Chaos in automatic control by Wilfrid Perruquetti, Jean-Pierre Barbot

By Wilfrid Perruquetti, Jean-Pierre Barbot

Chaotic habit arises in various regulate settings. in certain cases, it truly is invaluable to take away this habit; in others, introducing or benefiting from the prevailing chaotic elements should be invaluable for instance in cryptography. Chaos in computerized regulate surveys the newest tools for placing, profiting from, or removal chaos in quite a few functions. This ebook offers the theoretical and pedagogical foundation of chaos up to the mark platforms besides new recommendations and up to date advancements within the box. provided in 3 components, the e-book examines open-loop research, closed-loop keep watch over, and functions of chaos on top of things platforms. the 1st part builds a history within the arithmetic of normal differential and distinction equations on which the rest of the e-book relies. It comprises an introductory bankruptcy by way of Christian Mira, a pioneer in chaos examine. the following part explores strategies to difficulties coming up in statement and keep an eye on of closed-loop chaotic regulate platforms. those comprise model-independent keep watch over tools, thoughts similar to H-infinity and sliding modes, polytopic observers, general types utilizing homogeneous adjustments, and observability general kinds. the ultimate part explores purposes in instant transmission, optics, energy electronics, and cryptography. Chaos in computerized regulate distills the most recent considering in chaos whereas pertaining to it to the newest advancements and purposes on top of things. It serves as a platform for constructing extra powerful, independent, clever, and adaptive structures.

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1 Generalities on Discrete Models Different Forms of Models This section concerns dynamical systems, described directly or indirectly (link with ODEs defined below) by a “ discrete ” equation, whose solution is a sequence of points determined by an initial point (initial condition). 3 Generalities on Discrete Models 11 (or simply recurrence). 2) where X is a phase (or state) vector, is a parameter vector, and X0 is the initial condition. Depending on the scientific field, such an equation is also called iteration, or map, or point-mapping.

10 Conclusion . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . 1 34 35 Introduction Dynamics is a concise term referring to the study of time-evolving processes. The corresponding system of equations describing this evolution is called a dynamic system. Nonlinear dynamics is the scientific field concerning the behavior of real systems, linearity being always an approximation. This field, which embraces ordinary differential equations (continuous dynamics) and maps, also called recurrences (discrete dynamics), is too wide to be completely presented in the limited framework of this book.

2 Maps Obtained from an ODE by a Poincaré Section . 4 Singularities and Bifurcations Common to Invertible and Noninvertible Maps . . . . . . . . . . . . . . . 1 Singularities and Bifurcations . . . . . . . . . 2 Bifurcation Sets: Normal Forms of Exceptional Critical Cases . . . . . . . . . . . . . . . 3 Singularities Sense when the Map is Obtained from a Poincaré Section . . . . . . . . . . . 5 Map Singularities and Bifurcations Specific to Noninvertible Maps .

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