| Full text | |
| Author(s): |
de Saporta, Benoite
;
Costa, Eduardo F.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | IEEE Transactions on Automatic Control; v. 61, n. 8, p. 2035-2048, AUG 2016. |
| Web of Science Citations: | 2 |
| Abstract | |
The aim of this paper is to propose a new numerical approximation of the Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is based on the selection of typical trajectories of the driving semi-Markov chain of the process by using an optimal quantization technique. The main advantage of this approach is that it makes pre-computations possible. We derive a Lipschitz property for the solution of the Riccati equation and a general result on the convergence of perturbed solutions of semi-Markov switching Riccati equations when the perturbation comes from the driving semi-Markov chain. Based on these results, we prove the convergence of our approximation scheme in a general infinite countable state space framework and derive an error bound in terms of the quantization error and time discretization step. We employ the proposed filter in a magnetic levitation example with markovian failures and compare its performance with both the Kalman-Bucy filter and the Markovian linear minimum mean squares estimator. (AU) | |
| FAPESP's process: | 13/19380-8 - Control and filtering of stochastic systems |
| Grantee: | Eduardo Fontoura Costa |
| Support Opportunities: | Regular Research Grants |