Download Deterministic learning theory for identification, by Cong Wang PDF

By Cong Wang

Deterministic studying thought for id, attractiveness, and regulate offers a unified conceptual framework for wisdom acquisition, illustration, and information usage in doubtful dynamic environments. It presents systematic layout techniques for id, acceptance, and regulate of linear doubtful platforms. in contrast to many books at present on hand that target statistical ideas, this ebook stresses studying via closed-loop neural keep watch over, powerful illustration and popularity of temporal styles in a deterministic method.

A Deterministic View of studying in Dynamic Environments

The authors commence with an creation to the thoughts of deterministic studying concept, through a dialogue of the power excitation estate of RBF networks. They describe the weather of deterministic studying, and tackle dynamical trend attractiveness and pattern-based regulate strategies. the consequences are acceptable to parts corresponding to detection and isolation of oscillation faults, ECG/EEG trend acceptance, robotic studying and keep an eye on, and safety research and regulate of strength structures.

A New version of knowledge Processing

This publication elucidates a studying idea that is built utilizing options and instruments from the self-discipline of structures and regulate. basic wisdom approximately process dynamics is acquired from dynamical strategies, and is then applied to accomplish quick acceptance of dynamical styles and pattern-based closed-loop keep watch over through the so-called inner and dynamical matching of approach dynamics. This really represents a brand new version of knowledge processing, i.e. a version of dynamical parallel allotted processing (DPDP).

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2 The above two theorems establish the relationship between the PE condition and the exponential stability of two classes of LTV systems. The exponential stability of LTV systems can lead to accurate parameter convergence and system identification, which are elements of the deterministic learning mechanism introduced in the following chapters. Thus, it will be revealed that the nature of this deterministic learning mechanism is related to the exponential stability of LTV systems, which is caused by the satisfaction of the PE condition.

1 RBF Networks and the PE Condition It has been shown in system identification and adaptive control that to achieve accurate parameter convergence and the corresponding identification of system dynamics, the persistent excitation (PE) condition is normally required to be satisfied [139,161,199]. Defined as an intrinsic property of certain signals (called “regressor” vectors) in the system, the PE condition plays a central role in adaptive system theory. Nevertheless, for identification of general nonlinear systems as well as identification in closed-loop control, the PE condition is very difficult to characterize and usually cannot be verified a priori [140].

ZNζ 0 ]T in the neighborhood of Z (and also satisfying Zi0 − ξ ji ≤ ε), such that Aζ ( Z10 , . . , ZNζ 0 ) is nonsingular? The answer to the question is given as follows. Because det( Aζ ( Z)) is a composite function of radial basis functions (·), it is an analytic function of Z1 , . . , [255]). 40) is open and dense. Equivalently, VZc = {Z| det( Aζ ( Z)) = 0} is nowhere dense. 41) RBF Network Approximation and Persistence of Excitation 33 Thus, if Zi (i = 1, . . , Nζ ) are such that det( Aζ ( Z)) = 0 and 0 is an open neighborhood of Z, then there always exists Z0 ∈ 0 , such that det( Aζ ( Z0 )) = 0 which means that Aζ ( Z10 , .

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