Filter Stability, Observability and Robustness for Partially Observed Stochastic Dynamical Systems
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Authors
Mcdonald, Curtis
Date
Type
thesis
Language
eng
Keyword
Filter Stability , Stochastic Dynamical Systems , Observability
Alternative Title
Abstract
Filter stability refers to the correction of an incorrectly initialized filter for a partially observed stochastic dynamical system with increasing measurements. In this thesis, we study the filter stability problem, develop new methods and results for both controlled and control-free stochastic dynamical systems, and study the implications of filter stability on robustness of optimal solutions for partially observed stochastic control problems. We introduce a definition of non-linear stochastic observability and through this notion of observability, we provide sufficient conditions for when a falsely initialized filter merges with the correctly initialized filter over time. We study stability under different notions such as the weak topology, total variation, and relative entropy. Additionally, we investigate properties of the transition kernel and measurement kernel which result in stability with an exponential rate of merging. We generalize our results to the controlled case, which is an unexplored area in the literature, to our knowledge.
Stability results are then applied to stochastic control problems. Under filter stability, we bound the difference in the expected cost incurred for implementing an incorrectly designed control policy compared to an optimal policy and relate filter stability, robustness, and unique ergodicity of non-linear filters.
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License
CC0 1.0 Universal
Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.