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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Approximate Kalman-Bucy Filter for Continuous-Time Semi-Markov Jump Linear Systems

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Autor(es):
de Saporta, Benoite ; Costa, Eduardo F.
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: IEEE Transactions on Automatic Control; v. 61, n. 8, p. 2035-2048, AUG 2016.
Citações Web of Science: 2
Resumo

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)

Processo FAPESP: 13/19380-8 - Controle e filtragem de sistemas estocásticos
Beneficiário:Eduardo Fontoura Costa
Linha de fomento: Auxílio à Pesquisa - Regular
Processo FAPESP: 13/50759-3 - Controle de sistemas dinâmicos sujeitos a saltos estocásticos
Beneficiário:Eduardo Fontoura Costa
Linha de fomento: Auxílio à Pesquisa - Regular