Iterative Learning Control: Robustness and Monotonic - download pdf or read online

By Hyo-Sung Ahn

This monograph experiences the layout of strong, monotonically-convergent iterative studying controllers for discrete-time structures. It offers a unified research and layout framework that allows designers to think about either robustness and monotonic convergence for general uncertainty versions, together with parametric period uncertainties, iteration-domain frequency uncertainty, and iteration-domain stochastic uncertainty. The ebook indicates tips on how to use strong iterative studying regulate within the face of version uncertainty.

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Extra info for Iterative Learning Control: Robustness and Monotonic Convergence for Interval Systems (Communications and Control Engineering)

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N max < 1, i=k−n where N is the size of the square Markov matrix H. Proof. 19) where Ci := (Λi − HΓi ). 19) is expressed as ⎡ E k+1 ⎢ Ek ⎢ ⎢ Ek−1 ⎢ .. ⎣ . Ek−n+1 ⎤ ⎡ Ck ⎥ ⎢ I ⎥ ⎢ ⎥=⎢ 0 ⎥ ⎢ . ⎦ ⎣ .. 0 Ck−1 0 I .. Ck−2 0 0 .. 0 0 ⎤⎡ E ⎤ . . Ck−n k ... 0 ⎥ ⎢ Ek−1 ⎥ ⎥ ⎥⎢ ... 0 ⎥ ⎢ Ek−2 ⎥ . ⎥ ⎥ ⎢ . .. ⎦ ⎣ .. ⎦ . ... 20) For convenience, we denote the above equality as Ek+1 = H Ek , where H is the companion block matrix. 21) 32 3 The Super-vector Approach i=k Ek 1 = Ei 1. 22) i=k−n i=k i=k−n Also, if max (Ci )p 1 , p = 1, .

7 cover the cases when Γk+1 = 0. 9. 4, the MC is defined in the general lp -norm topology. 7, the MC condition is defined in the l1 -norm topology. 7 can also be extended to the l∞ -norm topology). 7, we defined two different MC conditions for HOILC when Γk+1 = 0. 4. However, it is still difficult to guarantee the MC of HOILC systems. The following discussion shows our concern. Let us assume that Γk+1 = 0, Λi are lower Toeplitz matrices, and Γi , i = k−n, . . , k−1 have the same structure as Γk . 7, the BSMC coni=k < dition for MC of HOILC is given as max i=k−n (Ci )p 1 , p = 1, .

See [202, 177]. Let us make the following substitutions: s1ij := aij if i = j; s1ij := max{|aij |, |aij |} if i = j; 42 4 Robust Interval Iterative Learning Control: Analysis s2ij := aij if i = j; s2ij := min{−|aij |, −|aij |} if i = j, where s1ij is the ith row and j th column element of the matrix S 1 ; s2ij is an element of the matrix S 2 , and aIij = [aij , aij ] is an element of the general interval matrix AI . 7. Let an interval matrix be given as A ≤ A ≤ A, A ∈ AI . If β = max{ρ(S 1 ), ρ(S 2 )} < 1, where ρ is the spectral radius, then the interval matrix AI is Schur stable.

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