A recursive LMI-based algorithm for efficient vertex reduction in LPV systems

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.

Keywords:

• Linear parameter varying (LPV)
• linear matrix inequalities (LMIs)
• vertex reduction
• state-feedback control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has been co-financed by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SCAV (ref. MINECO DPI2017-88403-R), by the European Regional Development Fund of the European Union in the framework of the ERDF Operational Program of Catalonia 2014-2020 (ref. 001-P-001643 Looming Factory) and by the DGR of Generalitat de Catalunya (SAC group ref. 2017/SGR/482).