Abstract
In this paper, we consider a continuous time filtering of a multi-dimensional Langevin stochastic differential system driven by a fractional Brownian motion process. It is shown that this filtering problem is equivalent to an optimal control problem involving convolutional integrals in its dynamical system. Then, a novel approximation scheme is developed and applied to this optimal control problem. It yields a sequence of standard optimal control problems. The convergence of the approximate standard optimal control problem to the optimal control problem involving convolutional integrals in its system dynamics is established. Two numerical examples are solved by using the method proposed. The results obtained clearly demonstrate its efficiency and effectiveness. © Dynamic Publishers, Inc.
| Original language | English |
|---|---|
| Pages (from-to) | 495-514 |
| Journal | Dynamic systems and applications |
| Volume | 19 |
| Issue number | 3-4 |
| Publication status | Published - Sept 2010 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Research Keywords
- Approximate optimal control computation
- Approximation scheme
- Convolutional integrals
- Fractional brownian motion
- Linear filtering
- Optimal control
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