P8

b12a21u - b22a11u (b11b22 -b21b12)u 2

(b11b22 - b21b12)u b21anu bna21u (b11b22 - b21b12)u2 bg

(b11b22 - b21b12)u 2

Since all the pi s include uncertainties, the control law is modified as follows:

cos\

where P represents parameter estimations, and the servo signals u and v are defined as before. The next step is to derive the adaptation law.

Let the estimation error of parameters be P i = pi - Pi . One can find the error dynamics by substituting (34) and (35) into the system dynamic equations. This results

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