By Stephen L. Campbell, Ramine Nikoukhah

ISBN-10: 0691099871

ISBN-13: 9780691099873

Many industries, corresponding to transportation and production, use keep an eye on structures to insure that parameters corresponding to temperature or altitude behave in a fascinating excess of time. for instance, pilots desire coverage that the aircraft they're flying will continue a selected heading. a vital part of keep watch over structures is a mechanism for failure detection to insure safeguard and reliability.

This publication bargains another failure detection method that addresses of the elemental difficulties within the secure and effective operation of contemporary regulate structures: failure detection--deciding while a failure has occurred--and version identification--deciding which sort of failure has happened. a lot of the paintings in either different types has been in accordance with statistical equipment and below the idea given approach was once monitored passively.

Campbell and Nikoukhah's booklet proposes an "active" multimodel technique. It demands employing an auxiliary sign that may impact the output in order that it may be used to simply confirm if there was a failure and what form of failure it's. This auxiliary sign has to be stored small, and infrequently short in length, so as to not intrude with approach functionality and to make sure well timed detection of the failure. The strategy is strong and makes use of instruments from powerful keep an eye on concept. in contrast to a few methods, it truly is acceptable to complicated structures. The authors current the speculation in a rigorous and intuitive demeanour and supply useful algorithms for implementation of the procedures.

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**Example text**

1) as a larger static system throws away all the structure of these equations. For many applications, particularly those that require computations to be done in real time, or close to real time, it is necessary to exploit the recursive structure of the difference equations. Note that, if we were to use the static approach, we would have to wait until the end of the test period before even starting our computations. Thus, while we can often turn to the static case during a theoretical argument, the results and algorithms have more in common with the continuous-time case.

1 holds. Suppose then that we are in the second case. 9) is not bounded below along the line ξ a multiple of φ. 5) holds. We can write ν0 = Ar a ˆ. Suppose then that φT AT⊥ ΓA⊥ φ = 0, which implies that ν0T ΓA⊥ ξ = (Ar a ˆ)T ΓA⊥ ξ = 0. 5). 6). But we know that a minimum exists under this assumption. 6) follows. 1. To see this, let ν= ν , Γ= z I 0 0 −I a = G1 u y = J, A = G2 = = −G11 −G21 I −I G12 G22 0 , −I u . 2). 3. 3. 2) where a runs over a set of measured outputs and inputs. If we want the solution to be ﬁnite for all possible a, then the situation greatly simpliﬁes.

4 The realizable set {u, y}. 54) with ν1 ν2 T ν1 ν2 < 1. 2. The realizable set is deﬁned by y 2 − 2uy < 1. 5 illustrates this set of realizable {u, y}. 5 The realizable set {u, y}. Suppose that u is ﬁxed and we are looking at the possible values of y. 5, we see a major difference between the additive 25 FAILURE DETECTION uncertainty and the model uncertainty cases. 2, as u varies, the set of realizable outputs y stays the same size but is translated. 5, we see that not only may the set of outputs be translated but it can change in size as u varies.

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