By Arjan J. van der Schaft, Hans Schumacher
This e-book is ready dynamical platforms which are "hybrid" within the feel that they comprise either non-stop and discrete nation variables. lately there was elevated examine curiosity within the research of the interplay among discrete and non-stop dynamics. the current quantity presents a primary try out in e-book shape to assemble recommendations and strategies facing hybrid platforms from numerous components, and to examine those from a unified perspective.
The authors have selected a style of exposition that's principally in response to illustrative examples instead of at the summary theorem-proof layout as the systematic learn of hybrid structures continues to be in its infancy. The examples are taken from many alternative program parts, starting from strength converters to conversation protocols and from chaos to mathematical finance.
Subjects lined contain the subsequent: definition of hybrid structures; description codecs; lifestyles and strong point of ideas; distinct subclasses (variable-structure structures, complementarity systems); reachability and verification; balance and stabilizability; regulate layout tools. The e-book may be of curiosity to scientists from a variety of disciplines together with: machine technological know-how, regulate concept, dynamical process idea, structures modeling and simulation, and operations research.
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Additional info for An introduction to hybrid dynamical systems
Variables are understood to be continuous across events by default, so we do not explicitly write conditions of the type x + = x~-; likewise, conditions of the form S -- b l a n k are not written explicitly. Also the empty event t h a t goes with each subsystem is not written explicitly. 1 Examples Hysteresis Consider a control system with a hysteresis element in the feedback loop (cf. 1) Chapter 2. 1. Note that this system is not just a differential equation whose right-hand side is piecewise continuous.
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.
2. 15) models of complex systems, and thus for most hybrid systems. Furthermore, mathematical models of the same system, which are exactly equivalent, may have very different properties from the user's point of view. Also, the mathematical model (or language) describing the functioning of the system may not be the same as the appropriate language formulating the requirements which the system is expected to satisfy (the specifications). These features are particularly present in the field of discrete-event systems (or distributed or concurrent systems) where one finds in the literature a wealth of different descriptions, from process-algebraic formalisms such as CCS, CSP, ACP, LOTOS and logical theories such as temporal logic to graphically oriented approaches (net theories) such as Petri nets and automata, all with their own advantages and disadvantages.
An introduction to hybrid dynamical systems by Arjan J. van der Schaft, Hans Schumacher