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**

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 . i I . . ' 2O i " i n ' ~ (sL,m ) ' ' ' ' 30 40 (b) IC O~ . . ~0 i 10 , . , . I , 20 Time (~) , , . 4. 5). 34 ' ' ' ' I ' ' ' ' I ' ' ' ' I ' , ~ , ,~o . . 5. 05. L n ~ • • n I I I , , , I . I I I I I n u , 01 > ¢;I n l l l l l l n n l l l l l l l u l l (q) O~ OtP 0~, . . O~ . . O~ . . m . . L O~ i . .

4p +. 5nl(k-2)+n2(k-l)). 80) The criteria used for evaluation of the identification results are the parametric distance defined by D = [inl(ai-ai(k))2_ ~ + (bi-Si (k))21½ and the output error e =y(k)-y(k). For the output excitation signal we have chosen a sequence of pulses whose frequency and amplitude have been adjusted to give a particular value of Y. 3. By increasing the norm of the initial 54 , , , , , , , 0 50 ,,, i00 ,1 ,,,, 150 200 K 4 ' ! 2. 1, 7=13, and llZ(ko)li=l. 3. Identification error due to higher initial condition UZ(k )II=15 using the parallel identifier for ~ = 0 .

93) ~6 = Afn + ~ATIBf6 where h T = [i i ... 94) i] and A=diag(Xi). 97) S W S 8 ffi AW S where y(0) = 0, Zs(0) = O, Ws(0) = 0. 99) where ~ ~ [ ( ~ . ( t ) - a . (t)-b_),(b(t)-b s l 1 ) T ] , and v = [y,~T]T, s s P ffi[U,Ws] . 92) and el, ¢, T are the output and parameter errors, respectively. 13) with E = 0 and, similarly as before, obtain the following result. 105) =gf m2 fl where gf -- IIA;lll IIAflBf II I[hll IIRII T~2 . 2,6, PARAMETERIZED ADAPTIVE OBSERVER The parameterlzed adaptive observer [ii],[12] is based on a state repre- sentatlon of the plant in which the unknown parameters are contained in an algebraic equation and an error criterion is defined.

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

by George

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