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An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information
Author(s) -
Oliveira André Marcorin,
Costa O. L. V.
Publication year - 2019
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.4771
Subject(s) - markov chain , mathematics , mathematical optimization , controller (irrigation) , context (archaeology) , iterative method , variable (mathematics) , upper and lower bounds , markov decision process , sequence (biology) , control theory (sociology) , computer science , markov process , control (management) , statistics , paleontology , mathematical analysis , genetics , artificial intelligence , agronomy , biology
Summary TheH 2 ,H ∞and mixedH 2 / H ∞dynamic output feedback control of Markov jump linear systems in a partial observation context is studied through an iterative approach . By partial information, we mean that neither the state variable x ( k ) nor the Markov chain θ ( k ) are available to the controller. Instead, we assume that the controller relies only on an output y ( k ) and a measured variableθ ^ ( k ) coming from a detector that provides the only information of the Markov chain θ ( k ). To solve the problem, we resort to an iterative method that starts with a state‐feedback controller and solves at each iteration a linear matrix inequality optimization problem. It is shown that this iterative algorithm yields to a nonincreasing sequence of upper bound costs so that it converges to a minimum value. The effectiveness of the iterative procedure is illustrated by means of two examples in which the conservatism between the upper bounds and actual costs is significantly reduced.