Fractal Control Theory by Shu-Tang Liu & Pei Wang

Author:Shu-Tang Liu & Pei Wang
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

(6.6.3)

The purpose is to make that (6.6.1) and (6.6.2) asymptotically achieve synchronization and identify the unknown parameter c by designing an appropriate synchronous controller when parameters of (6.5.1) are unknown.

For (6.6.2), the synchronous controller is

(6.6.4)

the parameter identifier is

(6.6.5)

where are real numbers satisfying

Theorem 6.5

For systems (6.6.1) and (6.6.2), when the synchronous controller is taken as (6.6.4), and the parameter identifier is taken as (6.6.5), then the global asymptotic synchronization between (6.6.1) and (6.6.2) can be achieved starting from an arbitrary initial value, and the parameter c of (6.6.1) can be identified.

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