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Probabilistic Hybrid State Estimation of Piecewise Affine Systems Through Qualitative Approximation


S. Richter


Piecewise affine (PWA) systems are an important hybrid modelling class for dynamical systems which have an implicit interaction between the continuous state and their behaviorial mode. This work introduces a novel hybrid estimation approach for PWA systems subject to non-negligible state disturbance and measurement noise. In this case, the number of possible evolutions of the system grows without bounds as time proceeds. Current estimation approaches do not explicitly account for this and thus their application is restricted to PWA systems with a fairly small number of modes. In order to make estimation also applicable to systems with a large number of modes, our main idea is to put emphasis on most probable evolutions of the system and reframe hybrid estimation as a discrete search problem. For this purpose, we introduce a likelihood measure for mode transitions which can be efficiently approximated by means of a qualitative abstraction of the underlying PWA dynamics. We prove that this approximation obeys an asymptotic argument, so that it is indeed an admissible approximation. Once we have found the most probable evolutions of the system, we apply standard continuous filtering techniques (e.g. Kalman Filters), to obtain continuous state estimates. Simulation results show that our approach concentrates computational resources on most likely evolutions of the system and thus significantly speeds up the estimation task while still maintaining sufficient estimation accuracy.

Thesis Supervisors:
Ao. Univ.-Prof. Dr. Michael W. Hofbaur, Graz University of Technology
Prof. Dr. Manfred Morari, Swiss Federal Institute of Technology Zurich


Type of Publication:

(12)Diploma/Master Thesis

M. Morari

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2007:IFA_2739
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