Comparisons of Interpolation Methods for the uncertain case

Abstract

A recent paper [13] proposed a new interpolation method which can enlarge feasible regions but requires fewer degrees of freedom then many existing approaches. This paper shows that one can use some, by now, common techniques to extend this to the uncertain case. Moroever, the paper gives a proper critique by providing a comparison with many existing interpolation methods. In addition, the example section makes use of some higher order examples whereas earlier papers have tended to focus on 2nd order models only. These examples demonstrate that the proposed approach has a useful place in the portfolio of algorithms available to a designer.

Approximate Predictive Control of Polytopic Systems

“…A similar approach based on the interpolation between offline computed tubes has for example been proposed in Lee and Kouvaritakis [2002] for a specific parameterization of the sets X i and controllers κ i . In Bacic et al [2003], Pluymers et al [2005], and Ding and Rossiter [2007] large invariant sets for MPC are constructed by taking the convex hull of multiple invariant sets centered on the origin. See also the references therein.…”