Modelling, state observation and diagnosis of quantised systems
This book is about supervision of continuous dynamical systems which are typically described by differential equations, e.g. a two-tank system is used by the author as a running example. However, uncertainties possibly occurring in descriptions often make the use of precise models very difficult. That is why continuous systems are considered here as discrete event systems. The core idea of the approach is that all signals in the system are quantised. The quantised system is then analyzed on the basis of finite stochastic automata theory. Input/output alphabets, set of states and the behavioral relation of the automaton are assumed to be known. The supervision problems, considered in the book, namely the \textit{state observation} and the \textit{fault diagnostic} tasks, have been studied earlier in journal articles [see, e.g. \textit{J. Lunze} and \textit{J. Schröder}, Discrete Event Dyn. Syst. 11, No. 4, 319--369 (2001; Zbl 1055.93056)]. In the state observation task, given a prior distribution of the initial state of the automaton and input/output sequences, a-posteriori probability distributions of the current and initial states should be obtained. The fault diagnostic task is reduced to the state observation one by introducing suitable additional states to the automaton. The results are generalized for networks of quantised systems. Applications the methods to a chemical plant are considered at the end of book.
scientific article; zbMATH DE number 1872985