H∞-filtering for Markov jump linear systems with partial information on the jump parameter. (30th September 2017)

• Record Type: Journal Article
• Authors: de Oliveira, A.M.; Costa, O.L.V.
• Is Part Of: IFAC journal of systems and control. Volume 1(2017)
• Page Start: 13
• Page End: 23
• Publication Date: 2017-09-30
• Subjects: Filtering -- Stochastic control -- Robust control -- Hidden Markov models -- Linear matrix inequality -- Fault-tolerant systems; Automatic control -- Periodicals; Relay control systems -- Periodicals; Embedded computer systems -- Periodicals; Feedback control systems -- Periodicals; Artificial intelligence -- Periodicals; Artificial intelligence; Automatic control; Embedded computer systems; Feedback control systems; Relay control systems; Electronic journals; Periodicals; 629.89
• DOI: 10.1016/j.ifacsc.2017.05.002
• Languages: English
• ISSNs: 2468-6018

Abstract

Abstract: We study in this work the H ∞ -filtering problem in a partial information context. We suppose that the state of the Markov chain θ ( k ) is not available to the filter, but only an estimation coming from a detector and represented by θ ^ ( k ) . We present two main results related to the synthesis of filters that depend only on θ ^ ( k ) such that the H ∞ norm in relation to the estimation error is limited: the case in which the transition and detection probabilities are not exactly known, but belong to distinct convex sets; and the Bernoulli case in which we derive necessary and sufficient conditions for the filter synthesis. All the results are given in terms of linear matrix inequalities and are illustrated by two numerical examples of systems prone to faults.