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

• Published in: International 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
• Language: English
• 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
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207721.2020.1795948

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.