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Paper details
Number 4 - December 2019
Volume 29 - 2019
An LMI-based heuristic algorithm for vertex reduction in LPV systems
Adrián Sanjuan, Damiano Rotondo, Fatiha Nejjari, Ramon Sarrate
Abstract
The linear parameter varying (LPV) approach has proved to be suitable for controlling many non-linear systems. However,
for those which are highly non-linear and complex, the number of scheduling variables increases rapidly. This fact makes
the LPV controller implementation not feasible for many real systems due to memory constraints and computational burden.
This paper considers the problem of reducing the total number of LPV controller gains by determining a heuristic
methodology that combines two vertices of a polytopic LPV model such that the same gain can be used in both vertices.
The proposed algorithm, based on the use of the Gershgorin circles, provides a combinability ranking for the different
vertex pairs, which helps in solving the reduction problem in fewer attempts. Simulation examples are provided in order to
illustrate the main characteristics of the proposed approach.
Keywords
linear parameter varying (LPV) paradigm, linear matrix inequality (LMI), Gershgorin circles, gain scheduling, controller design