hal-01192706
https://hal.science/hal-01192706
doi:10.1115/1.4030781
[UNIV-BREST] Université de Bretagne occidentale - Brest (UBO)
[INSTITUT-TELECOM] Institut Mines Télécom
[ENSTA-BRETAGNE] ENSTA Bretagne
[CNRS] CNRS - Centre national de la recherche scientifique
[UNIV-UBS] Université de Bretagne Sud
[ENSTA-BRETAGNE-STIC] Département STIC
[ENIB] Ecole Nationale d'Ingénieurs de Brest
[LAB-STICC] Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
[TDS-MACS] Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes
[INSTITUTS-TELECOM] composantes instituts telecom
Contractors and Linear Matrix Inequalities
Nicola, Jeremy
Jaulin, Luc
[SPI.AUTO] Engineering Sciences [physics]/Automatic
ART
interval analysis
linear matrix inequality
contractor programming
convex optimization
constraint propagation
robotics Read More: http://ascelibrary.org/doi/abs/10.1115/1.4030781
Linear matrix inequalities (LMIs) comprise a large class of convex constraints. Boxes, ellipsoids, and linear constraints can be represented by LMIs. The intersection of LMIs are also classified as LMIs. Interior-point methods are able to minimize or maximize any linear criterion of LMIs with complexity, which is polynomial regarding to the number of variables. As a consequence, as shown in this paper, it is possible to build optimal contractors for sets represented by LMIs. When solving a set of nonlinear constraints, one may extract from all constraints that are LMIs in order to build a single optimal LMI contractor. A combination of all contractors obtained for other non-LMI constraints can thus be performed up to the fixed point. The resulting propogation is shown to be more efficient than other conventional contractor-based approaches.Read More: http://ascelibrary.org/doi/abs/10.1115/1.4030781
2015-09-01
en
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
American Society of Mechanical Engineers (ASME)