Design of reduced complexity controllers for linear systems under constraints using data cluster analysis

A numerical method is proposed to reduce the complexity and computational effort involved in the application of the multiparametric linear programming technique in the design of offline controllers for linear systems subject to constraints. For this purpose, the concept of controlled invariant sets...

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Published inInternational journal of systems science Vol. 51; no. 14; pp. 2533 - 2548
Main Authors Dantas, Amanda D. O. S., Dantas, André F. O. A., Almeida, Túlio F. D., Dórea, Carlos E. T.
Format Journal Article
LanguageEnglish
Published London Taylor & Francis 25.10.2020
Taylor & Francis Ltd
Subjects
Algorithms
Cluster analysis
Complexity
Control theory
Controlled invariant sets
Controllers
Data analysis
data cluster analysis
Feedback control
Linear programming
Linear systems
linear systems under constraints
multiparametric linear programming
Numerical methods
Programmable logic devices
State feedback
Online AccessGet full text
ISSN0020-7721
1464-5319
DOI10.1080/00207721.2020.1795948

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Abstract A numerical method is proposed to reduce the complexity and computational effort involved in the application of the multiparametric linear programming technique in the design of offline controllers for linear systems subject to constraints. For this purpose, the concept of controlled invariant sets and the K q-flat data cluster analysis algorithm are applied. Specifically, we show how the K q-flat algorithm can be used to establish a smaller number of polyhedral regions associated with a piecewise affine explicit state feedback control law. We also propose a new approach in the design of sub-optimal controllers that further reduce the number of regions. Numerical examples show that a significant reduction in the complexity of the control law can be achieved by the proposed approach.
AbstractList A numerical method is proposed to reduce the complexity and computational effort involved in the application of the multiparametric linear programming technique in the design of offline controllers for linear systems subject to constraints. For this purpose, the concept of controlled invariant sets and the K q-flat data cluster analysis algorithm are applied. Specifically, we show how the K q-flat algorithm can be used to establish a smaller number of polyhedral regions associated with a piecewise affine explicit state feedback control law. We also propose a new approach in the design of sub-optimal controllers that further reduce the number of regions. Numerical examples show that a significant reduction in the complexity of the control law can be achieved by the proposed approach.
Author Almeida, Túlio F. D.
Dórea, Carlos E. T.
Dantas, Amanda D. O. S.
Dantas, André F. O. A.
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  organization: Computer and Automation Engineering Department (DCA), Federal University of Rio Grande do Norte
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SubjectTerms Algorithms
Cluster analysis
Complexity
Control theory
Controlled invariant sets
Controllers
Data analysis
data cluster analysis
Feedback control
Linear programming
Linear systems
linear systems under constraints
multiparametric linear programming
Numerical methods
Programmable logic devices
State feedback
Title Design of reduced complexity controllers for linear systems under constraints using data cluster analysis
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