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

By Petros A. Ioannou, Petar V. Kokotovic

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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 . . I O! i , , , I , , , ' o~ b"£ 36 The improvement of the bound by making the convergence rate m 2 larger may require trial and error selection of the adaptive gains. 135) (1 + n k 2 max ~[G]) 2 gives more information about the dependence of the error bound on other quantities.

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 . i and ~ = 13. 4. 1, 7=13, and liZ(ko)il=l. 093 i '! 5. Identification results with higher initial condition llz(k_)ll = 15 for the serles-parallel identifier for =0~i and y = 1 3 .

33) yields v~(k) = [1+ O~(k-1)Fp(k-1)Op(k-1)]{y(k)-yp(k) n + E c_[y(k-i)-y_(k-i)]}. 35) 48 where a ffi[aI a2 ... an]T and e = [cI, c2 ... Cn ]T. 37) or v;Ck+l) " (a+C)ep(k) + 0p(k)App(k) + YuCk+l). 39) or 0T(k)F (k)0 (k)b(a+c) ep(k+l) ffi A- P P P i + b If- I l+0~(k)~(k)0p(k) ep(k) + O~(k)Fp(k)0p(k)] 0T(k)App(k) 1 + o~(u)Fp(k)op(k)J 0~(k)Fp(k)ep(k) ] + b I-l+0~(k)Fp(k)0p(k)jYu(k+l). 32), then App(k+l) = App(k) - Fp(k)Op(k) [(a+C)ep(k) 1+ e~(k)Fp(k)Op(k) + O~(k)App(k) + Yu(k-l-l)]. 42) is not linear since A(k) depends on 8p(k) which includes yp(k), a part of Zp(k).

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