EN FR
EN FR
DISCO - 2017
Overall Objectives
New Software and Platforms
Bilateral Contracts and Grants with Industry
Bibliography
Overall Objectives
New Software and Platforms
Bilateral Contracts and Grants with Industry
Bibliography


Section: New Results

On the precision in polyhedral partition representation and the fragility of PWA control

Participants : Sorin Olaru, Rajesh Koduri [CentraleSupélec] , Pedro Rodriguez [CentraleSupélec] .

Explicit model predictive control (EMPC) solves a multi-parametric Quadratic Programming (mp-QP) problem for a class of discrete-time linear system with linear inequality constraints. The solution of the EMPC problem in general is a piecewise affine control function defined over non-overlapping convex polyhedral regions composing a polyhedral partition of the feasible region. In this work, we considered the problem of perturbations on the representation of the vertices of the polyhedral partition. Such perturbations may affect some of the structural characteristics of the PWA controller such as non-overlapping within the regions or the closed-loop invariance. We first showed how a perturbation affects the polyhedral regions and evoked the overlapping within the modified polyhedral regions. The major contribution of this work is to analyze to what extend the non-overlapping and the invariance characteristics of the PWA controller can be preserved when the perturbation takes place on the vertex representation. We determined a set called sensitivity margin to characterize for admissible perturbation preserving the non-overlapping and the invariance property of the controller. Finally, we show how to perturb multiple vertices sequentially and reconfigure the entire polyhedral partition