Deterministic learning theory for identification, by Cong Wang

By Cong Wang

Deterministic studying concept for identity, attractiveness, and Control provides a unified conceptual framework for wisdom acquisition, illustration, and information usage in doubtful dynamic environments. It presents systematic layout methods for id, popularity, and keep an eye on of linear doubtful structures. not like many books at the moment on hand that concentrate on statistical ideas, this booklet stresses studying via closed-loop neural keep an eye on, 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 idea, by means of a dialogue of the chronic excitation estate of RBF networks. They describe the weather of deterministic studying, and handle dynamical trend reputation and pattern-based keep watch over strategies. the implications are appropriate to parts equivalent to detection and isolation of oscillation faults, ECG/EEG trend acceptance, robotic studying and regulate, and safeguard research and keep watch over of energy platforms.

A New version of data Processing

This booklet elucidates a studying thought that's built utilizing thoughts and instruments from the self-discipline of structures and keep an eye on. basic wisdom approximately procedure dynamics is acquired from dynamical techniques, and is then applied to accomplish quick acceptance of dynamical styles and pattern-based closed-loop keep an eye on through the so-called inner and dynamical matching of approach dynamics. This truly represents a brand new version of knowledge processing, i.e. a version of dynamical parallel allotted processing (DPDP).

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Extra info for Deterministic learning theory for identification, recognition, and control

Example text

In Chapter 5, based on the deterministic learning mechanism, a unified, deterministic framework is presented for effective representation, similarity definition, and rapid recognition of dynamical patterns. This follows from the recent paper [244]. We show first that dynamical patterns can be effectively represented in a time-invariant manner using the locally accurate NN approximations of system dynamics F (x; p). The representation is also spatially distributed, because fundamental information is stored in a large number of neurons distributed along the state trajectory of a dynamical pattern.

M − ξ1 ) · · · φ( ξm − ξm ) One of the main results in RBF approximation is that the interpolation matrix A is nonsingular (sometimes even positive definite) for certain types RBF Network Approximation and Persistence of Excitation 19 of radial basis functions provided ξi are distinct points. The principal concepts that are useful to show nonsingularity of the interpolation matrix are positive definite functions and completely monotone functions [23]. 1 A function f : Rn → R is said to be semi-positive definite if for any set of points ξ1 , ξ2 , .

1 q −1 −2hk 2 /η2 It can be easily proven that the sum ∞ e has a limited k=0 3q (k + 2) 2 2 value, because the infinite series {3q (k + 2) q −1 e −2hk /η } (k = 0, . . , ∞) is convergent by the Ratio Test Theorem [39]. Apart from the above properties, the most important reason we use the localized RBF network is due to an essential property concerning the satisfaction of the PE condition. 2 Persistence of Excitation and Exponential Stability Persistence of excitation is of great importance in adaptive systems.

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