Perturbations in polyhedral partitions and the related fragility of piecewise affine control.

Rajesh Koduri 1 Sorin Olaru 2 Pedro Rodriguez-Ayerbe 1
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : The control design techniques for linear or hybrid systems under constraints lead often to off-line state-space partitions with non-overlapping convex polyhedral regions. This corresponds to a piecewise affine (PWA) state feedback control laws associated to polyhedral partition of the state-space. The aim of this paper is to consider perturbation in the representation of the vertices of such polyhedral regions. Another idea behind this study is to perform a quantization operation on the representation of the state-space regions and the associated PWA control laws in order to reduce the hardware requirements in terms of processor speed and memory unit. The quantized state-space partitions lose some of the important properties of the explicit controllers: non-overlapping, convexity and invariant characterization. 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 perturbation takes place on the vertex representation.
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Rajesh Koduri, Sorin Olaru, Pedro Rodriguez-Ayerbe. Perturbations in polyhedral partitions and the related fragility of piecewise affine control.. Bulletin mathématique de la Société des Sciences mathématiques de Roumanie, Société des Sciences mathématiques de Roumanie, 2018, 61, pp.439 - 452. ⟨hal-01968898⟩

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