By Arjan J. van der Schaft, Hans Schumacher
This ebook is ready dynamical platforms which are "hybrid" within the feel that they comprise either non-stop and discrete country variables. lately there was elevated examine curiosity within the research of the interplay among discrete and non-stop dynamics. the current quantity offers a primary test in publication shape to compile options and techniques facing hybrid platforms from numerous parts, and to examine those from a unified perspective.
The authors have selected a method of exposition that's mostly in keeping with illustrative examples instead of at the summary theorem-proof structure as the systematic research of hybrid platforms remains 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 coated comprise the subsequent: definition of hybrid structures; description codecs; life and strong point of options; designated subclasses (variable-structure structures, 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: desktop technological know-how, keep watch over thought, dynamical procedure concept, structures modeling and simulation, and operations research.
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Additional info for An introduction to hybrid dynamical systems
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.
For example, if we take the guards to be 0 :> 19, respectively 0 _< 20, then transition from one location to another is permitted while the temperature 0 is between 19 and 20, and the temperaturethermostat system will behave non-deterministically. This specification may be appropriate in particular when the thermostat is actually a human controller, or in other circumstances in which the thermostat takes other factors into consideration than just the one that is explicitly specified in the model.
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. 7 Simulation of hybrid systems After specifying a complete model for a correct model together with a univocal simulation and control.