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

By Wilfrid Perruquetti, Jean-Pierre Barbot

Chaotic habit arises in quite a few keep an eye on settings. now and again, it's helpful to take away this habit; in others, introducing or profiting from the present chaotic elements might be helpful for instance in cryptography. Chaos in automated keep an eye on surveys the most recent equipment for placing, making the most of, or removal chaos in numerous purposes. This booklet offers the theoretical and pedagogical foundation of chaos up to speed structures in addition to new strategies and up to date advancements within the box. provided in 3 elements, the e-book examines open-loop research, closed-loop regulate, and functions of chaos up to speed structures. the 1st part builds a historical past within the arithmetic of standard differential and distinction equations on which the rest of the ebook is predicated. It contains an introductory bankruptcy by means of Christian Mira, a pioneer in chaos examine. the following part explores recommendations to difficulties bobbing up in commentary and keep an eye on of closed-loop chaotic keep watch over structures. those contain model-independent regulate tools, suggestions similar to H-infinity and sliding modes, polytopic observers, general types utilizing homogeneous variations, and observability common kinds. the ultimate part explores purposes in instant transmission, optics, energy electronics, and cryptography. Chaos in computerized keep an eye on distills the most recent pondering in chaos whereas referring to it to the newest advancements and purposes up to the mark. It serves as a platform for constructing extra strong, self sustaining, clever, and adaptive platforms.

Show description

Read or Download Chaos in automatic control PDF

Similar robotics & automation books

Parallel Robots

Parallel robots are closed-loop mechanisms featuring first-class performances by way of accuracy, tension and skill to govern huge rather a lot. Parallel robots were utilized in various purposes starting from astronomy to flight simulators and have gotten more and more well known within the box of machine-tool undefined.

Advanced Neural Network-Based Computational Schemes for Robust Fault Diagnosis

The current booklet is dedicated to difficulties of model of synthetic neural networks to powerful fault prognosis schemes. It provides neural networks-based modelling and estimation strategies used for designing strong fault prognosis schemes for non-linear dynamic platforms. part of the booklet specializes in primary concerns corresponding to architectures of dynamic neural networks, equipment for designing of neural networks and fault analysis schemes in addition to the significance of robustness.

Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition

Greater than a decade in the past, world-renowned keep an eye on platforms authority Frank L. Lewis brought what could develop into a typical textbook on estimation, below the identify optimum Estimation, utilized in best universities through the global. The time has come for a brand new variation of this vintage textual content, and Lewis enlisted the help of complete specialists to carry the ebook thoroughly brand new with the estimation equipment using present day high-performance platforms.

Extra info for Chaos in automatic control

Sample text

A cycle is stable, if and only if, all the multipliers are such that Sj < 1. It is unstable when at least one of the multipliers is |Sl | > 1. When at least one of the multipliers is |Sl | = 1 for a parameter value = b , it corresponds to a critical case in the Liapunov’ sense. Crossing through this case by a variation gives rise to a local bifurcation. An unstable cycle with |Sr | > 1, |Ss | < 1, dim r + dim s = p, is called a saddle. The dimension s and the sign of each multiplier define different types of saddle.

An algorithm for the determination of bifurcations by homoclinic or heteroclinic tangency can be found in Kawakami [78], Kawakami and Matsuo [81], and Yoshinaga et al. [165]. 11). A period k-cycle of T corresponds to a subharmonic oscillation or to fractional harmonic (also called ultra-subharmonic) one, which is a periodic solution having a k-multiple period with respect to the earlier fundamental solution (see later for the definition of these two types of oscillations). 11) the period of the solution is kτ .

Such closed curves are discussed in Kawakami [79], Mira and Djellit [117], and Mira et al. [123]. Fractional harmonics are distinguished as nonreducible fractional harmonics (the ratio m/k cannot be reduced) and reducible ones. In the case of reducible harmonics, the ratio m/k can be reduced, but due to its relation with a k-cycle, it keeps this form to correctly identify its relation with a period k-cycle. Reducible harmonics have a more complex behavior, giving rise to specific bifurcation structures in a parameter plane [138, 158].

Download PDF sample

Rated 4.97 of 5 – based on 14 votes