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 existing conditions based on Gershgorin circles (Sanjuan, Rotondo, Nejjari, & Sarrate, 2019). The proposed algorithm is developed by defining a combinability metric that can be applied to an arbitrary partition of the set of vertices. 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, with the objective of reducing the number of gains of a polytopic controller, always preserving the original performance specifications. The proposed method is validated using numerical examples, a twin rotor MIMO system (TRMS) and a two-link robotic manipulator.

Fixed-structure parameter-dependent state feedback controller: A scaled autonomous vehicle path-tracking application

“…This issue has been tackled in a number of works on proposed algorithms for polytope size reduction, e.g. (Kwiatkowski and Werner, 2008;Hoffmann et al, 2012;Rizvi et al, 2016;Sanjuan et al, 2022), or on the use of ad-hoc methods for polytope reduction for some specific systems as in (Baldelli et al, 2008;Kapsalis et al, 2022).…”