K. Astr om and B. Wittenmark. Adaptive Control. Addison-Wesley, Reading, MA, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....have to be tuned and little structural information about the system to be controlled is needed. 1 Introduction A popular method for the robust stabilization of control systems is adaptive control. On the one hand, on line identi cation techniques are used for tuning the controller (see [1, 10] for a survey) In non identi er based adaptive control, on the other hand, the controller is directly tuned without estimating the parameters of the plant. This is usually done by increasing a gain as long as the control objective has not been achieved (see [7] for a survey) To increase the ....

K.J.  Astrom and B. Wittenmark. Adaptive Control. Addison-Wesley, Reading, MA, 2nd edition, 1995.

....s f (87g) with a given upper bound max ue , cf. 87d ) According to the above Theorem 6. 2, further stability results, especially the convergence E kdz(t)kjA t j 0 for j 1; t 1 (88a) of the mean absolute rst order tracking error can be obtained if, by using a suitable update law [1,2,4,10] for the parameter estimates, hence, for the a posteriori distribution P ( jA t j ) we have that, see (86f) var p D ( jA t j = var p D ( jA t j (t) 0 for j 1; t 1: 88b) 6.3. The 2nd order di erential d 2 q In order to derive a representation of the second order ....

Astrom, K.J.; Wittenmark, B.: Adaptive Control. Reading, Mass. [etc.]: Addison-Wesley cop., 1995.

....cases where it is possible to detect a number of operating points, a reduction of the conservatism can be obtained by designing robust controllers around each operating point and then switch between the controllers according to some gain scheduling rules. This approach has been described in e.g. [2]. Gain scheduling techniques are motivated by the large number of control applications that have signi cant nonlinearities which can not always be handled well by linear control design techniques. Quite a number of papers dealing with gain scheduling control for non linear systems has emerged in ....

K. J.  Astrom and B. Wittenmark. Adaptive Control. Addison-Wesley, 1989.

....criterion allows one to ensure robust stability in the presence of uncertain constant parameters and exogenous bounded disturbances. 1 Introduction One of the well estabilished approaches for dealing in control with plant model uncertainty is the introduction of adaptation in the feedback loop [2]. However, conventional continuous adaptation is not always capable of performing satisfactorily. This may be particulartly true whenever the plant switches among di erent modes of operation or if closed loop signals are not suciently exciting. In both circumstances undesirable transients may ....

K. J.  Astrom, and B. Wittenmark, \Adaptive Control", Addison Wesley, NY, 1995.

....in Figure 3, the feedback noise Z t h tjt 1 will not be independent of h t ijt i 1 when Z t 6= 0, even when there is no correlation. The loop could become unstable if the learning lter has too high gain, and this must be taken into account in any stability analysis. The small gain theorem [42] provides (conservative) sucient conditions for stability, formalized in [28] In [28] 26] three important scenarios are discussed in which an exact stability and performance analysis can be performed when assuming v t , t and e t to be independent. These results are summarized below. h t ....

....for k = 1 and noting from (3.16) that L 1 0 = r 1, we obtain h t h tjt 1 = Q 0 q 1 Q 1 D R 1 t t = r 1 r R 1 t t ; which is (2.14) with = r 1) r. The relation 1 1=r = Q 0 0 follows from (3. 17) Proof of Lemma 2: We will use the small gain theorem, see e.g. [42] and observe that the inverse of the estimator (3.7) for k = 0 can be expressed as f t = R Q 0 h tjt = R r r D h tjt = R 1 1 D r h tjt ; in which D=r is always stable. According to the small gain theorem, the inverse estimator will be stable if D(e ) r (e ) 1 ....

K. J.  Astrom and B. Wittenmark, Adaptive Control. third ed. Addison-Wesley, 1996. 12

....map the inputs to the targets is measured by an objective function. The parameters of the learner are adjusted to optimize this performance measure. Unfortunately, in learning control there are no explicit training targets. 1 Propotional Integral (PI) or Proportional Integral Derivative (PID) Astr om and Wittenmark 1989). controller environment observation action Figure 1.1: An autonomous system formed by the application of a controller to its environment. Unsupervised learning uses an objective function built in to the learning agent to group together exemplars of various kinds. For example, this kind of ....

Astršom, K. and Wittenmark, B. (1989). Adaptive Control, Addison-Wesley series in electrical engineering: control engineering, Addison-Wesley, Reading, Massachusettes.

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K. Astr om and B. Wittenmark. Adaptive Control. Addison-Wesley, Reading, MA, 1995.

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K. J. Astr o m and B. Wittenmark, Adaptive Control, Addison-Wesley, 1989.

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