A recursive LMI-based algorithm for efficient vertex reduction in LPV systems
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 th...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/362454 |
| Acceso en línea: | https://hdl.handle.net/2117/362454 https://dx.doi.org/10.1080/00207179.2021.1973682 |
| Access Level: | acceso abierto |
| Palabra clave: | System theory Mathematical models Predictive control Linear parameter varying (LPV) Linear matrix inequalities (LMIs) Vertex reduction State-feedback control Sistemes, Teoria de Models matemàtics Control predictiu Àrees temàtiques de la UPC::Informàtica::Automàtica i control |
| Sumario: | 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 a previous approach based on Gershgorin circles. A combinability metric that can be applied to an arbitrary partition of the set of vertices is defined. 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, always preserving the original control performance specifications. The proposed method is validated using numerical examples, a twin rotor MIMO system and a two-link robotic manipulator. |
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