<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Research Center for Supervision, Safety and Automatic Control (CS2AC)

Polytechnic University of Catalonia (UPC)

Institute of Robotics and Industrial Informatics (CSIC-UPC)

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"An Lmi\u2013Based 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...

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

Published Online: Dec 31, 2019

Page range: 725 - 737

Received: Nov 09, 2018

Accepted: May 30, 2019

DOI: https://doi.org/10.2478/amcs-2019-0054

Keywords
linear parameter varying (LPV) paradigm, linear matrix inequality (LMI), Gershgorin circles, gain scheduling, controller design

© 2019 Adrián Sanjuan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Dec 31, 2019

Page range: 725 - 737

Received: Nov 09, 2018

Accepted: May 30, 2019

DOI: https://doi.org/10.2478/amcs-2019-0054

Keywordslinear parameter varying (LPV) paradigm, linear matrix inequality (LMI), Gershgorin circles, gain scheduling, controller design

© 2019 Adrián Sanjuan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
linear parameter varying (LPV) paradigm, linear matrix inequality (LMI), Gershgorin circles, gain scheduling, controller design