Tham khảo tài liệu 'discrete time systems part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | A General Approach to Discrete-Time Adaptive Control Systems with Perturbed Measures for Complex Dynamics - Case Study Unmanned Underwater Vehicles 259 with p and q being Lipschitz vector functions located at the right-hand memberships of 1 and 2 respectively. Here no exogenous perturbation was considered as agreed above. Let us contemplate an approximation of first order of an Adams-Bashforth approximator Jordán Bustamante 2009b . It is valid vn 1 vtn hM-1 pSln Tn 12 nn 1 ntn hqtn 13 where nn i and vn i are one-step-ahead predictions at the present time tn. Moreover Tn is the discrete-time control action at tn which is equal to the sample T tn because of the employed zero-order sample holder. More precisely it is valid with 1 - 2 6 ptn - E Ci. x Cv vt -DI vt - 14 6 - E Dq n vtn-B1 gin-B2 g2n i 1 qtn Jtn vtn 15 where Cvmeans C vt gitn and g2n mean gi h. and g2 ntn respectively J- means J nt and v t is an element of vtn. Similar expressions can be obtained for the other sampled functions pt and qt in 18 - 19 . Besides the control action T is retained one sampling period h by a sample holder so it is valid Tn Ttn. The accuracy of one-step-ahead predictions is defined by the local model errors as v 1 vt 1 -vn i 16 ntn 1 -nn 1 17 with y 1 v 1 O h and O being the order function that expresses the order of magnitude of the sampled-data model errors. It is noticing that local errors are by definition completely lacking of the influence from sampled-data disturbances. Since p and q are Lipschitz continuous in the attraction domains in v and n then the samples predictions and local errors all yield bounded. So it is valid the property vn i vtn 1 and nn i ntn i for h 0. Next the disturbed dynamics subject to sampled-data noisy measures is dealt with in the following. predictor with disturbances The one-step-ahead predictions with disturbances result from 18 and 19 as vn 1 vtn ỗvtn hM-1 p0 n Tn 18 nn 1 ntn 5ntn hqỏln 19 260 Discrete Time Systems where vtn gvtn .
