Institut de Mathématiques de Toulouse

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SPOT 18 - Séminaire Pluridisciplinaire d’Optimisation de Toulouse

par Delphine Dallariva - publié le , mis à jour le

Séminaire Pluridisciplinaire d’Optimisation de Toulouse (SPOT)

SPOT 18. Lundi 12 mai, 2014.
Lieu : À l’amphithéâtre des thèses à l’ENSEEIHT,
26 rue Pierre-Paul Riquet (métro François Verdier), au centre-ville de Toulouse.

Ouverture de la conférence VORACE.

14h : Colin N. Jones (Ecole Polytechnique Fédérale de Lausanne)
Multi-Convex Splitting for Real-Time Model Predictive Control

Pushing predictive controllers, which require the solution of an optimization problem at each sampling interval, into the millisecond range opens up both new possibilities, as well as new challenges for control. Computational limits invalidate basic assumptions made when proving the stability, or invariance of constrained control laws and as a result cannot be used in fast, real-time implementations with confidence. In this talk, I will discuss some of our recent work that brings the benefits of optimization-based control to high-speed systems, while simultaneously providing the computational flexibility and hard real-time guarantees required by modern embedded control platforms. We’ll begin with an overview of fast-MPC methods, and then argue that operator-splitting approaches have a lot to offer in this domain. I’ll introduce a new technique for solving a class of nonlinear optimal control problems for distributed systems, or on parallel hardware, that comes with a formal guarantee of stability under fixed-time computation. Finally, I will report on a new fast code-generation toolbox, SPLIT, which provides a method to easily deploy real-time, optimisation-based control laws on various embedded platforms.

15h : Assalé Adjé (ONERA Toulouse)
Constrained optimisation and policy iteration applied to abstract interpretation

To test a program is not enough to show that they are correct. They have to be formally verified to ensure exhaustiveness of the analysis. However correction is not decidable in general and abstract interpretation aims at overcoming this undecidability by loosing completness. This method amounts to solve a non-linear fixed point equation involving a monotonic function describing the program behavior. In this talk, we are interested in verifying numerical programs. More precisely, we compute bounds on the values taken by the variable of a program (e.g. to prove that the set of reachable values is bounded, or to prove absence of critical values). We show that this problem can be formulated in term of values of a constrained maximisation problem and can be reduced to solve the upper value of a two-player zero-sum game thanks to Lagrange duality. This latter observation allows us to use algorithms from game theory such as policy iteration.

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