Volume-Optimal Inner and Outer Ellipsoids

  • L. Pronzato
  • É. Walter
Chapter

Abstract

Approximating a complex set K by a simple geometrical form (such as a polytope, an orthotope, a sphere or an ellipsoid) is often of practical interest. Consider for instance the situation where a vector u has to be chosen so as to satisfy the property
$$ p\left( {u,x} \right) \in T,\forall x \in S, $$
(8.1)
where x and p(.,.) are vector-valued and where T and S are given sets. This can be of interest for instance in robust control, where the controller characterized by u must be designed in order to guarantee some given performances—at least stability—corresponding to a target set T for the process under study, given the information that the model parameters x lie in some specified feasible domain S. The information about S can be derived using the parameter bounding methodology, where one assumes that observations with bounded errors are performed on the process.(1)

Keywords

Support Point Active Constraint Optimal Distribution Supporting Hyperplane Ellipsoidal Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • L. Pronzato
    • 1
  • É. Walter
    • 2
  1. 1.Laboratoire 13S, CNRS URA-1376, Sophia AntipolisValbonneFrance
  2. 2.Laboratoire des Signaux et SystèmesCNRS-École Supérieure d’ElectricitéGif-sur-Yvette CedexFrance

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