Frontiers in Adaptive Control Part 11

Tham khảo tài liệu 'frontiers in adaptive control part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Lipschitzian Parameterization-Based Approach for Adaptive Controls of Nonlinear Dynamic Systems with Nonlinearly Parameterized Uncertainties A Theoretical Framework and Its Applications 241 T K S Y â - fjv x 0 - s x 3 85 with e s x diag sat 1 si wi ar . sat n together with the update laws ẩ -raYTs J r wT Is l .s2 . -s 86 yield K t s Kps . Finally by a similar andysis as done in Section the error s I of the system converges to 0 or equivalently lini s v y . From relation 68 the tracking error converges to -------- as t oc. We are now in a position to sum up our results. Theorem 6 The adaptive controller defined by equations 78 79 84 - 86 enables system to c 3 1 asymptotically track a desired trajectory q I within a precision of .Il. 2Aj Remark 1 In the general case where G e IỈ1 it follows in a straightforward manner from lemma 5 that 3 Â1 A2 Therefore with a Lyapunov function defined in 81 where properly designed to make the Theorem 6 remains valid for 0 - Ji1 . Remark 2 The new variable 78 and the function 79 are stabilizing control 72 continuous. Of course there are other appropriate choices other than the variable 78 and the function 79 which also make the stabilizing control 72 continuous too. 1-dimension estimator In the design of sections and the dimensions of estimators are equal to the number of unknown parameters in the system . á c 1 . ổ E IJ- . Thus increasing the 242 Frontiers in Adaptive Control number of links may result in estimators of excessively large dimension. Tuning updating gains r . r j for those estimators then becomes a very laborious task. In this section we show that it is possible to design an adaptive controller for system 58 with simple 1-dimension estimators i. independently of the dimensions of the unknown parameters a and d. For that purpose first consider the term Ya in 69 where Y c L .aC 7 . It is clear that 52 Yijdj max y I 52 lajl i 1 n. j i V . 0 7 j i Also note from 70 that Wj x 3j max wjj x ji .

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