An Lmi–Based Heuristic Algorithm for Vertex Reduction in LPV Systems

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 rea...

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Bibliographic Details
Published in:International journal of applied mathematics and computer science 2019-12, Vol.29 (4), p.725-737
Main Authors: Sanjuan, Adrián, Rotondo, Damiano, Nejjari, Fatiha, Sarrate, Ramon
Format: Article
Language:English
Subjects:
Algorithms
Apexes
Automatic control
Automàtica i control
Computer simulation
Control automàtic
Control system synthesis
Control theory
Controller design
Controllers
Gain scheduling
Gershgorin circles
Heuristic methods
Informàtica
linear matrix inequality (LMI)
Linear parameter varying (LPV) paradigm
Linear systems
Nonlinear control
Nonlinear systems
Reduction
Àrees temàtiques de la UPC
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Summary: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.
ISSN:2083-8492
1641-876X
2083-8492
DOI:10.2478/amcs-2019-0054