Interval methods for nonlinear identification and robust control

Luc Jaulin (1, 2, 3) , Isabelle Braems (4) , Michel Kieffer (5, 6, 7) , Eric Walter (5)

1 STIC - Département STIC [Brest]
2 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
3 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés
4 LEMHE - Laboratoire d'étude des matériaux hors équilibre
5 L2S - Laboratoire des signaux et systèmes
6 LTCI - Laboratoire Traitement et Communication de l'Information
7 IUF - Institut universitaire de France

Interval methods can provide guaranteed solutions to difficult nonlinear problems, such as the global optimization of non-convex criteria or the characterization of sets defined by nonlinear inequalities. They can even deal with problems involving quantifiers, as encountered for example in robust control design. For high dimensional problems; their efficiency can be considerably improved by resorting to constraint propagation. In this paper, key ideas of interval analysis and constraint propagation are presented and applied to two problems. The first one is the guaranteed characterization of the set of all parameter vectors that are consistent with experimental dat up to bounds on the acceptable errors. The second one is the design of a PI controller robustly stabilizing a set of models that may have been obtained as the solution to the first problem.

Mots clés: bounded-error estimation; constraint propagation; interval analysis; reliable methods; robust control; set computation

Domaines: Sciences de l'ingénieur [physics]

Luc Jaulin, Isabelle Braems, Michel Kieffer, Eric Walter. Interval methods for nonlinear identification and robust control. 41st IEEE Conference on Decision and Control (CDC), Dec 2002, Las Vegas (Nevada ), United States. pp.x-x. ⟨hal-00845884⟩