tailieunhanh - Adaptive Control System Part 3

Tham khảo tài liệu 'adaptive control system part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Adaptive Control Systems 31 a t 1 ộ t - đ TP t - l ự f - đ a t 1 ộ t - đ TP t - l ự f - đ a t 1 ộ t - d TP t - 1U Z - đ __aơ 1 ộ t - đfp t - l ự í - d X dtf - 5 f - 7 0 ỔƠ - e 2 7T tf 0 ỔƠ 1 - 1 J - Ì - e t 2 e t 2 so J __ - e t 2 Co 1 0 t - dfp t - l ự f - d - A- ------------ y -------------- Co 1 0 t - dfp t - l ự f - d where the fact that a t e t 2 f t e t f r 2 has been used. Therefore following the same arguments in 20 21 23 the results in Lemma are thus proved. If using the same adaptive control law as in equation then with the parameter estimation properties i - v in Lemma the global stability and convergence results of the new adaptive control system can be established as in 26 11 as long as the estimated 1 is small enough which are summarized in the following theorem. Theorem The direct adaptive control system satisfying assumptions Al - A4 with the adaptive controller described in equations and is globally stable in the sense that all the signals in the loop remain bounded. In this approach we have eliminated the requirement for the knowledge of the parameters of the upper bounding function on the modelling uncertainties. But the requirement for the knowledge of the lower bound on the leading coefficient of the parameter vector . assumption A4 is still there. In the next section the technique of the parameter correction procedure will be combined with the algorithm developed in this section to ensure the least prior knowledge on the plant. That is only assumptions A1 - A3 are needed. 32 An algorithm for robust adaptive control with less prior knowledge Robust adaptive control with least prior knowledge The following modified least squares algorithm will be used for robust parameter estimation P t - l r - d e t e t -1 a t ý At 1 ộ t d p t l t d P P -1 - y 7 y t 7 - 7 f -11 1 ộ t - d Tp t - l ự í - d p -l kữI k0 0 and the parameter estimate is then .

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