23 juin 2020
will take place in the form of a video conference Teams
Set Programming : Theory and Computation by Benoît LEGAT
Pour l’obtention du grade de Docteur en sciences de l’ingénieur et technologie
The complexity of systems that are relevant to engineering today has grown tremendously.The control techniques based on frequency analysis that were perfectly adequate for simple systems tend to be difficult to use for more complex systems.An important challenge arising for these complex systems is the need to obtain sets satisfying given properties. Once the intended end-use of the sets as well as the properties they should satisfy are clarified, a specific family of sets, called template, is chosen to formulate the search of the appropriate sets as a problem that is numerically tractable.
this thesis, we introduce Set Programming as an interface between the requirements that sets should satisfyand the numerical algorithms used to compute sets satisfying given requirements.Several templates are studied in this thesis including the classical templates (polyhedra, zonotopes and ellipsoids) but also more elaborate ones that provide a richer family of sets butare more complicated to implement both theoretically and algorithmically.These includes polysets, piecewise semi-ellipsoids, and piecewise polysets.We study two questions in detail about set programs that both examine different aspects of duality:1) Conic duality: we analyse what the infeasibility of a set program for a specific template means for the set programs for other templates, e.g., is it infeasible only for this template or for all of them ?1) Geometric duality: we discuss the choices of represention of convex sets, either in the primal or dual space, depending on the class of set programs that should be solved. terestingly, this choice seems to be mostly template-independent as it mostly relies on geometric arguments.Finally, we apply our results to several applications ranging from cruise control to energy and information theory.
Jury members :
- Prof. Raphaël Jungers (UCLouvain), supervisor
- Prof. Pablo Parrilo (MIT, USA), supervisor
- Prof. Roland Keunings (UCLouvain), chairperson
- Prof. Yurii Nesterov (UCLouvain), secretary
- Prof. Anthony Papavasiliou (UCLouvain)
- Prof. Paulo Tubuada (UCLA, USA)
Pay attention :
The public defense of Benoît Legat scheduled for Tuesday 23 June at 04:00 p.m will indeed take place in the form of a video conference Teams.