indicate logical disjunction between several expressions on one line or between successive lines, and a left curly bracket is used to indicate logical conjunction between successive lines. Furthermore, [[ indicates parallel composition between two subsystems. The symbols associated with a given subsystem are not listed explicitly but are understood as being the symbols t h a t occur in the Boolean expressions in the E F F for t h a t subsystem.

Moreover, if m ( t i ) is finite, then S(ti+l) S(t'~(tD~). This defines the behavior of a discrete-event system. Note, however, t h a t in general the set of "discrete time instants" . . , ~247176 § ' t~~, . ,t'~(tl)U, ~1 . §176, ~§ , t~2~, . '~2 § . ' v§3. ' ~§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.

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