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

Autor(es)

de Saporta, Benoite ; Costa, Eduardo F.

• 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