Construction of invariant polytopic sets with specified complexity

The problem of construction of controlled invariant polytopic sets with specified complexity, for linear systems subject to linear state and control constraints, is investigated. First, geometric conditions for the enlargement of a polytopic set by adding a new vertex, in order to produce a polytopi...

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Bibliographic Details
Published inInternational journal of control Vol. 87; no. 8; pp. 1681 - 1693
Main Authors Athanasopoulos, Nikolaos, Bitsoris, George, Lazar, Mircea
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.08.2014
Taylor & Francis Ltd
Subjects
Algorithms
Complexity
constraints
Construction
Construction specifications
contractive sets
Control systems
controlled invariant sets
Enlargement
Invariants
Linear systems
Mathematical models
positively invariant sets
Preserves
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ISSN0020-7179
1366-5820
DOI10.1080/00207179.2014.882518

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Summary:The problem of construction of controlled invariant polytopic sets with specified complexity, for linear systems subject to linear state and control constraints, is investigated. First, geometric conditions for the enlargement of a polytopic set by adding a new vertex, in order to produce a polytopic set of specified complexity, are established. Next, conditions for such an enlargement of controlled invariant sets to preserve the controlled invariance property are presented. The established theoretical results are used to develop methods for the construction of admissible controlled invariant sets with specified complexity. Two numerical examples show how these results can be used for the computation of monotonic sequences of admissible controlled invariant sets of specified complexity.
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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2014.882518