On asymptotic stability of continuous-time risk-sensitive filters with respect to initial conditions
✍ Scribed by Subhrakanti Dey; Charalambos D. Charalambous
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 128 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0167-6911
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✦ Synopsis
In this paper, we consider the problem of risk-sensitive ÿltering 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 ÿlters initialized with arbitrary Gaussian initial conditions asymptotically approach the optimal risk-sensitive ÿlter 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 ÿlter asymptotically approaches the optimal risk-sensitive ÿlter in the mean square sense under a boundedness condition satisÿed by the fourth order absolute moment of the initial non-Gaussian density and a slow growth condition satisÿed by a certain Radon-Nikodym derivative.