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Mixed H 2 / H ∞ control of hidden Markov jump systems
Author(s) -
Oliveira A.M.,
Costa O.L.V.
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3952
Subject(s) - norm (philosophy) , upper and lower bounds , mathematics , markov chain , parametric statistics , mathematical optimization , markov process , jump , jump process , uniform norm , control theory (sociology) , computer science , control (management) , discrete mathematics , statistics , artificial intelligence , mathematical analysis , physics , quantum mechanics , political science , law
Summary In this work, we study the mixed H 2 / H ∞ control for Markov jump linear systems with hidden Markov parameters. The hidden Markov process is denoted by ( θ ( k ) , θ ^ ( k ) ) , where the nonobservable component θ( k ) represents the mode of operation of the system, whereas θ ^ ( k ) represents the observable component provided by a detector. The goal is to obtain design techniques for mixed H 2 / H ∞ control problems, with the controllers depending only on the estimate θ ^ ( k ) , for problems formulated in 3 different forms: (i) minimizing an upper bound on the H 2 norm subject to a given restriction on the H ∞ norm; (ii) minimizing an upper bound on the H ∞ norm, while limiting the H 2 norm; and (iii) minimizing a weighted combination of upper bounds of both the H 2 and H ∞ norms. We propose also new conditions for synthesizing robust controllers under parametric uncertainty in the detector probabilities and in the transition probabilities. The so‐called cluster case for the mixed H 2 / H ∞ control problem is also analyzed under the detector approach. The results are illustrated by means of 2 numerical examples.