Adaptive Control - download pdf or read online

By Edited by: Kwanho You

ISBN-10: 9537619478

ISBN-13: 9789537619473

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Now we are ready to show that for that | φi − φ j |> D > t it ' ε any s > 0, there always exists t > s such that | yt − yit |> D . In fact, suppose that it is not true, then there must exist s > 0 such that any t > s, correspondingly φt − φit | yt − yit |> D for > D´. 35) Now we consider Let d n = Dn ,in , Dt ,it − D j ,i j . 36) so we can conclude that {dn, n > s} is bounded. 41) From Eq. 45) and consequently { | Bt | } must be bounded. 46) which contradicts the former assumption! Step 4: According to the results in Step 3, for any s > 0, there always exists t > s such that | yt − yit |≤ D .

Let vn = ytn , then obviously {vn} is bounded. 50) as n → ∞ . 53) for any n > n0. Thus based on definition of tn, we conclude that tn+1 = tn + 1! 54) which means that the sequence {yt} is bounded. 1 is true. 4 Simulation Study In this section, two simulation examples will be given to illustrate the effects of the adaptive controller designed above. d. randomly taken from uniform distribution 10 U(0, 1). The simulation results for two examples are depicted in Figure 8 and Figure 9, respectively.

F ( x1 ) − f ( x 2 ) ≤ L | x1 − x 2 | for some constant L > 0. • Function f is monotone (increasing or decreasing) with respect to its arguments. • Function f is convex (or concave). • Function f is even (or odd). 3 As to the unknown noise term knowledge: εk , here are some possible examples of a priori • Sequence ε k = 0. This case means that no noise/disturbance exists. • Sequence εk is is bounded in a known range, that is to say, ε ≤ εk ≤ ε for any k. One special case ε = −ε . g, | ε k |≤ 1 k for any k .

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Adaptive Control by Edited by: Kwanho You


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