By Uwe Schöning
In kompakter shape macht das Buch mit den wesentlichen Themen vertraut, die in einer Vorlesung ?ber Algorithmen behandelt werden. Im Mittelpunkt stehen dabei die verschiedensten sequentiellen Algorithmen, deren Komplexit?tsanalyse und allgemeine Algoithmen-Paradigma. Prof. Sch?ning gelingt es, kurz, konkret und verst?ndlich die wichtigsten algorithmischen Aufgabenstellungen (Selektion, Sortieren, Hashing), Algorithmen auf Graphen, algebraische und zahlentheoretische Verfahren zu behandeln. Hinzu kommen heuristische Algorithmenprinzipien wie z.B. genetisches Programmieren.
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PID_NN u y Plant ? Controller N Fig. 16 Switching Control Using NN controller to update the PID parameters. The combination of neural networks with the switching adaptive control does not alter the stability of the switched system. Once the RBFNN is combined with the selected controller, the switched controller remains in the candidate controller set, in which all controllers are supervised by the switching law. When the measured data start revealing instability, the currently active controller is quickly switched out of the loop and replaced by another, as yet unfalsified one.
For an aperiodical run, a performance-dependent function should be defined to decide when to run it. 7 shows an algorithm for a generic unfalsified learning processor. 17) in which to work. The “Choose the best” block identifies the best hypothesis to be used in the adaptive (and also identification) problems. The basic components of this algorithm are defined in the truncated signal space obtained from the use of the observations operator. 40 2 Safe Switching Adaptive Control: Theory Fig. 7 Unfalsified learning processor • Goal: A cost function measuring the error between the actual and desired performances represents the goal.
1. 7) where α , β , and γ are arbitrary positive numbers. The constant α is used to prevent division by zero when r˜ = y = u = 0 (unless Σ has zero-input zero-output property), β ensures V > 0 even when ||K|| ≡ 0, and γ > 0 ensures coerciveness of V (K, z,t). 4: V (K, z,t) = max τ ≤t ||y||2τ + ||u||2τ + β + γ ||K||2 . , monotonicity in time, coerciveness on K, equicontinuity of the restricted cost family W , and cost detectability. 8). The justification for the last two properties is as follows.
Algorithmen kurz gefasst by Uwe Schöning