By Petros A. Ioannou, Petar V. Kokotovic
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Extra resources for Adaptive Systems with Reduced Models
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], 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