Download Modelling, State Observation and Diagnosis of Quantised by Jochen Schröder (auth.) PDF

By Jochen Schröder (auth.)

The publication matters quantised structures which emerge from continuous-variable structures by way of quantising the values of all indications. it truly is proven how this ends up in an summary process description through a stochastic automaton. in accordance with stochastic automata, new tools for the answer to country remark and fault diagnostic difficulties are derived. The equipment are prolonged to networks of stochastic automata, permitting component-oriented modelling and, therefore, to house advanced platforms. the sensible applicability and value of the method is proven at a number of examples.

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Additional resources for Modelling, State Observation and Diagnosis of Quantised Systems

Example text

Set representation problem of quantised systems. Determine the set [Y(k | X 0 , [U (0 . . 17) of currently possible output symbols [y(k)] at time k, for given symbolical input sequence [U (0 . . k)] and initial set of states X 0 .

That is, like the input and output space, the relevant state space of the continuous–variable system is partitioned into N sets. As before, the partition is such that each quantised state [x(k)] ∈ Nx = {1, 2, . . , N } corresponds to one bounded set Qx (i) in the state space. In summary, this means that the following is set: Nz := Nx , Nv := Nu , Nw := Ny , and [x] = z , [u] = v , [y] = w . With these settings, the SA is called a qualitative model of the quantised system. The states, inputs and outputs of the qualitative model are called qualitative states, qualitative inputs and qualitative outputs, respectively.

56], [87] or [188]. Stationary and limiting distribution. The probability distribution of the current state of the autonomous SA is according to eqn. 28) given by: Prob(z(k)) = Ga (z(k) | z(k−1)) · Prob(z(k−1)) . 48) 28 2. Basics of Stochastic Automata Theory Using the vector notation pz (k) = ( Prob(zp (k) = 1) Prob(zp (k) = 2) . . Prob(zp (k) = N )) for the probability distributions of the state at time k, eqn. 48) reads as pz (k) = Ga · pz (k−1) . 50) holds. 51) is called limiting distribution of the initialised autonomous SA with initial distribution pz (0) if the limit exists.

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