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By Michael W. Hofbaur

This monograph presents a tool-set for hybrid estimation that may effectively display screen the habit of complicated artifacts with a good number of attainable operational and failure modes reminiscent of creation vegetation, automobile or aeronautic platforms, and self sufficient robots. For this objective, principles from the fields of procedure concept and synthetic Intelligence are taken and hybrid estimation is reformulated as a seek challenge. this enables to concentration the estimation onto hugely most likely operational modes, with no lacking signs that would be hidden one of the noise within the method. also a unique method of proceed hybrid estimation within the presence of unknown behavioral modes and to automate process research and synthesis initiatives for online operation are awarded. This ends up in a versatile model-based hybrid estimation scheme for advanced artifacts that robustly copes with unexpected events.

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1 To avoid confusion in terminology, we refer to the HMM state as the mode and reserve the term state to refer to the state of the overall probabilistic hybrid automaton. W. Hofbaur: Hybrid Estimation of Complex Systems, LNCIS 319, pp. 29–43, 2005. © Springer-Verlag Berlin Heidelberg 2005 30 3 Probabilistic Hybrid Automata An observation of the component only reveals whether the component works (modes standby and on) or whether it experiences a fault. These two observations are indicated in terms of the discrete values {ok, faulty}.

005 . 005. 472 . 820 . 1% cmax of the overall probability space. This number can serve as an indicator about how well the set of hypotheses that were calculated so far approximate the overall hybrid estimate for the time-step under consideration. The first two hypotheses define estimates at mode partly-open. It is now interesting to see, whether we can guarantee that the most likely mode at k = 3 is in fact partly-open, based on the two leading hypotheses only. 392 for the mode partly-open. 08 . Thus, even if all other hypotheses are at a different mode than partly-open, they can never revert the decision on the most likely mode anymore.

392 for the mode partly-open. 08 . Thus, even if all other hypotheses are at a different mode than partly-open, they can never revert the decision on the most likely mode anymore. Thus, in calculating a portion of the hypothesis tree only, we still guarantee that the mode estimate is correct. We will later use this criteria do decide on the number of hypotheses that we need in order to guarantee correctness of our estimation result. A∗ search together with a termination criteria as given above allows us to perform sub-optimal hybrid estimation where only few hypotheses are used to represent the hybrid estimate at a given time-step.

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