A recursive LMI-based algorithm for efficient vertex reduction in LPV systems. Issue 12 (2nd December 2022)

• Record Type: Journal Article
• Authors: Sanjuan, Adrián; Rotondo, Damiano; Nejjari, Fatiha; Sarrate, Ramon
• Is Part Of: International journal of control. Volume 95:Issue 12(2022)
• Page Start: 3379
• Page End: 3391
• Publication Date: 2022-12-02
• Subjects: Linear parameter varying (LPV) -- linear matrix inequalities (LMIs) -- vertex reduction -- state-feedback control; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2021.1973682
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : This paper proposes a new algorithm to reduce the number of gains of a polytopic LPV controller considering generic tuples of vertices, for which a common controller gain can be used. The use of Frobenius norm and the inclusion of the input matrix in the LMIs perturbation matrix allows decreasing the conservativeness to select vertices which are combinable, with respect to a previous approach based on Gershgorin circles. A combinability metric that can be applied to an arbitrary partition of the set of vertices is defined. Then, a recursive algorithm finds a lesser-fragmented combinable partition at each iteration by combining together two elements of a partition. The algorithm aims at finding combinable partitions with minimal cardinality in fewer attempts, always preserving the original control performance specifications. The proposed method is validated using numerical examples, a twin rotor MIMO system and a two-link robotic manipulator.