By Milos Marek, Igor Schreiber

ISBN-10: 0521438306

ISBN-13: 9780521438308

Surveying either theoretical and experimental facets of chaotic habit, this e-book offers chaos as a version for lots of possible random tactics in nature. easy notions from the idea of dynamical platforms, bifurcation conception and the houses of chaotic ideas are then defined and illustrated by way of examples. A assessment of numerical equipment used either in reports of mathematical versions and within the interpretation of experimental info can be supplied. furthermore, an in depth survey of experimental statement of chaotic habit and techniques of its research are used to emphasize common positive factors of the phenomenon.

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Extra resources for Chaotic behaviour of deterministic dissipative systems

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Multi-objective Control: Whereas in [151] all design freedom is attributed to eliminating the periodic disturbance, the developed design methodology allows accounting for a variety of additional design specifications, such as transient response, control effort, etc. Plant Uncertainty: Contrary to [151], the design methodology allows accounting for plant uncertainty. 2 provides some background on estimated disturbance feedback control and reviews the disturbance feedback controller design of [151].

10c) follows from the worst-case uncertainty Δ (ω ) which has modulus |Δ (ω )| = 1 and its phase aligns [(Ko (ω ) + KdFB (ω ))G(ω )WG (ω )Δ (ω )] opposite to [1 + Ko (ω )G(ω )]. 10d) is convex in x but, however, not simultaneously convex in x and Vl,wc . 10d) for given Vl,wc . 10d) only complies with the gridding solution approach. Third, KdFB (z) affects the robust closed-loop performance related to reference input wr (k). 4 Numerical Results 53 |Wr (ω )| |Hr,Δ (ω )|wc ≤ 1 , ∀ω ∈ [0, π fs ] . 10); it involves the structured singular value and is elaborated in Appendix C.

The developed design methodology, on the other hand, provides the flexibility to incorporate additional design specifications and allows accounting for uncertainty on the input period as well as plant uncertainty. The latter two advantages are illustrated by numerical results. 1 Introduction State of the Art The appeal of feedforward control is to a large extent related to the following properties: (i) the only stability concern in a feedforward controller design is its own stability whereas a feedback controller must additionally guarantee stability of the closed-loop system; (ii) the effect of a feedforward controller is restricted to the input channel to which it is added, not affecting other inputs and the related performance; and (iii) many applications can cope with limited noncausality of a feedforward controller, whereas a feedback controller must be causal.

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Chaotic behaviour of deterministic dissipative systems by Milos Marek, Igor Schreiber

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