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By Petros A. Ioannou, Petar V. Kokotovic

ISBN-10: 3540121501

ISBN-13: 9783540121503

ISBN-10: 3540395474

ISBN-13: 9783540395478

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Extra resources for Adaptive Systems with Reduced Models

Example text

High On the other It is appropriate to use a dominantly rich input with a low value of Y still giving an acceptable rate of convergence. 32 d ' . ~. . ' '''' ' ''' 2 ,'o -2 -4 . . | rT O i i 0 . i . . I 20 T,me (sL~) , J 30 , , 40 Co) .... I .... I I .... 24 0 i , , i LO , i J , I , J , , r 20 T,me {sec) 30 2O 30 . . 5l ' , , ! 3. Identification results for B - O . 2 and u = S s i n t + S s i n 2 . 5). 33 . . i I0 . . i . . 20 T , m e (r~eC) i , i h i 30 40 (o) ~4 w ,co a i i m 11,~ i m .

4) A21 + PAll- ~A22 P - ~PAI2P = 0 -i having the property that P÷-A21AII as ~ ÷ 0 . 4) follows from the implicit function theorem. 5) y(k) ffi ClX(k) + ~C2z(k) so that the parasitics are weakly observable from the plant output. obae~abi~ty This w e ~ assumption is found to be crucial in establishing robustness of the adaptive schemes. The case of strongly observable parasltlcs requires a different treatment and will be discussed in Chapter 4. 1 to define the parasitic state n(k) ffi z(k) + Px(k)-bfu(k).

Bn(k)], 8 (k-l) = [yp(k-l) ... yp(k-n) P u(k-l) ... 18) 43 and yp(k), y~(k)_ are the a posteriori and a priori output of the estimation model, respectively, at the instant k. 5, 1~i starting with an arbitrary positive definite matrix Fp(ko). 22) is not exponentially stable. , Re(H(z)} > 0, Vz : Izl =i. The robustness of this identifier wlth respect to parasltlcs Is established as follows. 24) is bounded for all k and where ep(k) = [y(k)-yp(k),y(k-l)-yp(k-l) ..... y(k-n+l)-yp(k-n+l) ] T dpp(k) = [al-al(k),a2-a2(kl .....

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Adaptive Systems with Reduced Models by Petros A. Ioannou, Petar V. Kokotovic


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