Dey, Subhrakanti and Charalambous, Charalambos D. (2000) On asymptotic stability of continuous-time risk-sensitive filters with respect to initial conditions. Systems and Control Letters, 41 (1). pp. 9-18. ISSN 0167-6911

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Abstract

In this paper, we consider the problem of risk-sensitive filtering for continuous-time stochastic linear Gaussian time-invariant systems. In particular, we address the problem of forgetting of initial conditions. Our results show that suboptimal risk-sensitive filters initialized with arbitrary Gaussian initial conditions asymptotically approach the optimal risk-sensitive filter for a linear Gaussian system with Gaussian but unknown initial conditions in the mean square sense at an exponential rate, provided the arbitrary initial covariance matrix results in a stabilizing solution of the (H∞-like) Riccati equation associated with the risk-sensitive problem. More importantly, in the case of non-Gaussian initial conditions, a suboptimal risk-sensitive filter asymptotically approaches the optimal risk-sensitive filter in the mean square sense under a boundedness condition satisfied by the fourth order absolute moment of the initial non-Gaussian density and a slow growth condition satisfied by a certain Radon–Nikodym derivative.

Item Type:	Article
Keywords:	Risk-sensitive filtering; Riccati equation; Forgetting of initial conditions; Non-Gaussian density; Mean square convergence;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	14409
Identification Number:	https://doi.org/10.1016/S0167-6911(00)00030-X
Depositing User:	Subhrakanti Dey
Date Deposited:	10 May 2021 15:42
Journal or Publication Title:	Systems and Control Letters
Publisher:	Elsevier
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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