Open Access

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

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
New Perspectives in Nonlinear and Intelligent Control (In Honor of Alexander P. Kurdyukov) (special section, pp. 629-712), Julio B. Clempner, Enso Ikonen, Alexander P. Kurdyukov (Eds.)


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.

Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics